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Heuristics : intelligent search strategies for computer problem solving

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Heuristics: Intelligent Search Strategies for Computer Problem Solving Hardcover – Jan. 1 1753

• Language English
• Publisher Addison-Wesley
• Publication date Jan. 1 1753
• Dimensions 17.15 x 1.91 x 24.13 cm
• ISBN-10 0201055945
• ISBN-13 978-0201055948
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• Publisher ‏ : ‎ Addison-Wesley (Jan. 1 1753)
• Language ‏ : ‎ English
• ISBN-10 ‏ : ‎ 0201055945
• ISBN-13 ‏ : ‎ 978-0201055948
• Item weight ‏ : ‎ 680 g
• Dimensions ‏ : ‎ 17.15 x 1.91 x 24.13 cm
• #158 in AI Heuristic & Constrained Search
• #615 in Business Operations Research
• #624 in Operations Research (Books)

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Heuristics: Intelligent Search Strategies for Computer Problem Solving Hardcover – 1 Jan. 1984

• Print length 399 pages
• Language English
• Publisher Addison Wesley Longman Publishing Co
• Publication date 1 Jan. 1984
• Dimensions 17.15 x 1.91 x 24.13 cm
• ISBN-10 0201055945
• ISBN-13 978-0201055948
• See all details

Product details

• Publisher ‏ : ‎ Addison Wesley Longman Publishing Co (1 Jan. 1984)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 399 pages
• ISBN-10 ‏ : ‎ 0201055945
• ISBN-13 ‏ : ‎ 978-0201055948
• Dimensions ‏ : ‎ 17.15 x 1.91 x 24.13 cm
• 185,793 in Reference (Books)

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Heuristics: Intelligent Search Strategies for Computer Problem Solving Hardcover – Import, 1 January 1984

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• ISBN-10 0201055945
• ISBN-13 978-0201055948
• Publisher Addison Wesley Longman Publishing Co
• Publication date 1 January 1984
• Language English
• Dimensions 17.15 x 1.91 x 24.13 cm
• Print length 399 pages
• See all details

Product details

• Publisher ‏ : ‎ Addison Wesley Longman Publishing Co (1 January 1984)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 399 pages
• ISBN-10 ‏ : ‎ 0201055945
• ISBN-13 ‏ : ‎ 978-0201055948
• Item Weight ‏ : ‎ 680 g
• Dimensions ‏ : ‎ 17.15 x 1.91 x 24.13 cm

About the author

Judea pearl.

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Memory-bounded search ( Memory Bounded Heuristic Search ) in AI

Search algorithms are fundamental techniques in the field of artificial intelligence (AI) that let agents or systems solve challenging issues. Memory-bounded search strategies are necessary because AI systems often encounter constrained memory resources in real-world circumstances. The notion of memory-bound search, often referred to as memory-bounded heuristic search, is examined in this article along with its importance in AI applications. We will review how AI effectively manages search jobs when memory resources are limited and provide a useful how-to manual for putting memory-bound search algorithms into practice.

Table of Content

Understanding Memory-Bound Search

Benefits of memory-bound search, implementing memory-bound search, pseudocode: memory-bounded a* algorithm, implemented of memory-bounded search strategy for the 8-puzzle problem, applying memory-bound search in ai, faqs on memory-bounded search (or memory bounded heuristic search).

When memory resources are restricted, AI uses a method called memory-bound search to solve issues and make judgments quickly. Conventional search methods, such as the A* or Dijkstra’s algorithms, sometimes require infinite memory, which may not be realistic in many circumstances.

Memory-bound search algorithms, on the other hand, are created with the limitation of finite memory in mind. The goal of these algorithms is to effectively use the memory that is available while finding optimum or nearly optimal solutions. They do this by deciding which information to keep and retrieve strategically, as well as by using heuristic functions to direct the search process.

Finding a balance between the quality of the answer produced and the quantity of memory consumed is the main notion underlying memory-bound search. Even with constrained resources, these algorithms may solve problems effectively by carefully allocating memory.

• Efficiency in Memory-Limited Situations: Memory-bound search algorithms perform well when memory is limited. They don’t need a lot of memory to hold the whole search space or exploration history to locate solutions.
• Real-world Applicability: Memory-bound search algorithms are useful for a variety of AI applications, particularly those integrated into hardware with constrained memory. IoT devices, robots, autonomous cars, and real-time systems fall under this category.
• Optimal or Near-Optimal Remedies: Memory-bound search looks for the optimal answer given the memory restrictions. These algorithms may often effectively provide optimum or almost ideal answers by using well-informed heuristics.
• Dynamic Memory Management: The memory allocation and deallocation techniques used by these algorithms are dynamic. They make decisions about what data to keep and when to remove or replace it, so memory is used effectively during the search process.

The method must be carefully designed to efficiently handle the memory resources available to implement memory-bound search. Let us go through a simple Pseudocode that illustrates the main ideas of creating memory-bound search code samples.

Explanation:

The MemoryBoundedSearch function in this pseudocode accepts an issue and a memory limit as input. The nodes to be investigated and the nodes that have already been explored are stored in the open and closed lists, respectively, which are initialized. The algorithm then goes into a loop where it keeps track of whether memory use goes above the predetermined threshold. If that’s the case, memory is freed up by pruning the open and closed lists.

Based on a heuristic assessment, the select_best_node function selects the most promising node from the open list. The answer is sent back if this node is in the desired state. If not, the node is transferred from the open list to the closed list, and if its heirs have previously been investigated or are already on the open list, they are created and added to the open list.

This is an example of a straightforward memory-bounded search strategy for the 8-puzzle problem implemented in Python:

code steps:

• Node Class : Defines a class representing nodes in the search tree, with attributes state , parent , and action .
• Heuristic Function : Calculates the Manhattan distance heuristic for a given state.
• Memory Usage Function : Computes the total memory usage based on the length of the open and closed lists.
• Prune Memory Function : Prunes the least promising nodes from the open list to reduce memory usage.
• Select Best Node Function : Selects the node with the lowest heuristic value from the open list.
• Goal State Check Function : Checks if a given node’s state matches the goal state.
• Generate Successors Function : Generates successor nodes by swapping the blank space with neighboring tiles.
• Redundancy Check Function : Determines if a successor node is redundant by checking if its state is already present in either the open or closed list.
• Memory-Bounded Search Function : Performs a memory-bounded search using A* algorithm, considering memory limit.
• Goal State Definition : Defines the goal state of the puzzle.
• Possible Moves Definition : Defines the possible moves for each position on the puzzle grid.
• Example Usage : Specifies an initial state of the puzzle and sets a memory limit for the search.
• Solution Found Check : Checks if a solution node is found within the memory limit.
• Print Solution Path : If a solution is found, prints the sequence of actions and states leading from the initial state to the goal state.
• Memory Limit Exceeded Check : Prints a message if the memory limit is exceeded without finding a solution.

Memory-bound search is useful in many AI disciplines, particularly for addressing complex problems or working in resource-constrained contexts. Here are few instances:

• Robotics Pathfinding: Robots that operate in complex surroundings often possess restricted memory and processing capabilities. They can effectively identify optimum or nearly optimal courses while avoiding obstacles and achieving their objectives thanks to memory-bound search techniques.
• Autonomous Vehicles: Due to limited onboard memory, autonomous vehicles must make judgments in real time. In order to provide effective and secure navigation, memory-bound search may help with route planning, obstacle avoidance, and traffic optimization.
• Agents who Play Games: