problem solving by searching in artificial intelligence pdf

Browse Course Material

Course info, instructors.

Prof. Tomás Lozano-Pérez
Prof. Leslie Kaelbling

Departments

Electrical Engineering and Computer Science

As Taught In

Algorithms and Data Structures
Artificial Intelligence
Cognitive Science

Learning Resource Types

Techniques in artificial intelligence (sma 5504), lecture notes.

Notes from lectures 6 and 21 are not available.

Lecture 1: What is Artificial Intelligence (AI)? ( PDF )

Lecture 2: Problem Solving and Search ( PDF )

Lecture 3: Logic ( PDF )

Lecture 4.: Satisfiability and Validity ( PDF - 1.2 MB )

Lecture 5.: First-Order Logic ( PDF )

Lecture 7.: Resolution Theorem Proving: Propositional Logic ( PDF )

Lecture 8.: Resolution Theorem Proving: First Order Logic ( PDF )

Lecture 9: Logic Miscellanea ( PDF )

Lecture 10: Planning ( PDF )

Lecture 11: Partial-Order Planning Algorithms ( PDF )

Lecture 12: Graph Plan ( PDF )

Lecture 13: Planning Miscellany ( PDF )

Lecture 14: Probability ( PDF )

Lecture 15: Bayesian Networks ( PDF )

Lecture 16: Inference in Bayesian Networks ( PDF )

Lecture 17: Where do Bayesian Networks Come From? ( PDF )

Lecture 18: Learning With Hidden Variables ( PDF )

Lecture 19: Decision Making under Uncertainty ( PDF )

Lecture 20: Markov Decision Processes ( PDF )

Lecture 22: Reinforcement Learning ( PDF )

You are leaving MIT OpenCourseWare

Analysis of Searching Algorithms in Solving Modern Engineering Problems

Ieee account.

Change Username/Password
Update Address

Purchase Details

Payment Options
Order History
View Purchased Documents

Profile Information

Communications Preferences
Profession and Education
Technical Interests
US & Canada: +1 800 678 4333
Worldwide: +1 732 981 0060
Contact & Support
About IEEE Xplore
Accessibility
Terms of Use
Nondiscrimination Policy
Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. © Copyright 2024 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.

We will keep fighting for all libraries - stand with us!

Internet Archive Audio

problem solving by searching in artificial intelligence pdf

This Just In
Grateful Dead
Old Time Radio
78 RPMs and Cylinder Recordings
Audio Books & Poetry
Computers, Technology and Science
Music, Arts & Culture
News & Public Affairs
Spirituality & Religion
Radio News Archive

Flickr Commons
Occupy Wall Street Flickr
NASA Images
Solar System Collection
Ames Research Center

All Software
Old School Emulation
MS-DOS Games
Historical Software
Classic PC Games
Software Library
Kodi Archive and Support File
Vintage Software
CD-ROM Software
CD-ROM Software Library
Software Sites
Tucows Software Library
Shareware CD-ROMs
Software Capsules Compilation
CD-ROM Images
ZX Spectrum
DOOM Level CD

Smithsonian Libraries
FEDLINK (US)
Lincoln Collection
American Libraries
Canadian Libraries
Universal Library
Project Gutenberg
Children's Library
Biodiversity Heritage Library
Books by Language
Additional Collections

Prelinger Archives
Democracy Now!
Occupy Wall Street
TV NSA Clip Library
Animation & Cartoons
Arts & Music
Computers & Technology
Cultural & Academic Films
Ephemeral Films
Sports Videos
Videogame Videos
Youth Media

Search the history of over 866 billion web pages on the Internet.

Mobile Apps

Wayback Machine (iOS)
Wayback Machine (Android)

Browser Extensions

Archive-it subscription.

Explore the Collections
Build Collections

Save Page Now

Capture a web page as it appears now for use as a trusted citation in the future.

Please enter a valid web address

Donate Donate icon An illustration of a heart shape

Artificial intelligence : structures and strategies for complex problem solving

Bookreader item preview, share or embed this item, flag this item for.

Graphic Violence
Explicit Sexual Content
Hate Speech
Misinformation/Disinformation
Marketing/Phishing/Advertising
Misleading/Inaccurate/Missing Metadata

plus-circle Add Review comment Reviews

8 Favorites

Better World Books

DOWNLOAD OPTIONS

No suitable files to display here.

IN COLLECTIONS

Uploaded by station43.cebu on July 15, 2020

ARTIFICIAL INTELLIGENCE PROBLEM SOLVING AND SEARCH

Related Papers

Mihai Zaharia

Classical search procedures by forward or backward reasoning are memory and time consuming because they are uninformed procedures that don't take into account domain knowledge. In this paper a heuristic solution is presented for the generalized water jugs problem, which finds the optimal solution linearly, with no additional memory requirements.

Hassan Sebak

International Journal of Scientific Research in Science, Engineering and Technology

International Journal of Scientific Research in Science, Engineering and Technology IJSRSET

Problem-solving strategies in Artificial Intelligence are steps to overcome the barriers to achieve a goal, the "problem-solving cycle". Most common steps in such cycle involve- recognizing a problem, defining it, developing a strategy in order to fix it, organizing knowledge and resources available, monitoring progress, and evaluating the effectiveness of the solution. Once a solution is obtained, another problem usually comes, and the cycle starts again. Searching techniques in problem-solving by using artificial intelligence (A.I) are surveyed in this paper. An overview of definitions, development and dimensions of A.I in the light of search for solutions to problems are accepted. Dimensions as well as relevance of search in A.I research is reviewed. A classification of searching in the matter of depth of known parameters of search was also investigated. At last, the forethoughts of searching in AI research are brought into prominence. Search is noticed that it is the common thread that binds most of the problem-solving strategies in AI together.

Philip P Petrov

One generalized form of this problem is: “3 vessels of volumes M, N and P contain respectively m, n and M-(m+n) liters liquid, where M=N+P, N >P, mM, nN and M-(m+n)P. Divide the liquid in two equal parts.” The solution is frequently done by trial-error. Perelman provided a “billiard” solution to the problem without prescriptions how to guess to solve it like this. There are numerous articles on this topic, but there are no known to us attempts for exhaustive analysis, synthesis and systematization of them. We consider briefly the most interesting ones with didactics perspective. We prescribe ideas for solutions, generalizations, investigations, generating of new problems and proofs, based on representation of the quantities of liquid in the three vessels as ordered triples - projective (or barycentric) coordinates of points in a Euclidean plane. The pourings are visualized through directed segments between the respective points. This representation provides good visualization for finding all possible solutions, the optimal one in concrete steps, etc. Eventual 3D-representation of the points would lead to more difficulties in the imagination of the spatial objects. The opportunity for systematical approach in seeking for solution enables creation of didactical approach for teaching “how to solve it”, including creation of Educational Dialogue Computer Programs. We consider another discrete optimization problem (DOP) with notion how to find the solution. It is an open question in didactics how to guess how to solve a DOP and we make some first steps in dealing with this topic.

Sarvesh Kumar

— Artificial Intelligence is the science and technology appertained to make machines intelligent. The main aim of researchers is to develop universal intelligent system to rival the intelligence capabilities of human beings. It should be kept in mind that for the time being, the most important applications of AI is to develop intelligent systems to solve real world problems. Which otherwise take considerable amount of time and human efforts, and hence become uneconomical as well as inefficient at times? Hence problem solving becomes major area of study, which involves methods and various techniques used in problem solving using AI.

Badrul Anwar

This paper has been presenting at The 2nd Annual Applied Science and Engineering Conference (AASEC 2017) in Bandung, Indonesia on 24 August 2017, this paper had upload in InArXIV for other researcher before the paper publish by IOP Publisher

For IEEE Members

Ieee spectrum, follow ieee spectrum, support ieee spectrum, enjoy more free content and benefits by creating an account, saving articles to read later requires an ieee spectrum account, the institute content is only available for members, downloading full pdf issues is exclusive for ieee members, downloading this e-book is exclusive for ieee members, access to spectrum 's digital edition is exclusive for ieee members, following topics is a feature exclusive for ieee members, adding your response to an article requires an ieee spectrum account, create an account to access more content and features on ieee spectrum , including the ability to save articles to read later, download spectrum collections, and participate in conversations with readers and editors. for more exclusive content and features, consider joining ieee ., join the world’s largest professional organization devoted to engineering and applied sciences and get access to all of spectrum’s articles, archives, pdf downloads, and other benefits. learn more →, join the world’s largest professional organization devoted to engineering and applied sciences and get access to this e-book plus all of ieee spectrum’s articles, archives, pdf downloads, and other benefits. learn more →, access thousands of articles — completely free, create an account and get exclusive content and features: save articles, download collections, and talk to tech insiders — all free for full access and benefits, join ieee as a paying member., ai copilots are changing how coding is taught, professors are shifting away from syntax and emphasizing higher-level skills.

Photo-illustration of a mini AI bot looking at a laptop atop a stock of books, sitting next to human hands on a laptop.

Generative AI is transforming the software development industry. AI-powered coding tools are assisting programmers in their workflows, while jobs in AI continue to increase. But the shift is also evident in academia—one of the major avenues through which the next generation of software engineers learn how to code.

Computer science students are embracing the technology, using generative AI to help them understand complex concepts, summarize complicated research papers, brainstorm ways to solve a problem, come up with new research directions, and, of course, learn how to code.

“Students are early adopters and have been actively testing these tools,” says Johnny Chang , a teaching assistant at Stanford University pursuing a master’s degree in computer science. He also founded the AI x Education conference in 2023, a virtual gathering of students and educators to discuss the impact of AI on education.

So as not to be left behind, educators are also experimenting with generative AI. But they’re grappling with techniques to adopt the technology while still ensuring students learn the foundations of computer science.

“It’s a difficult balancing act,” says Ooi Wei Tsang , an associate professor in the School of Computing at the National University of Singapore . “Given that large language models are evolving rapidly, we are still learning how to do this.”

Less Emphasis on Syntax, More on Problem Solving

The fundamentals and skills themselves are evolving. Most introductory computer science courses focus on code syntax and getting programs to run, and while knowing how to read and write code is still essential, testing and debugging—which aren’t commonly part of the syllabus—now need to be taught more explicitly.

“We’re seeing a little upping of that skill, where students are getting code snippets from generative AI that they need to test for correctness,” says Jeanna Matthews , a professor of computer science at Clarkson University in Potsdam, N.Y.

Another vital expertise is problem decomposition. “This is a skill to know early on because you need to break a large problem into smaller pieces that an LLM can solve,” says Leo Porter , an associate teaching professor of computer science at the University of California, San Diego . “It’s hard to find where in the curriculum that’s taught—maybe in an algorithms or software engineering class, but those are advanced classes. Now, it becomes a priority in introductory classes.”

“Given that large language models are evolving rapidly, we are still learning how to do this.” —Ooi Wei Tsang, National University of Singapore

As a result, educators are modifying their teaching strategies. “I used to have this singular focus on students writing code that they submit, and then I run test cases on the code to determine what their grade is,” says Daniel Zingaro , an associate professor of computer science at the University of Toronto Mississauga . “This is such a narrow view of what it means to be a software engineer, and I just felt that with generative AI, I’ve managed to overcome that restrictive view.”

Zingaro, who coauthored a book on AI-assisted Python programming with Porter, now has his students work in groups and submit a video explaining how their code works. Through these walk-throughs, he gets a sense of how students use AI to generate code, what they struggle with, and how they approach design, testing, and teamwork.

“It’s an opportunity for me to assess their learning process of the whole software development [life cycle]—not just code,” Zingaro says. “And I feel like my courses have opened up more and they’re much broader than they used to be. I can make students work on larger and more advanced projects.”

Ooi echoes that sentiment, noting that generative AI tools “will free up time for us to teach higher-level thinking—for example, how to design software, what is the right problem to solve, and what are the solutions. Students can spend more time on optimization, ethical issues, and the user-friendliness of a system rather than focusing on the syntax of the code.”

Avoiding AI’s Coding Pitfalls

But educators are cautious given an LLM’s tendency to hallucinate . “We need to be teaching students to be skeptical of the results and take ownership of verifying and validating them,” says Matthews.

Matthews adds that generative AI “can short-circuit the learning process of students relying on it too much.” Chang agrees that this overreliance can be a pitfall and advises his fellow students to explore possible solutions to problems by themselves so they don’t lose out on that critical thinking or effective learning process. “We should be making AI a copilot—not the autopilot—for learning,” he says.

“We should be making AI a copilot—not the autopilot—for learning.” —Johnny Chang, Stanford University

Other drawbacks include copyright and bias. “I teach my students about the ethical constraints—that this is a model built off other people’s code and we’d recognize the ownership of that,” Porter says. “We also have to recognize that models are going to represent the bias that’s already in society.”

Adapting to the rise of generative AI involves students and educators working together and learning from each other. For her colleagues, Matthews’s advice is to “try to foster an environment where you encourage students to tell you when and how they’re using these tools. Ultimately, we are preparing our students for the real world, and the real world is shifting, so sticking with what you’ve always done may not be the recipe that best serves students in this transition.”

Porter is optimistic that the changes they’re applying now will serve students well in the future. “There’s this long history of a gap between what we teach in academia and what’s actually needed as skills when students arrive in the industry,” he says. “There’s hope on my part that we might help close the gap if we embrace LLMs.”

How Coders Can Survive—and Thrive—in a ChatGPT World ›
AI Coding Is Going From Copilot to Autopilot ›
OpenAI Codex ›

Rina Diane Caballar is a writer covering tech and its intersections with science, society, and the environment. An IEEE Spectrum Contributing Editor, she's a former software engineer based in Wellington, New Zealand.

Yes! Great summary of how things are evolving with AI. I’m a retired coder (BS comp sci) and understand the fundamentals of developing systems. Learning the lastest systems is now the greatest challenge. I was intrigued by Ansible to help me manage my homelab cluster, but who wants to learn one more scripting language? Turns out ChatGPT4 knows the syntax, semantics, and work flow of Ansible and all I do is tell is to “install log2ram on all my proxmox servers” and I get a playbook that does just that. The same with Docker Compose scripts. Wow.

Engineering Needs More Futurists

What can ai researchers learn from alien hunters, how nasa is hacking voyager 1 back to life, related stories, ai spam threatens the internet—ai can also protect it, what is generative ai, generative ai has a visual plagiarism problem.

Red-billed blue magpie optimizer: a novel metaheuristic algorithm for 2D/3D UAV path planning and engineering design problems

Open access
Published: 03 May 2024
Volume 57 , article number 134 , ( 2024 )

Cite this article

You have full access to this open access article

Shengwei Fu 1 , 3 ,
Ke Li 1 , 3 ,
Haisong Huang 1 , 3 , 4 ,
Chi Ma 1 , 3 ,
Qingsong Fan 1 , 2 &
Yunwei Zhu 1 , 3

220 Accesses

Explore all metrics

Numerical optimization, Unmanned Aerial Vehicle (UAV) path planning, and engineering design problems are fundamental to the development of artificial intelligence. Traditional methods show limitations in dealing with these complex nonlinear models. To address these challenges, the swarm intelligence algorithm is introduced as a metaheuristic method and effectively implemented. However, existing technology exhibits drawbacks such as slow convergence speed, low precision, and poor robustness. In this paper, we propose a novel metaheuristic approach called the Red-billed Blue Magpie Optimizer (RBMO), inspired by the cooperative and efficient predation behaviors of red-billed blue magpies. The mathematical model of RBMO was established by simulating the searching, chasing, attacking prey, and food storage behaviors of the red-billed blue magpie. To demonstrate RBMO’s performance, we first conduct qualitative analyses through convergence behavior experiments. Next, RBMO’s numerical optimization capabilities are substantiated using CEC2014 (Dim = 10, 30, 50, and 100) and CEC2017 (Dim = 10, 30, 50, and 100) suites, consistently achieving the best Friedman mean rank. In UAV path planning applications (two-dimensional and three − dimensional), RBMO obtains preferable solutions, demonstrating its effectiveness in solving NP-hard problems. Additionally, in five engineering design problems, RBMO consistently yields the minimum cost, showcasing its advantage in practical problem-solving. We compare our experimental results with three categories of widely recognized algorithms: (1) advanced variants, (2) recently proposed algorithms, and (3) high-performance optimizers, including CEC winners.

Dung beetle optimizer: a new meta-heuristic algorithm for global optimization

A review of nature-inspired algorithms on single-objective optimization problems from 2019 to 2023

Secretary bird optimization algorithm: a new metaheuristic for solving global optimization problems

Avoid common mistakes on your manuscript.

1 Introduction

With the rapid advancement of UAV technology, they have emerged as a groundbreaking tool in modern technology, offering unprecedented opportunities and challenges in fields such as military, marine remote sensing, environmental monitoring, disaster response, and logistics (Wu et al. 2023 ). In the pursuit of these tasks, the 3D path planning problem for UAV has become a prominent research focus. Traditional path planning methods often fall short in three−dimensional environments. Swarm intelligence algorithms, as a heuristic approach simulating collective behaviors in nature, have shown great promise in addressing the 3D path planning problem for UAV (Wang et al. 2023 ). By emulating behaviors of natural groups like ant colonies and bird flocks, swarm intelligence enables high levels of cooperation among group members. The introduction of swarm intelligence algorithms in 3D UAV path planning not only enhances planning efficiency but also ensures the safety and stability of paths, providing a higher degree of controllability for UAV movements in three−dimensional space (Gugan and Haque 2023 ).

The optimization problem is to find a set of decision variables to maximize or minimize the objective function under certain constraints (Pozna et al. 2022 ; Zhou et al. 2022 ). With the increasing complexity of real-world optimization Dengproblems, the performance of deterministic algorithms is significantly reduced. Stochastic algorithms show good performance in dealing with such complex problems. The metaheuristic algorithm is a stochastic algorithm that performs well in complex nonlinear problems. Therefore, metaheuristic algorithms are widely used to solve practical problems, such as feature selection (Said et al. 2023 ; Talapula et al. 2023 ), scheduling (Fontes et al. 2023 ), identification (Minh et al. 2022 ), cloud computing (Attiya et al. 2022 ), neural networks (Jain et al. 2022 ), engineering problems (Abdel-Basset et al. 2023 ; Zhu et al. 2024 ), classification (Pashaei and Pashaei 2022 ), global optimization (Alrahhal and Jamous 2023 ; Seyyedabbasi and Kiani 2023 ), medicine data classification (Zhong et al. 2023 ), diabetic retinopathy detection (Prabhakar et al. 2024 ), etc. The metaheuristic algorithm has four advantages in solving these complex nonlinear problems (Mirjalili et al. 2014 ): simplicity, flexibility, derivation-free mechanism, and local optima avoidance.

Generally, we divide metaheuristic algorithms into four categories (Abualigah et al. 2021 ): Swarm Intelligence (SI) algorithms, Physics-based Algorithms (PhA), Evolutionary Algorithms (EA) and Human-based algorithms. The swarm intelligence algorithm is the most representative metaheuristic algorithm, which solves problems by simulating group behavior in nature (Smith 2000 ). For example, Kennedy et al. (Kennedy and Eberhart 1995 ) proposed the Particle Swarm Optimization (PSO) algorithm by imitating the process of bird swarms foraging. The PSO is the most popular swarm intelligence algorithm and has been widely studied by scholars. Physics-based algorithms often mimic physical rules and chemical reactions. For instance, Kirkpatrick et al. (Kirkpatrick et al. 1983 ) proposed a simulated annealing algorithm inspired by the metal annealing process. Evolutionary algorithms are based on biological principles (Bäck and Schwefel 1993 ). For example, Holland (Holland 1992 ) proposed a Genetic Algorithm (GA) based on Darwin’s evolution theory. Human-based algorithms imitate human cognitive and behavioral processes. For instance, Rao et al. (Rao et al. 2011 ) proposed a Teaching-Learning-Based Optimization (TLBO) by simulating the classroom teaching process. Since we propose a swarm intelligence algorithm, we mainly introduce the swarm intelligence algorithm and its application.

In the past time, the PSO algorithm has been used to deal with many practical problems, for example, task scheduling (Alsaidy et al. 2022 ), wireless sensor networks (Wang et al. 2018 ), image enhancement (Zhang et al. 2023b ) and other problems. Karaboga et al. (Karaboga and Basturk 2008 ) proposed an artificial bee colony (ABC) inspired by bee population behavior. It has been used to solve the clustering of wind power scenarios (Yao et al. 2022 ), prediction of sports economic development (Liu and Song 2022 ), flexible job-shop scheduling (Long et al. 2022 ), image threshold segmentation (Huo et al. 2022 ) and so on. Grey Wolf Optimizer (GWO) is an optimization algorithm developed by Mirjalili et al. (Parizi et al. 2020 ) to simulate the hunting behavior of grey wolf groups. It has been successfully applied in 5G frequency selection surface design (He et al. 2022 ), dam deformation prediction (He and Wu 2023 ), path planning for mobile robots (Hou et al. 2022 ), predictive current control (Mahmoudi et al. 2022 ), Capacitor Placement in Radial Distribution Systems (Jayabarathi et al. 2022 ) and others. Mirjalili et al. (Mirjalili 2015 ) proposed a Moth-flame optimization algorithm (MFO) based on the moth navigation method in nature, which has been used to solve automatic parking path optimization (Chen et al. 2022 ), parameter estimation of induction motor (Ma et al. 2022 ), UAV formation path planning (Wu et al. 2023 ) and so on. Yu et al. (Yu & Li 2015 ) proposed the social spider algorithm by the foraging behavior of social spiders in nature, which has been widely used to solve practical problems, including cloud detection in satellite images (Gupta and Nanda 2022 ), line balancing (Liang et al. 2023 ), efficient data dissemination in VANET (Shankar et al. 2022 ), classify microscopic biopsy images of cancer (Balaji and Chidambaram 2022 ), and job scheduling (Kuppusamy et al. 2022 ). Parizi et al. (Morteza et al. 2020) introduced the Woodpecker Mating Algorithm (WMA) to simulate the mating behavior of woodpeckers, successfully applied in various domains, including neural networks (Parizi et al. 2021b ), software development effort estimation (Parizi et al. 2021a ), economic load dispatch (Karimzadeh et al. 2021 ), and other problems (Gonga and Parizi 2022 ; Zhang et al. 2023a ). Moreover, many high-performance algorithms have been proposed recently, for example, the Dwarf Mongoose Optimization algorithm (DMO) proposed by Agushaka et al. (Agushaka et al. 2022 ) based on the foraging behavior of the dwarf mongoose. Zamani et al. (Nadimi-Shahraki and Zamani 2022 ) came out with Starling Murmuration Optimizer (SMO) by imitating Starlings’ behaviors. Inspired by the particular mating behavior of snakes, Hashim et al. (Hashim and Hussien 2022 ) proposed Snake Optimizer (SO). Zhong et al. proposed Beluga Whale Optimization (BWO) by simulating the behaviors of beluga whales. Ezugwu et al. (Ezugwu et al. 2022 ) proposed Prairie Dog Optimization (PDO) by impersonating the behavior of prairie dogs. Jia et al. (Jia et al. 2023 ) proposed the Crayfish Optimization Algorithm (COA) by simulating the summer escape behavior, competition behavior, and foraging behavior of crayfish. Deng et al. (Deng and Liu 2023b ) emulated the sublimation and melting behavior of snow to introduce the Snow Ablation Optimizer (SAO). Tian et al. proposed the Snow Geese Algorithm (SGA) by simulating the migration behavior of snow geese (Tian et al. 2024 ). The algorithm Greylag Goose Optimization (GGO), proposed by El-kenawy et al. (El-kenawy et al. 2024 ), is inspired by the flying habits of grey geese. These advanced algorithms are widely used in different optimization problems, and most have achieved varying degrees of success (Akinola et al. 2022 ; Fu et al. 2022 ; Li et al. 2022 ; Nadimi-Shahraki et al. 2023 ; Rizk-Allah et al. 2023 ).

In particular, our research team has achieved some positive results in optimizing algorithms. For example, we have proposed a new imbalance fault diagnosis framework based on an MFO-optimized LS-SVM classifier and successfully applied it to limited and complex bearing data (Wei et al. 2020 ). Based on innovative updating rules and opposition-based learning, we proposed a modified EO (Fan et al. 2021 ). We introduced self-adaptive into the marine predator algorithm and applied it to framework and engineering problems (Fan et al. 2022 ). For the grey wolf optimizer, we proposed BGWO (Fan et al. 2021b ) and AGWO (Ma et al. 2022 ) by giving the leader wolf hearing and flying abilities, respectively. The latest research achievements of our team include IDMO (Fu et al. 2023 ) and MENGO (Li et al. 2023 ). The No Free Lunch (NFL) theorem (Wolpert and Macready 1997 ) states that no optimization algorithm can solve all optimization problems effectively. Therefore, it is still challenging to find a new efficient metaheuristic algorithm.

Based on our team’s previous research and NFL incentives, in this work, we propose a new metaheuristic algorithm called Red-billed Blue Magpie Optimizer (RBMO) for numerical optimization, engineering design problems, and UAV path planning. It overcomes the problems of initialization sensitivity, premature convergence and stagnation in the local optimum of most algorithms. RBMO is an algorithm based on swarm intelligence, inspired by the hunting process of the red-billed blue magpie, which includes searching, attacking prey, and food storage. The red-billed blue magpie is a flexible and adaptable predator. It primarily feeds on fruits, insects, and small vertebrates, exhibiting a diverse hunting behavior. These magpies usually move in small groups or clusters, aiding them in locating food resources more efficiently. Collective action enhances their search effectiveness. Additionally, they obtain food from both the ground and trees. Finally, they store food in tree holes or other suitable locations for future consumption, ensuring a reliable food source during times of scarcity. The hunting behavior of the red-billed blue magpie underscores its flexibility as a predator, proficient in employing a range of strategies and techniques to secure food. Furthermore, it exhibits social and cooperative tendencies. The mathematical model of RBMO encompasses both exploration and exploitation phases. RBMO’s performance was evaluated using the CEC2014 and CEC2017 test suites. Moreover, RBMO was applied to address five engineering design problems and UAV path planning. Comparative experiments reveal that the proposed method outperforms popular metaheuristic approaches, showcasing significant application potential.

The rest of this paper is organized as follows: Sect. 2 describes the RBMO inspiration and mathematical model. In Sect. 3 , we conduct the numerical experiment and analyze them in detail. In Sect. 4 , we apply RBMO to solve 2D and 3D UAV path planning. In Sect. 4 , we apply the RBMO to address five engineering design problems, providing a comprehensive analysis of both its strengths and weaknesses. Summarizes and prospects this work in Sect. 6 .

2 The Red-billed blue magpie optimizer (RBMO)

2.1 inspiration.

The red-billed blue magpie is a bird mainly living in Asia, which is common in China, India, Myanmar, and other places (Wolpert and Macready 1997 ). As shown in Fig. 1 , it depicts the red-billed blue magpie, which is characterized by its large size, bright blue feathers, and distinctive red mouth. The red-billed blue magpie mainly feeds on insects, small vertebrates, plants, etc., and has a relatively rich hunting behavior (Madge 2020 ). While foraging, the red-billed blue magpie employs a combination of jumping, ground-walking, and searching on branches to locate its food. The red-billed blue magpie exhibits heightened activity levels during the early morning and evening hours, often congregating in small groups of 2–5 or even exceeding 10 members. They engage in cooperative hunting efforts. For example, a magpie may find a fruit or an insect, and then it will attract other members to share. This allows them to work together to capture large insects or small vertebrates, and group action can help them overcome the defense mechanisms of prey. In addition, the red-billed blue magpie will also store some food for later use. To prevent theft by other birds or animals, they conceal food items in places like tree holes, tree forks, and rock crevices (Dronen and Tkach 2014 ; Guo et al. 2022 ). In general, the red-billed blue magpie is a flexible predator who acquires and stores food in a variety of ways, while also demonstrating sociality and cooperation in hunting behavior. Inspired by this, a new meta-heuristic algorithm RBMO is proposed. Next, we will provide detailed explanations of the mathematical models associated with these processes.

Red-billed Blue Magpie

2.2 Population initialization

As in most algorithms, RBMO candidate solutions produced through Eq. ( 1 ). Stochastically produced within the constraints of the given problem and need to be updated after each iteration.

where \(X\) denotes the position of the search agent generated by Eq. 2 , \(n\) represents the population size, and \(\text{d}\text{im}\) denotes the dimension of solving the problem.

where \(ub\) and \(lb\) are the upper and lower bounds of the problem, respectively, and \(Rand\) represents a random number from 0 to 1.

2.3 The mathematical model of RBMO

2.3.1 search for food.

In their quest for food, red-billed blue magpies typically operate in small groups (2 to 5) or clusters (more than 10) to enhance search efficiency. They employ various techniques such as jumping on the ground, walking, or scouring trees for food resources. This adaptability and flexibility enable red-billed blue magpies to employ diverse hunting strategies based on environmental conditions and available resources, ensuring access to an ample food supply. When small groups explore food, Eq. ( 3 ) is used, and Eq. ( 4 ) is utilized in cluster search.

where \(t\) demonstrates the current number of iterations, \({\varvec{X}}^{\varvec{i}}\left(t+1\right)\) represents the i th new search agent position, \(p\) signifies the number of red-billed blue magpies hunting in small groups, between 2 and 5, randomly selected from all searched individuals, X m represents the m th individual chosen at random, \({\varvec{X}}^{i}\) denotes the i th individual, and \({\varvec{X}}^{rs}\left(t\right)\) denotes randomly selected search agents in the current iteration.

where \(q\) represents the number of search agents when the cluster explores food, between 10 and \(n\) . Similarly, it is also randomly selected from the entire population.

2.3.2 Attacking prey

The red-billed blue magpie exhibits a high level of hunting proficiency and cooperation when pursuing prey. They employ tactics such as quick pecking, leaping to catch prey, or flying to capture insects. In instances of small group actions, the primary targets are typically small prey or plants. The corresponding mathematical model is presented in Eq. ( 5 ). When operating in clusters, red-billed blue magpies are capable of jointly targeting larger prey like large insects or small vertebrates. The mathematical representation for this behavior is outlined in Eq. ( 6 ). This predatory hunting behavior underscores the diverse strategies and skills possessed by the red- billed blue magpie, enabling it to be a versatile predator adept at securing food successfully in various scenarios.

where \({\varvec{\mathbf{X}}}^{food}\left(t\right)\) represents the position of the food, \(CF={\left(1-\left(\frac{t}{T}\right)\right)}^{\left(2\times \frac{t}{T}\right)}\) , and \(Randn\) represents a random number used to generate a standard normal distribution (mean 0, standard deviation 1).

2.3.3 Food storage

In addition to searching for and attacking food, red-billed blue magpies also store excess food in tree holes or other concealed locations for future consumption, ensuring a steady food supply during scarcity. This process retains solution information, facilitating individuals in locating the globally optimal value. The mathematical model for this is presented in Eq. ( 7 ).

where, \({fitness}_{old}^{i}\) and \({fitness}_{new}^{i}\) represent the fitness values before and after the location update of the i th red-billed blue magpie, respectively.

To summarize, in RBMO, the optimization process commences by generating a random set of candidate solutions, referred to as populations. The search strategy of RBMO explores the suitable position, either a suboptimal or optimal solution, through repeated trajectories. The food storage phase enhances the exploration and exploitation abilities of RBMO. Finally, the RBMO search process concludes upon meeting the end criterion. It’s worth noting that the population size of the red-billed blue magpie differs during the hunting process, but the total number of small-scale populations and clusters remains similar. In this paper, we propose a coefficient \(\epsilon\) for the equilibrium population, setting it to 0.5. The pseudocode for RBMO is provided in Algorithm 1.

2.4 Computational complexity

In this section, we described the general computational complexity of RBMO. The computational complexity of RBMO typically depends on two rules: solutions initialization and the main algorithm functions, including calculating the fitness functions and updating the solutions. Assume that the number of search agents is \(n\) , \(T\) denotes the maximum number of iterations, \(dim\) represents the dimension size of solving the problem, and \(O\left(n\right)\) demonstrates the computational complexity of the solutions’ initialization process. The computational complexity of the solutions’ updating process is \(O\left(T\times n\right)+O(2\times T\times n\times dim)\) . It includes finding the best position and updating the position of all solutions. Accordingly, the total computational complexity of the proposed RBMO is \(O(n\times T\times (2\times dim+1\left)\right)\) .

3 Numerical experiment

In this section, we evaluate the performance of RBMO on different function test suites. In order to verify the effectiveness of RBMO, we conducted convergence behavior analysis experiments. Meanwhile, numerical experimental results were compared with other advanced algorithms. Moreover, the scalability of RBMO has been demonstrated by solving largE − scale global optimization problems. Finally, two nonparametric tests, including the Wilcoxon signed rank test and the Friedman mean rank tests, were used to analyze the difference and overall performance of the competitors. All experiments were conducted on an Intel Core i7-12700 F computer with a 2.10 GHz CPU and 16 GB RAM using the MATLAB 2023a platform.

3.1 Benchmark test functions

The benchmark test function plays a crucial role in assessing the algorithm’s feasibility, offering an evaluation platform for testing and comparing various optimization algorithms. In this study,, we utilize the CEC2014 (Liang et al. 2013 ) and CEC2017 (Wu et al. 2016 ) test suites to assess the performance of the proposed RBMO, setting the dimensions to 30, 50, and 100, respectively. As the dimension increases, the number of locally optimal solutions also rises. Consequently, these test suites effectively scrutinize the algorithm’s global optimization capabilities and are among the most widely used suites. Detailed information regarding the CEC2014 and CEC2017 test suites are reported in Tables 1 and 2 , respectively. Both suites encompass four types of functions: Unimodal, Multimodal, Hybrid, and Composition functions, which effectively validate the algorithm’s abilities in local exploitation and global exploration.

3.2 Competitor algorithms and parameters setting

We compare RBMO’s results to 11 other well-known algorithms, including MELGWO (Ahmed et al. 2023 ), E_WOA (Nadimi-Shahraki et al. 2022 ), HPHHO (Su et al. 2021 ), COA (Jia et al. 2023 ), DBO (Xue and Shen 2023 ), BWO (Zhong et al. 2022 ), OMA (Cheng and Sholeh 2023 ), EBOwithCMAR (Kumar et al. 2017 ), LSHADE_cnEpSin (Mohamed et al. 2017 ), MadDE (Biswas et al. 2021 ), and EA4eig (Bujok et al. 2022 ). Table 3 summarizes the parameters of these competitors. To plot the convergence curves, a consistent maximum number of iterations ( T ) set at 500 was applied to all algorithms. The number of evaluations ( FES ) and the population size ( n ) as detailed in Table 3 . All experiments were independently repeated 30 times, and the corresponding results were recorded.

3.3 Convergence behavior evaluation

In order to examine whether RBMO is convergent, we design experiments to analyze the convergence behavior of RBMO. As shown in Fig. 2 , the first column displays a threE − dimensional image of the benchmark function, which intuitively reflects the complexity of the search space. The second column denotes the search trajectory of the search agent. The third column represents the change in the average fitness value of the search agent. At the beginning of the iteration, this value is tremendous, meaning that the search agent is exploring the entire search space extensively and then decreases rapidly, indicating that most search agents have reached the best position or are nearby. The fourth column denotes the search trajectory of the search agent, which fluctuates to stable, representing the process from global exploration to local exploitation. The last column shows the convergence curve of the algorithm. The unimodal function continues to decline, indicating that the algorithm can find the optimal value as long as the number of iterations is sufficient. For the multimodal function, the image becomes step-wise, indicating that the algorithm can constantly jump out of the local optimum to obtain the global optimum. From the convergence behavior, it is clear that RBMO is convergent.

The convergence behavior of RBMO

3.4 Sensitivity analysis of parameters

In this section, we present an analysis of the parameter \(\epsilon\) . Experiments were conducted using all dimensions of the two test sets, CEC2014 and CEC2017, with experimental parameters consistent with those used previously. We calculated the average ranking of different values of \(\epsilon\) for each dimension and illustrated it as a curve in Fig. 3 . From the experimental results, it is evident that the optimal overall effect occurs when \(\epsilon =0.5\) , while the least favorable effect is observed when \(\epsilon =0.9\) . Therefore, in this paper, we set ε to 0.5.

Parametric sensitivity analysis average ranking graph

3.5 Quantitative analysis

In this section, we evaluate the numerical optimization performance of different competitive algorithms using CEC2014 and CEC2017 test suites.

3.5.1 Comparison with other competitive algorithms on CEC2014

In this section, we conduct performance testing using the CEC2014 suite. The dimensions are set to 10, 30, 50, and 100, respectively. The experimental results, including averages (Ave) and standard deviations (Std), are presented in Tables 4 , 5 , 6 and 7 . The best results among the 11 competitors are highlighted in bold. To visualize the ranking distribution of each algorithm, we present a stacked bar chart in Fig. 4 . It is evident that our proposed RBMO basically ranks in the top five, showcasing exceptional performance akin to the CEC winners. Furthermore, it is observed that RBMO exhibits less sensitivity to changes in dimension. Figure 5 depicts the convergence curves of different competitors across various dimensions. To mitigate potential random fluctuations, we plot the average iteration curve of the algorithm over 30 repeated runs. The results demonstrate that our proposed optimizer boasts both faster convergence speed and superior accuracy. Overall, RBMO outperforms state−of-the−art optimization algorithms.

The ranking stacked bar chart of different competitors on CEC2014

where t demonstrates the current number

Comparison of the convergence speed of different competitors on CEC2014

3.5.2 Comparison with other competitive algorithms on CEC2017

We conduct performance testing utilizing the CEC2017 suite, in this section. The Ave and Std were recorded, with the best results among the 11 competitors highlighted in bold. Similarly, we set the dimensions to 10, 30, 50, and 100, and present the experimental results in Tables 8 , 9 , 10 and 11 . In Fig. 6 , we illustrate the Sankey ranking of the 12 algorithms, demonstrating that our proposed optimizer mostly maintains the top three positions in different test functions. Notably, for all three dimensions, RBMO achieves the highest number of first-place rankings. To further delve into the convergence speed of various competitors in the optimization process, we display the experimental results in Fig. 7 . These results unequivocally establish the developed RBMO as the most competitive algorithm. Thus, in consideration of the test functions and optimization algorithms in question, the all-around performance and robustness of RBMO are particularly striking.

The ranking Sankey of different competitors on CEC2017

Comparison of the convergence speed of different competitors on CEC2017

3.6 Statistical analysis

3.6.1 wilcoxon signed rank test.

We employ the nonparametric Wilcoxon signed rank test (Derrac et al. 2011 ) to compare the differences between RBMO and other competitor algorithms, and the results are presented in Tables 12 , 13 , 14 , 15 , 16 , 17 , 18 and 19 . The results present that RBMO is statistically more successful than most of the compared algorithms with a statistical significance value of α = 0.05. The symbols ‘+/=/−’ are employed to indicate whether RBMO performs better than, similarly to, or worse than the competitors. The last row of the table describes the total number of statistical results, it is evident from the results that as the dimension’s complexity increases, the distinction between RBMO and other algorithms becomes more pronounced. Therefore, in conjunction with the analyses from earlier sections, it is apparent that RBMO distinguishes itself from competitors and exhibits the most outstanding comprehensive performance.

3.6.2 Friedman mean rank test

In this section, we apply the nonparametric Friedman mean rank test (Nadimi-Shahraki and Zamani 2022) to assess and rank the experimental results of RBMO in comparison to other competitor algorithms on CEC2014 and CEC2017 global optimization suites. The results of this analysis are presented in Table 20 , showing the average ranking (A.R) and the overall ranking (O.R), respectively. It is evident from the experimental data that RBMO. This outcome signifies the superior performance of our proposed RBMO in the evaluated test suites compared to other competitor algorithms.

4 2D/3D UAV path planning

In the previous section, we used benchmark test functions to verify the performance of RBMO. The Friedman ranking test verifies the overall effectiveness. An efficient algorithm needs to pass the test of practical problems. Therefore, in this section, we use our proposed RBMO to solve real-world applications that are more complex than test functions, which is a tremendous challenge for the new algorithm. We applied RBMO to 2D and 3D UAV path planning problems. We compare RBMO’s results to 11 other well-known algorithms, including MELGWO (Ahmed et al. 2023 ), E_WOA (Nadimi-Shahraki et al., 2022 ), HPHHO (Su et al. 2021), COA (Jia et al., 2023), DBO (Xue and Shen 2023), BWO (Zhong et al. 2022), OMA (Cheng and Sholeh 2023), EBO with CMAR (Kumar et al. 2017), LSHADE_cnEpSin (Mohamed et al. 2017), MadDE (Biswas et al. 2021), EA4eig (Bujok, et al., 2022). Table 3 summarizes the parameters of these competitors. We recorded the optimal solution (Best), median values (Median), worst cost (Worst), average (Ave), standard deviation (Std), Friedman ranking (F-ranking), Wilcoxon signed rank test (Wilcoxon), and highlight the best results.

4.1 Two-dimensional UAV path planning

4.1.1 two-dimensional mathematical model.

Unmanned aerial vehicles (UAVs) have demonstrated remarkable effectiveness and superiority in both everyday life and military applications (Nelson et al. 2007 ). Among these applications, UAV path planning stands out as a crucial technology for achieving autonomous control systems. Our objective is to determine a safe and optimal path from the starting point to the end point, subject to various constraints. This constitutes a challenging constrained optimization problem. In recent years, with the proliferation of UAV types and diverse usage scenarios, path planning has emerged as a prominent area of research. Many scholars have turned to meta-heuristic algorithms for addressing UAV path planning problems (Deng and Liu 2023a ). The specific 2D mathematical model for this problem is outlined below.

In 2D UAV path planning, we mainly consider the threat cost and fuel cost, and Eq. 8 reports its mathematical model.

where \({F}_{t}\) indicates the total cost, \({F}_{tc}\) represents the threat cost, which are calculated through Eq. ( 9 ), \({F}_{hc}\) shows fuel cost,, which are calculated by Eq. ( 10 ), and \({k}_{i}\) ( i = 1,2) is weight. The constraints on the weight coefficients are given in Eq. ( 11 ).

where, \({x}_{end}\) represents the abscissa value of the flight end point, and \(path\left(j\right)\) represents the j th subpath.

where \({C}_{b}\) is the coordinate of the b th threat center and \({P}_{b}\) is the threat level of the b th threat center. dis is the distance function between two points.

4.1.2 Two-dimensional simulation experiment

In this work, we set \({k}_{1}\) and \({k}_{2}\) to 0.5 each. The UAV initiates from (0, 0) and concludes at (100, 100). Employing cubic spline interpolation alongside other methods, we achieve a feasible and seamless trajectory. The experimental setup aligns with prior chapters. Table 21 presents the relevant results, highlighting RBMO’s superior performance over alternative optimization approaches, with OMA exhibiting less favorable outcomes. Moreover, Fig. 8 displays the convergence trend, emphasizing RBMO’s rapid convergence. Meanwhile, Fig. 9 showcases the trajectories of the 12 contenders. It’s evident that RBMO’s path is notably smoother, reinforcing its potential in addressing 2D UAV path planning challenges.

Convergence curve of 12 competitors on the 2D UAV path planning problem

The UAV best 2D path obtained by 12 competitors

4.2 ThreE − dimensional UAV path planning

4.2.1 three − dimensional mathematical model.

Let the starting point of the UAV flight be denoted as \({(x}_{s},{y}_{s},{z}_{s})\) and the ending point as \({(x}_{e},{y}_{e},{z}_{e})\) . Based on cubic spline interpolation, a smooth curve is generated with g discrete points \({(x}_{s},{y}_{s},{z}_{s})\) , \({(x}_{1},{y}_{1},{z}_{1})\) , …, \({(x}_{g-1},{y}_{g-1},{z}_{g-1})\) , \({(x}_{e},{y}_{e},{z}_{e})\) . This curve is subsequently represented as a discrete series of points ( h 1 , h 2 , …, h g ), where the coordinates of h m are \({(x}_{m},{y}_{m},{z}_{m})\) . Thus, the objective function for this problem can be derived, as expressed in Eq. ( 12 ). (Roberge et al. 2013 ).

where \({F}_{tc}\) denotes the total cost, \({F}_{pc}\) represents the cost of path length, \({F}_{hc}\) shows the cost of the height’s standard deviation, \({F}_{sc}\) indicates the cost of the planning path’s smoothness, and \({w}_{i}\) ( i = 1,2,3) is weight. The constraints on the weight coefficients are given in Eq. ( 13 ).

Usually, UAV flight needs to save time and reduce costs as much as possible while ensuring safety, so the length of path planning is crucial. The mathematical model of A is shown in Eq. ( 14 ).

where \(({x}_{m},{y}_{m},{z}_{m})\) denotes the m th waypoint in the UAV planning path.

In addition, the flight altitude of the UAV has a great impact on the control system and safety, so we need to consider the influence of this factor. Eq. ( 15 ) represents the mathematical model.

Finally, we also need to consider the influence of the UAV when it turns, and the mathematical model is reported in Eq. ( 16 ).

where \({\phi }_{m}\) represents \(\left({x}_{m+1}-{x}_{m},{y}_{m+1}-{y}_{m},{z}_{m+1}-{z}_{m}\right).\)

In summary, we can obtain the model of the UAV path planning optimization problem, which is reported in Eq. ( 17 ).

where \(L\) represents the flyable path, \(Ground\) and \(Obstacle\) are the ground and obstacles respectively. In this paper, we model the ground and obstacle sets by Eq. ( 18 ).

4.2.2 ThreE − dimensional simulation experiment

In this study, we assign the values of \({w}_{1}\) , \({w}_{2}\) , and \({w}_{3}\) as 0.5, 0.3, and 0.2, respectively. The UAV’s starting point is set at (0, 0, 20), and the end point at (200, 200, 30). Utilizing cubic spline interpolation alongside varRobergeious competitors, we obtain a feasible and smooth path. The experimental parameters remain consistent with those outlined in preceding chapters. The pertinent experimental results are documented in Table 22 , and RBMO demonstrates superior performance compared to other optimization techniques, with EBOwithCMAR yielding the least favorable results. Furthermore, Fig. 10 presents the convergence curve, clearly indicating RBMO’s faster convergence. Simultaneously, Fig. 11 illustrates the paths of the 12 competitors. It is evident that the curve generated by RBMO is notably smoother, further validating the potential of RBMO in solving 3D UAV path planning problems.

Convergence curve of 12 competitors on the UAV path planning problem

The UAV best 3D path obtained by 12 competitors

5 Engineering design problems

In this section, we applied RBMO to five engineering design problems, namely the Pressure vessel design problem (PVD) (Kumar et al. 2020 ), Welded beam design problem (WBD) (Deb 1991 ), Tension/compression spring design problem (T-BTD) (Belegundu and Arora 1985a ), Cantilever beam design problem (CBD) (Patel et al. 2020 ), and ThreE − bar truss design problem (T-BTD) (Belegundu and Arora 1985b ).

5.1 Pressure vessel design problem (PVD)

The PVD problem is to optimize head thickness ( T h ), length of the container barring head ( L ), container thickness ( T S ), and inner radius ( R ) to obtain the optimal welding cost, material and form. The structural diagram is shown in Fig. 12 , and the mathematical model is described by Eq. ( 19 ).

Schematic representation of the PVD

The results and statistical analysis of the 11 competitors for the PVD problem are shown in Table 23. . RBMO can find the optimal cost of PVD within the maximum number of iterations used in all experiments. Meanwhile, RBMO has the least mean and standard deviation, indicating its superiority and robustness in solving this engineering problem. Wilcoxon rank sum test showed that RBMO was significantly different from all other competitors.

5.2 Welded beam design problem (WBD)

The main objective of this problem is to optimize the thickness( h ), length( l ), height( t ), thickness( b ), and weld of the beam bars to minimize the cost of welded beam. Figure 13 describes the structure of the WBD, and the mathematical model is reported in Eq. ( 20 ).

Schematic representation of the WBD

The results and statistical analysis of the nine optimizers for solving the WBD problem are described in Table 24. . The RBMO, EBOwithCMAR, OMA, and DBO can find the global minimum cost of WBD. Our algorithm has the same result as the CEC winner, so RBMO can be classified as a high performance optimizer for this problem.

5.3 Tension/compression spring design problem (T/CSD)

The design problem is to find three parameters of the spring, including the coil diameter ( D ), the wire diameter ( d ), and the number of coils n to minimize the weight of the tension/compression spring. The structure of the T/CSD problem is denoted in Fig. 14 , and the mathematical model is displayed in Eq. ( 21 ).

Schematic representation of the T/CSD

The results in Table 25. compare RBMO with 11 other optimization algorithms from multiple perspectives. The RBMO, EA4eig, MadDE, LSHADE_cnEpSin, and EBOwithCMAR return the minimum cost of the objective function. However, RBMO produces the minimum Median, Worst, Ave and Std, which means the effectiveness and robustness of the proposed algorithm results. Similarly, the Wilcoxon rank sum test results show significant differences between RBMO and the considered algorithms.

5.4 Cantilever beam design problem (CBD)

The CBD problem is an engineering structure design problem. It consists of 5 hollow square blocks of constant thickness, and its height (or width) is constrained to minimize its production cost. Figure 15 denotes the structure of the CBD, and its mathematical model is reported in Eq. ( 22 ).

Schematic representation of the CBD

The optimization results of different competitors are shown in Table 26. . Overall, we see that RBMO outperforms all algorithms and produces the lowest mean and standard deviation values. The potential of the proposed technology to solve practical problems is further verified. Wilcoxon signed rank test showed that RBMO significantly differed from all other competitors.

5.5 ThreE − bar truss design problem (T-BTD)

The threE − bar truss design problem is from civil engineering. According to each bar’s stress ( \(\sigma\) ) constraints, the overall structure weight is minimized. Figure 16 denotes the structure of the T-BTD, and Eq. ( 23 ) represents its mathematical model.

Schematic representation of the T-BTD

Table 27 shows the optimization results of nine competitors. The optimal values of RBMO, EA4eig, MadDE, LSHADE_cnEpSin, EBOwithCMAR, DBO, and HPHHO are the same, which are superior to other algorithms. Similarly, four of them are CEC winners, so we can classify RBMO as a high performance algorithm.

5.6 RBMO strengths and limitations

In theory, the proposed RBMO algorithm can find better global optimal solutions for various optimization problems compared to some algorithms mentioned in the literature. The RBMO algorithm simulates the search, pursuit, prey attack, and food storage behaviors of the AzurE − winged Magpie. It randomly generates and improves a set of candidate solutions for a given optimization problem. The AzurE − winged Magpie is a flexible and highly adaptive predator, primarily feeding on fruits, insects, and small vertebrates, exhibiting diverse hunting behaviors. These magpies usually act in groups, aiding them in efficiently searching for food resources. This group behavior enhances RBMO’s exploration capabilities. Additionally, they store food in tree holes or other suitable places for future consumption, ensuring a reliable food source during scarcity periods. This behavior empowers RBMO with strong exploitation capabilities.

Through experimental observation on the CEC2014 and CEC2017 test sets, it was found that the RBMO algorithm converges quickly in most cases. However, there is sometimes a risk of falling into a local optimum (e.g., CEC2014-F25 and CEC2017-F26). Applying RBMO to 2D/3D drone path planning and five engineering problems, we observed that RBMO outperforms existing statE − of-thE − art algorithms in terms of convergence speed and accuracy. Moreover, RBMO only has two tuning parameters ( \(CF\) and ε ). However, the smoothness of RBMO’s optimization process is not guaranteed. Specifically, RBMO may stagnate due to insufficient population diversity during the iteration process (e.g., CEC2014-F9 and CEC2017-F1), and the algorithm needs to wait for \(CF\) to decrease before progressing to better solutions, necessitating more iterations. Further testing of RBMO on parallel machine scheduling and other real-world problems is necessary to validate its performance.

6 Summary and prospect

In this study, we presented a novel metaheuristic approach named RBMO, drawing inspiration from the cooperative hunting behavior of red-billed blue magpies. The algorithm incorporates effective search and attack strategies, exhibiting remarkable performance across various optimization suites. Extensive testing was conducted using both CEC2014 and CEC2017 suites, accompanied by comprehensive qualitative, quantitative, and scalability analyses. Furthermore, we applied statistical methods to validate the effectiveness and robustness of RBMO. The application of RBMO to engineering problems and UAV path planning demonstrated its versatility and superiority when compared to 11 statE − of-thE − art algorithms. Our experiments conclusively established RBMO’s dominance over MELGWO, E_WOA, HPHHO, COA, DBO, BWO, OMA, EBOwithCMAR, LSHADE_cnEpSin, MadDE, and EA4eig.

In future research, there are still numerous areas to be explored. We intend to conduct in-depth research on RBMO from the following perspectives:

Population Initialization and Border Control: Extensively studying the algorithm’s population initialization and border control strategy will enhance the algorithm’s exploration and development capabilities.

Integration with Other Algorithms: Integrating RBMO with other metaheuristic algorithms, leveraging the strengths of each algorithm, will further enhance the accuracy and robustness of problem-solving.

Adaptive and Self-Learning Algorithm: Incorporating machine learning and deep learning technologies will reinforce RBMO’s adaptive and self-learning capabilities. This will enable RBMO to adapt to changes in different problem scenarios and environments. It allows RBMO to learn from data, adjust parameters and strategies autonomously, and improve the effectiveness and adaptability of problem-solving.

Multi-objective and Constraint Optimization: As real-world problems become increasingly complex, multi-objective and constraint optimization become more important. In future research, we will enhance RBMO’s ability to handle multi-objective problems, providing more comprehensive solutions to optimization challenges.

Expanded Application Fields: Metaheuristic algorithms were designed to solve real-life problems. Therefore, we will further expand RBMO’s application fields to make it applicable to a wider range of fields. This includes human-computer cooperation, fault diagnosis, drone path planning, wireless sensor networks, cloud computing, and 3D reconstruction, among others.

Data availability

Enquiries about data availability should be directed to the authors.

Abdel-Basset M, Mohamed R, Abouhawwash M (2023) Nutcracker optimizer: a novel naturE − inspired metaheuristic algorithm for global optimization and engineering design problems. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2022.110248

Article Google Scholar

Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-qaness MA, Gandomi AH (2021) Aquila Optimizer: A novel meta-heuristic optimization algorithm. Comput Indus Eng. https://doi.org/10.1016/j.cie.2021.107250

Agushaka E, Abualigah (2022) Dwarf mongoose optimization algorithm. Comput Methods Appl Mech Eng 391:114570. https://doi.org/10.1016/j.cma.2022.114570

Article MathSciNet Google Scholar

Ahmed R, Mahadzir, Mirjalili H, Kamel (2023) Memory, evolutionary operator, and local search based improved Grey Wolf Optimizer with linear population size reduction technique. Knowl Based Syst 264:110297. https://doi.org/10.1016/j.knosys.2023.110297

Akinola E, Agushaka O (2022) A hybrid binary dwarf mongoose optimization algorithm with simulated annealing for feature selection on high dimensional multi-class datasets. Sci rep. https://doi.org/10.1038/s41598-022-18993-0

Alrahhal, Jamous (2023) AFOX: a new adaptive naturE − inspired optimization algorithm. Artif Intell Rev 56:15523–15566. https://doi.org/10.1007/s10462-023-10542-z

Alsaidy A, Sahib (2022) Heuristic initialization of PSO task scheduling algorithm in cloud computing. J King Saud University-Computer Inform Sci 34:2370–2382. https://doi.org/10.1016/j.jksuci.2020.11.002

Attiya A, Elaziz, Abualigah N, Abd El-Latif (2022) An Improved Hybrid Swarm Intelligence for Scheduling IoT Application tasks in the Cloud. IEEE Trans Industr Inf 18:6264–6272. https://doi.org/10.1109/tii.2022.3148288

Bäck, Schwefel (1993) An overview of evolutionary algorithms for parameter optimization. Evolution Comput 1:1–23. https://doi.org/10.1162/evco.1993.1.1.1

Balaji P, Chidambaram K (2022) Cancer diagnosis of microscopic biopsy images using a social spider optimisation-tuned neural network. Diagnostics. https://doi.org/10.3390/diagnostics12010011

Belegundu AD, Arora JS (1985a) A study of mathematical programming methods for structural optimization. Part I: theory. Int J Numer Methods Eng 21:1583–1599. https://doi.org/10.1002/nme.1620210904

Belegundu AD, Arora JS (1985b) A study of mathematical programmingmethods for structural optimization. Part II: Numerical results. Int J Numerical Methods Eng 21:1601–1623. https://doi.org/10.1002/nme.1620210905

Biswas S, Saha D, De S, Cobb AD, Das S, Jalaian BA (2021) Improving Differential Evolution through Bayesian Hyperparameter Optimization. IEEE Congress on Evolutionary Computation (CEC). IEEE, New York, pp 832–840. https://doi.org/10.1109/cec45853.2021.9504792

Chapter Google Scholar

Bujok P, Kolenovsky P (2022) Eigen crossover in cooperative model of evolutionary algorithms applied to CEC 2022 single objective numerical optimisation. 2022 IEEE Congress on Evolutionary Computation (CEC). IEEE, Padua, pp 1–8. https://doi.org/10.1109/cec55065.2022.9870433

Chen Y, Wang L, Liu G, Xia B (2022) Automatic parking path optimization based on immune moth flame algorithm for intelligent vehicles. Symmetry. https://doi.org/10.3390/sym14091923

Cheng MY, Sholeh MN (2023) Optical microscope algorithm: a new metaheuristic inspired by microscope magnification for solving engineering optimization problems. Knowl Based Syst 279:110939. https://doi.org/10.1016/j.knosys.2023.110939

Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J. https://doi.org/10.2514/3.10834

Deng, Liu (2023a) A multi-strategy improved slime mould algorithm for global optimization and engineering design problems. Comput Methods Appl Mech Eng 404:115764. https://doi.org/10.1016/j.cma.2022.115764

Deng L, Liu S (2023b) Snow ablation optimizer: A novel metaheuristic technique for numerical optimization and engineering design. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2023.120069

Derrac, Garcia M, Herrera (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1:3–18. https://doi.org/10.1016/j.swevo.2011.02.002

Dronen NO, Tkach VV (2014) Key to the species of Morishitium Wienberg, 1928 (Cyclocoelidae), with the description of a new species from the red-billed blue magpie, Urocissa erythrorhyncha (Boddaert) (Corvidae) from Guizhou Province, people’s Republic of China. Zootaxa 3835:273–282. https://doi.org/10.11646/zootaxa.3835.2.7

El-kenawy ES, Khodadadi N, Mirjalili S, Abdelhamid AA, Eid MM, Ibrahim A (2024) Greylag goose optimization: naturE − inspired optimization algorithm. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2023.122147

Ezugwu A, Abualigah M, Gandomi (2022) Prairie Dog optimization Algorithm. Neural Comput Appl 34:20017–20065. https://doi.org/10.1007/s00521-022-07530-9

Fan H, Li, Han H, Huang (2021) Beetle antenna strategy based grey wolf optimization. Expert Syst Appl 165:113882. https://doi.org/10.1016/j.eswa.2020.113882

Fan Q, Huang H, Yang K, Zhang S, Xiong S et al (2021b) A modified equilibrium optimizer using opposition-based learning and novel update rules. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2021.114575

Fan, Huang, Chen, Yao Y, Huang (2022) A modified self-adaptive marine predators algorithm: framework and engineering applications. Engineering with Computers 38:3269–3294. https://doi.org/10.1007/s00366-021-01319-5

Fontes H, Goncalves (2023) A hybrid particle swarm optimization and simulated annealing algorithm for the job shop scheduling problem with transport resources. Eur J Oper Res 306:1140–1157. https://doi.org/10.1016/j.ejor.2022.09.006

Fu S, Xu, Shao (2022) Research on Gas Outburst Prediction Model based on multiple Strategy Fusion Improved Snake optimization algorithm with temporal Convolutional Network. IEEE Access 10:117973–117984. https://doi.org/10.1109/access.2022.3220765

Fu H, Ma, Wei L, Fu (2023) Improved dwarf mongoose optimization algorithm using novel nonlinear control and exploration strategies. Expert Syst Appl 233:120904. https://doi.org/10.1016/j.eswa.2023.120904

Gonga, Parizi (2022) GWMA: the parallel implementation of woodpecker mating algorithm on the GPU. J Chin Inst Eng 45:556–568. https://doi.org/10.1080/02533839.2022.2078418

Gugan G, Haque A (2023) Path planning for autonomous drones: challenges and future directions. Drones. https://doi.org/10.3390/drones7030169

Guo W, Hu Z, Lin B, Kuang Y, Cao H, Wang C (2022) Nest site selection and breeding ecology of the red-billed blue magpie Urocissa erythrorhyncha in central China. Animal Biology 72:153–164. https://doi.org/10.1163/15707563-bja10076

Gupta, Nanda (2022) Objective reduction in many-objective optimization with social spider algorithm for cloud detection in satellite images. Soft Comput 26:2935–2958. https://doi.org/10.1007/s00500-021-06655-8

Hashim FA, Hussien AG (2022) Snake Optimizer: A novel meta-heuristic optimization algorithm. KnowledgE − Based Syst. https://doi.org/10.1016/j.knosys.2022.108320

He J, Wang (2022) A novel grey wolf optimizer and its applications in 5G frequency selection surface design. Front Inform Technol Electron Eng 23:1338–1353. https://doi.org/10.1631/fitee.2100580

He P, Wu W (2023) Levy flight-improved grey wolf optimizer algorithm-based support vector regression model for dam deformation prediction. Front Earth Sci. https://doi.org/10.3389/feart.2023.1122937

Holland (1992) Genetic algorithms. Sci Am 267:66–73. https://doi.org/10.1038/scientificamerican0792-66

Hou G, Du W et al (2022) Improved Grey Wolf Optimization Algorithm and Application. Sensors. https://doi.org/10.3390/s22103810

Huo W, Ren (2022) Improved artificial bee colony algorithm and its application in image threshold segmentation. Multimedia Tools Appl 81:2189–2212. https://doi.org/10.1007/s11042-021-11644-y

Jain T, Neelakandan P, Natrayan (2022) Metaheuristic optimization-based resource allocation technique for Cybertwin-Driven 6G on IoE Environment. IEEE Trans Industr Inf 18:4884–4892. https://doi.org/10.1109/tii.2021.3138915

Jayabarathi R, Sanjay, Jha M, Cherukuri (2022) Hybrid Grey Wolf Optimizer Based Optimal Capacitor Placement in Radial distribution systems. Electr Power Compon Syst 50:413–425. https://doi.org/10.1080/15325008.2022.2132556

Jia R, Wen, Mirjalili (2023) Crayfish optimization algorithm. Artif Intell Rev. https://doi.org/10.1007/s10462-023-10567-4

Karaboga, Basturk (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8:687–697. https://doi.org/10.1016/j.asoc.2007.05.007

Karimzadeh Parizi K, Khatibi Bardsiri (2021) Woodpecker Mating Algorithm for Optimal Economic Load Dispatch in a power system with conventional generators. Int J Industrial Electron Control Optim 4:221–234. https://doi.org/10.22111/ieco.2020.35116.1296

Kennedy J, Eberhart R (1995) Particle swarm optimization. In Proceedings of ICNN’95 - International Conference on Neural Networks (Vol. 4, pp. 1942–1948 vol.1944). https://doi.org/10.1109/ICNN.1995.488968

Kirkpatrick G Jr, Vecchi (1983) Optimization by simulated annealing. Science 220:671–680. https://doi.org/10.1126/science.220.4598.671

Kumar M, Singh, Ieee (2017) Improving the local search capability of Effective Butterfly Optimizer using Covariance Matrix Adapted Retreat phase. In IEEE Congress on Evolutionary Computation (CEC) (pp. 1835–1842). Spain

Kumar W, Ali, Mallipeddi S, Das (2020) A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm Evol Comput 56:100693. https://doi.org/10.1016/j.swevo.2020.100693

Kuppusamy P, Kumari NM, Rashid M et al (2022) Job scheduling problem in fog-cloud-based environment using reinforced social spider optimization. J Cloud Comput Adv Syst Appl. https://doi.org/10.1186/s13677-022-00380-9

Li (2015) A social spider algorithm for global optimization. Appl Soft Comput 30:614–627. https://doi.org/10.1016/j.asoc.2015.02.014

Li Y, Tang B, Xue X et al (2022) A Denoising Method for Ship-Radiated Noise Based on Optimized Variational Mode Decomposition with Snake Optimization and Dual-Threshold Criteria of Correlation Coefficient. Math Prob Eng. https://doi.org/10.1155/2022/8024753

Li H, Fu, Ma F, Zhu (2023) A multi-strategy enhanced northern goshawk optimization algorithm for global optimization and engineering design problems. Comput Methods Appl Mech Eng 415:116199. https://doi.org/10.1016/j.cma.2023.116199

Liang Q, Suganthan (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization

Liang Z, Zhang X, Yin (2023) Improved social spider algorithm for partial disassembly line balancing problem considering the energy consumption involved in tool switching. Int J Prod Res 61:2250–2266. https://doi.org/10.1080/00207543.2022.2069059

Liu L, Song G (2022) The prediction of sports economic development prospect in different regions by improved artificial bee colony algorithm. Discret Dyn Nat Soc. https://doi.org/10.1155/2022/7720250

Long X, Jin T et al (2022) Dynamic Self-Learning Artificial Bee Colony Optimization Algorithm for Flexible Job-Shop Scheduling Problem with Job Insertion. Processes. https://doi.org/10.3390/pr10030571

Ma C, Huang H, Fan Q, Wei J, Du Y, Gao W (2022) Grey wolf optimizer based on Aquila exploration method. Expert Syst Appl 205. https://doi.org/10.1016/j.eswa.2022.117629

Madge (2020) Red-billed BluE − Magpie (Urocissa erythroryncha), version 1.0. In Birds of the World (J. del Hoyo, A. Elliott, J. Sargatal, D. A. Christie, and E. de Juana, Editors). Cornell Lab of Ornithology, Ithaca, NY, USA. https://doi.org/10.2173/bow.rbbmag.01

Mahmoudi A, Jlassi I, Cardoso AJ, Yahia L (2022) Model free predictive current control based on a grey wolf optimizer for synchronous reluctance motors. Electronics. https://doi.org/10.3390/electronics11244166

Minh HL, Sang-To T, Wahab MA, Cuong-Le T (2022) A new metaheuristic optimization based on K-means clustering algorithm and its application to structural damage identification. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2022.109189

Mirjalili (2015) Moth-flame optimization algorithm: a novel naturE − inspired heuristic paradigm. Knowl Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf Optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

Mohamed H, Fattouh, Jambi (2017) LSHADE with semi-parameter adaptation hybrid with CMA-ES for solving CEC 2017 benchmark problems. In 2017 IEEE Congress on Evolutionary Computation (CEC) (pp. 145–152). https://doi.org/10.1109/CEC.2017.7969307

Nadimi-Shahraki MH, Zamani H, Mirjalili S (2022) Enhanced whale optimization algorithm for medical feature selection: A COVID-19 case study. Comput Biol Med. https://doi.org/10.1016/j.compbiomed.2022.105858

Nadimi-Shahraki MH, Zamani H (2022) Diversity-maintained multi-trial vector differential evolution algorithm for non-decomposition largE − scale global optimization. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2022.116895

Nadimi-Shahraki MH, Varzaneh Z, Zamani H, Mirjalili S (2023) Binary starling murmuration optimizer algorithm to select effective features from medical data. Appl Sci. https://doi.org/10.3390/app13010564

Nelson DR, Beard DB et al (2007) Vector Field path following for Miniature Air vehicles. IEEE Trans Robot 23:519–529. https://doi.org/10.1109/TRO.2007.898976

Parizi KM, Keynia F, Bardsiri KA (2020) Woodpecker mating algorithm (WMA): a naturE − inspired algorithm for solving optimization problems. Int J Nonlinear Anal Appl 11:137–157. https://doi.org/10.22075/IJNAA.2020.4245

Parizi K, Bardsiri (2021a) HSCWMA: a New Hybrid SCA-WMA Algorithm for solving optimization problems. Int J Inform Technol Decis Mak 20:775–808. https://doi.org/10.1142/s0219622021500176

Parizi K, Bardsiri (2021b) OWMA: an improved self-regulatory woodpecker mating algorithm using opposition-based learning and allocation of local memory for solving optimization problems. J Intell Fuzzy Syst 40:919–946. https://doi.org/10.3233/jifs-201075

Pashaei, Pashaei (2022) An efficient binary chimp optimization algorithm for feature selection in biomedical data classification. Neural Comput Appl 34:6427–6451. https://doi.org/10.1007/s00521-021-06775-0

Patel JL, Rana PB, Lalwani DI (2020) Optimization of five stage cantilever beam design and three stage heat exchanger design using amended differential evolution algorithm. Mater Today 26:1977–1981

Google Scholar

Pozna P, Horváth, Petriu (2022) Hybrid particle filter–particle swarm optimization algorithm and application to fuzzy controlled Servo systems. IEEE Trans Fuzzy Syst 30:4286–4297. https://doi.org/10.1109/TFUZZ.2022.3146986

Prabhakar, Rao M, Chigurukota (2024) Exponential gannet firefly optimization algorithm enabled deep learning for diabetic retinopathy detection. Biomed Signal Process Control. https://doi.org/10.1016/j.bspc.2023.105376

Rao S, Vakharia (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43:303–315. https://doi.org/10.1016/j.cad.2010.12.015

Rizk-Allah, El-Fergany G, Kotb (2023) Characterization of electrical 1-phase transformer parameters with guaranteed hotspot temperature and aging using an improved dwarf mongoose optimizer. Neural Comput Appl. https://doi.org/10.1007/s00521-023-08449-5

Roberge V, Tarbouchi M, Labonte G (2013) Comparison of parallel genetic algorithm and particle swarm optimization for real-time UAV path planning. IEEE Trans Industr Inf 9:132–141. https://doi.org/10.1109/TII.2012.2198665

Said E, Bechikh C Coello, Said (2023) Discretization-based feature selection as a Bilevel optimization Problem. IEEE Trans Evol Comput 27:893–907. https://doi.org/10.1109/tevc.2022.3192113

Seyyedabbasi, Kiani (2023) Sand cat swarm optimization: a naturE − inspired algorithm to solve global optimization problems. Engineering with Computers 39:2627–2651. https://doi.org/10.1007/s00366-022-01604-x

Shankar D, Chakraborty D, Kumar (2022) A modified social spider algorithm for an efficient data dissemination in VANET. Environ Dev Sustain. https://doi.org/10.1007/s10668-021-01994-w

Smith (2000) Swarm intelligence: from natural to artificial systems. IEEE Trans Evolutionary Comput 4:192–193. https://doi.org/10.1109/TEVC.2000.850661

Su D, Liu (2021) A hybrid parallel Harris hawks optimization algorithm for reusable launch vehicle reentry trajectory optimization with no-fly zones (Sept, 10.1007/s00500-021-06039-y, 2021). Soft Comput 25:14967–14968. https://doi.org/10.1007/s00500-021-06287-y

Talapula R, Kumar, Kumar (2023) SAR-BSO meta-heuristic hybridization for feature selection and classification using DBNover stream data. Artif Intell Rev 56:14327–14365. https://doi.org/10.1007/s10462-023-10494-4

Tian L, Lv (2024) Snow Geese Algorithm: a novel migration-inspired meta-heuristic algorithm for constrained engineering optimization problems. Appl Math Model 126:327–347. https://doi.org/10.1016/j.apm.2023.10.045

Wang W, Ye C, Tian J (2023) SGGTSO: A Spherical Vector-Based Optimization Algorithm for 3D UAV Path Planning. Drones. https://doi.org/10.3390/drones7070452

Wang J, Gao S, Kim (2018) A PSO based Energy Efficient Coverage Control Algorithm for Wireless Sensor Networks. CMC-Computers Mater Continua 56:433–446. https://doi.org/10.3970/cmc.2018.04132

Wei H, Yao H, Fan, Huang (2020) New imbalanced fault diagnosis framework based on Cluster-MWMOTE and MFO-optimized LS-SVM using limited and complex bearing data. Eng Appl Artif Intell 96:103966. https://doi.org/10.1016/j.engappai.2020.103966

Wolpert, Macready (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. https://doi.org/10.1109/4235.585893

Wu M, Suganthan (2016) Problem definitions and evaluation criteria for the CEC 2017 competition and special session on constrained single objective real-parameter optimization

Wu Y, Ma X, Liu X et al (2023) Co-evolutionary algorithm-based multi-unmanned aerial vehicle cooperative path planning. Drones. https://doi.org/10.3390/drones7100606

Wu, Xu Z, Wu (2023) Global and local moth-flame optimization algorithm for UAV formation path planning under multi-constraints. Int J Control Autom Syst 21:1032–1047. https://doi.org/10.1007/s12555-020-0979-3

Xue, Shen (2023) Dung beetle optimizer: a new meta-heuristic algorithm for global optimization. J Supercomputing 79:7305–7336. https://doi.org/10.1007/s11227-022-04959-6

Yao W, Huang M, Du (2022) Clustering of typical wind power scenarios based on K-Means Clustering Algorithm and Improved Artificial Bee colony algorithm. IEEE Access 10:98752–98760. https://doi.org/10.1109/access.2022.3203695

Zhang J, Li H, Parizi MK (2023a) HWMWOA: a hybrid WMA-WOA algorithm with adaptive Cauchy mutation for global optimization and data classification. Int J Inform Technol Decis Mak 22:1195–1252. https://doi.org/10.1142/s0219622022500675

Zhang X, Ren Y, Zhen G, Shan Y, Chu C et al (2023b) A color image contrast enhancement method based on improved PSO. PLOS ONE. https://doi.org/10.1371/journal.pone.0274054

Zhong C, Meng Z et al (2022) Beluga whale optimization: A novel naturE − inspired metaheuristic algorithm. Knowl Based Syst 251:109215. https://doi.org/10.1016/j.knosys.2022.109215

Zhong M, Wen J, Ma J, Cui H, Zhang Q, Parizi MK (2023) A hierarchical multi-leadership sine cosine algorithm to dissolving global optimization and data classification: The COVID-19 case study. Comput Biol Med. https://doi.org/10.1016/j.compbiomed.2023.107212

Zhou Y, He X et al (2022) A Neighborhood Regression optimization algorithm for computationally expensive optimization problems. IEEE Trans Cybernetics 52:3018–3031. https://doi.org/10.1109/TCYB.2020.3020727

Zhu F, Li G, Tang H, Li Y, Lv X, Wang X et al (2024) Dung beetle optimization algorithm based on quantum computing and multi-strategy fusion for solving engineering problems. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2023.121219

Download references

This work was supported by the National Natural Science Foundation of China (52165063), the Science and Technology Foundation of Guizhou Province (Qiankehe pingtai rencai-GCC [2022] No.006 − 1), the Guizhou Provincial Key Technology R&D Program (Qiankehe support normal [2023] No.348 and No.309, Qiankehe support normal [2022] No.165 and No.008), the Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX1600).

Author information

Authors and affiliations.

Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang, 550025, Guizhou, China

Shengwei Fu, Ke Li, Haisong Huang, Chi Ma, Qingsong Fan & Yunwei Zhu

Institute of Automotive Engineers, Hubei University of Automotive Technology, Shiyan, 442002, China

Qingsong Fan

Guizhou Equipment Manufacturing Digital Workshop Modeling and Simulation Engineering Research Center, Guiyang, 550025, Guizhou, China

Shengwei Fu, Ke Li, Haisong Huang, Chi Ma & Yunwei Zhu

Information Engineering Institute, Chongqing Vocational and Technical University of Mechatronics, Chongqing, 402760, China

Haisong Huang

You can also search for this author in PubMed Google Scholar

Contributions

S.F: Conceptualization, Methodology, Writing–original draft, Formal analysis, Data curation, Writing–review & editing, Software. K.L: Visualization, Formal analysis, Writing–review & editing. H.H: Conceptualization, Resources, Supervision, Formal analysis. C.M: Software, Writing–review & editing, Resources. Q.F: Methodology, Visualization Resources, Software. Y.Z: Software, Supervision, Resources.

Corresponding author

Correspondence to Haisong Huang .

Ethics declarations

Competing interests.

The authors declare that they have no conflict of interest. The authors have no relevant financial or non-financial interests to disclose.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

This article does not contain any studies with human participants. So informed consent is not applicable here.

Additional information

Publisher’s note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Fu, S., Li, K., Huang, H. et al. Red-billed blue magpie optimizer: a novel metaheuristic algorithm for 2D/3D UAV path planning and engineering design problems. Artif Intell Rev 57 , 134 (2024). https://doi.org/10.1007/s10462-024-10716-3

Download citation

Accepted : 31 January 2024

Published : 03 May 2024

DOI : https://doi.org/10.1007/s10462-024-10716-3

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Artificial intelligence
Red-billed blue magpie optimizer
2D and 3D UAV path planning
NP-hard problems
Numerical optimization
Engineering design problems
Find a journal
Publish with us
Track your research

Help | Advanced Search

Computer Science > Artificial Intelligence

Title: instance-conditioned adaptation for large-scale generalization of neural combinatorial optimization.

Abstract: The neural combinatorial optimization (NCO) approach has shown great potential for solving routing problems without the requirement of expert knowledge. However, existing constructive NCO methods cannot directly solve large-scale instances, which significantly limits their application prospects. To address these crucial shortcomings, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) for better large-scale generalization of neural combinatorial optimization. In particular, we design a powerful yet lightweight instance-conditioned adaptation module for the NCO model to generate better solutions for instances across different scales. In addition, we develop an efficient three-stage reinforcement learning-based training scheme that enables the model to learn cross-scale features without any labeled optimal solution. Experimental results show that our proposed method is capable of obtaining excellent results with a very fast inference time in solving Traveling Salesman Problems (TSPs) and Capacitated Vehicle Routing Problems (CVRPs) across different scales. To the best of our knowledge, our model achieves state-of-the-art performance among all RL-based constructive methods for TSP and CVRP with up to 1,000 nodes.

Submission history

Access paper:.

HTML (experimental)
Other Formats

References & Citations

Google Scholar
Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

IMAGES

(PDF) ARTIFICIAL INTELLIGENCE PROBLEM SOLVING AND SEARCH
Problem Solving Techniques in Artificial Intelligence (AI)
Problem Solving Agents in Artificial Intelligence
Artificial Intelligence PDF (Tutorial & Study Notes)
Solving Problems by Searching: Artificial Intelligence
Depth Limited Search-Artificial Intelligence-Unit-1-Problem Solving-Uninformed Searching Strategies

VIDEO

Searching for solutions in Artificial Intelligence
AI is dangerous for humans OR Useful for humans #ai #video #viral #educational #educationalvideo
Resolution Principle in Artificial Intelligence || Explained in Hindi || Part -1 || Study Fever
Artificial Intelligence : Search Methods For Problem solving week-5 solution #nptel2023 #nptel
Lecture 13: Constraint Satisfaction Problem (CSP)
AI for Ecology, Biodiversity, and Conservation

COMMENTS

PDF AI Handbook
A. Overview In Artificial Intelligence the terms problem solving and search refer to a large body of core ideas that deal with deduction, inference, planning, commonsense reasoning, theorem proving, and related processes. Applications ofthese general ideas are found inprograms for natural language understanding, information retrieval, automatic programming,robotics, scene analysis, game ...
PDF Chapter 3 Solving problems by searching
CS461 Artificial Intelligence © Pinar Duygulu Spring 2008 3 Outline • Problem-solving agents • Problem types • Problem formulation • Example problems
PDF Fundamentals of Artificial Intelligence Chapter 03: Problem Solving as
2Problem formulation: deﬁne arepresentation for states deﬁnelegal actionsandtransition functions. 3Search: ﬁnd a solution by means of asearch process. solutions aresequences of actions. 4Execution: given the solution, perform the actions =)Problem-solving agentsare (a kind of)goal-based agents. 4/96.
(PDF) Search In Artificial Intelligence Problem Solving
Abstract. In this paper, search methods/ techniques in problem solving using artificial intelligence (A.I) are surveyed. An overview of the definitions, dimensions and development of A.I in the ...
PDF Problem solving and search
Tree search algorithms Basic idea: o ine, simulated exploration of state space by generating successors of already-explored states (a.k.a. expanding states) function Tree-Search(problem,strategy) returns a solution, or failure initialize the search tree using the initial state of problem loop do if there are no candidates for expansion then ...
PDF Artificial Intelligence V03: Problem solving through search
Zurich University of Applied Sciences and Arts InIT Institute of Applied Information Technology (stdm) 6 Suitable agent structure If the task is represented as a graph of atomic states, and the solution is a sequence of state changes a model based agent may solve it by searching function Simple-Problem-Solving-Agent(percept) returns an action
PDF Problem Solving and Search
6.825 Techniques in Artificial Intelligence Problem Solving and Search Problem Solving • Agent knows world dynamics [learning] • World state is finite, small enough to enumerate [logic] • World is deterministic • Utility for a sequence of states is a sum over path • Agent knows current state Relaxation of assumptions later in the course
(PDF) Problem solving using artificial intelligence techniques
This paper reviews the area of problem solving in the field of Artificial Intelligence. This includes problem representation for computation, "weak" methods of searching for a problems solution ...
(PDF) Autonomous Intelligence in Problem-Solving by Searching in the
Searching techniques in problem-solving by using artificial intelligence (A.I) are surveyed in this paper. An overview of definitions, development and dimensions of A.I in the light of search for ...
PDF PROBLEM SOLVING AND SEARCH IN ARTIFICIAL INTELLIGENCE
Artiﬁcial Intelligence, Computational Logic PROBLEM SOLVING AND SEARCH IN ARTIFICIAL INTELLIGENCE Lecture 5 Answer-Set Programming: Motivation and Introduction slides adapted from Torsten Schaub [Gebser et al.(2012)] ... ASP allows for solving all search problems in NP (and NPNP)
(PDF) Search Strategies for Artificial Intelligence Problem Solving and
Problem-solving strategies in Artificial Intelligence are steps to overcome the barriers to achieve a goal, the "problem-solving cycle". Most common steps in such cycle involve- recognizing a problem, defining it, developing a strategy in order to fix it, organizing knowledge and resources available, monitoring progress, and evaluating the effectiveness of the solution.
Chapter 3 Solving Problems by Searching
3.3 Search Algorithms. A search algorithm takes a search problem as input and returns a solution, or an indication of failure. We consider algorithms that superimpose a search tree over the state-space graph, forming various paths from the initial state, trying to find a path that reaches a goal state.
Lecture Notes
Lecture 1: What is Artificial Intelligence (AI)? Lecture 2: Problem Solving and Search . Lecture 3: Logic . Lecture 4.: Satisfiability and Validity (PDF - 1.2 MB) Lecture 5.: First-Order Logic . Lecture 7.: Resolution Theorem Proving: Propositional Logic . Lecture 8.: Resolution Theorem Proving: First Order Logic
PDF Cs 380: Artificial Intelligence Problem Solving
Problem Formulation • Initial state: S 0 • Initial configuration of the problem (e.g. starting position in a maze) • Actions: A • The different ways in which the agent can change the state (e.g. moving to an adjacent position in the maze) • Goal condition: G • A function that determines whether a state reached by a given sequence of actions constitutes a solution to the problem or not.
Artificial Intelligence: Session 3 Problem Solving Agent and searching
Problem-solving strategies in Artificial Intelligence are steps to overcome the barriers to achieve a goal, the "problem-solving cycle". Most common steps in such cycle involve- recognizing a problem, defining it, developing a strategy in order to fix it, organizing knowledge and resources available, monitoring progress, and evaluating the effectiveness of the solution.
(PDF) AI 03 Solving Problems by Searching
• A search algorithm takes a problem as input and returns a solution in form of an action sequence. Zell: Artificial Intelligence (after Russel/Norvig, 3rd Ed.) 3 Simple Problem-Solving Agent Zell: Artificial Intelligence (after Russel/Norvig, 3rd Ed.) 4 2 3.2 Example Problem: Romania Tour • On holiday in Romania; currently in Arad.
Solving Problems by Searching: Artificial Intelligence
Solving Problems by Searching: Artificial Intelligence | PDF | Abstraction | Applied Mathematics. 2020 CS300 Lecture03 P1 ProblemSolvingBySearching - Free download as PDF File (.pdf), Text File (.txt) or view presentation slides online.
Analysis of Searching Algorithms in Solving Modern Engineering Problems
Many current engineering problems have been solved using artificial intelligence search algorithms. To conduct this research, we selected certain key algorithms that have served as the foundation for many other algorithms present today. This article exhibits and discusses the practical applications of A*, Breadth-First Search, Greedy, and Depth-First Search algorithms. We looked at several ...
[PDF] Problem-solving methods in artificial intelligence
A problem-solving framework in which aspects of mathematical decision theory are incorporated into symbolic problem-resolution techniques currently predominant in artificial intelligence is described, illustrated by application to the classic monkey and bananas problem. Expand. 135. PDF.
Artificial intelligence : structures and strategies for complex problem
Artificial intelligence, Knowledge representation (Information theory), Problem solving, Prolog (Computer program language), LISP (Computer program language), Intelligence artificielle, Représentation des connaissances, Résolution de problème, Prolog (Langage de programmation), LISP (Langage de programmation), Kunstmatige intelligentie ...
PDF Problem-solving Approach in Artificial Intelligence Problems
Problem-solving agent The problem-solving agent perfoms precisely by defining problems and its several solutions. • According to psychology, "a problem-solving refers to a state where we wish to reach to a definite goal from a present state or condition." • According to computer science, a problem-solving is a part of artificial ...
(PDF) Combining Human and Artificial Intelligence: Hybrid Problem
Organizations increasingly use artificial intelligence (AI) to solve previously unexplored. problems. While routine tasks can be automated, the intricate nature of exploratory tasks, such as ...
[2404.18766] PECC: Problem Extraction and Coding Challenges
View PDF HTML (experimental) Abstract: Recent advancements in large language models (LLMs) have showcased their exceptional abilities across various tasks, such as code generation, problem-solving and reasoning. Existing benchmarks evaluate tasks in isolation, yet the extent to which LLMs can understand prose-style tasks, identify the underlying problems, and then generate appropriate code ...
ARTIFICIAL INTELLIGENCE PROBLEM SOLVING AND SEARCH
Searching techniques in problem-solving by using artificial intelligence (A.I) are surveyed in this paper. An overview of definitions, development and dimensions of A.I in the light of search for solutions to problems are accepted. Dimensions as well as relevance of search in A.I research is reviewed. A classification of searching in the matter ...
AI Copilots Are Changing How Coding Is Taught
Computer science students are embracing the technology, using generative AI to help them understand complex concepts, summarize complicated research papers, brainstorm ways to solve a problem ...
GOLD: Geometry Problem Solver with Natural Language Description
View PDF Abstract: Addressing the challenge of automated geometry math problem-solving in artificial intelligence (AI) involves understanding multi-modal information and mathematics. Current methods struggle with accurately interpreting geometry diagrams, which hinders effective problem-solving. To tackle this issue, we present the Geometry problem sOlver with natural Language Description ...
Red-billed blue magpie optimizer: a novel metaheuristic ...
Numerical optimization, Unmanned Aerial Vehicle (UAV) path planning, and engineering design problems are fundamental to the development of artificial intelligence. Traditional methods show limitations in dealing with these complex nonlinear models. To address these challenges, the swarm intelligence algorithm is introduced as a metaheuristic method and effectively implemented. However ...
[2405.01906] Instance-Conditioned Adaptation for Large-scale
The neural combinatorial optimization (NCO) approach has shown great potential for solving routing problems without the requirement of expert knowledge. However, existing constructive NCO methods cannot directly solve large-scale instances, which significantly limits their application prospects. To address these crucial shortcomings, this work proposes a novel Instance-Conditioned Adaptation ...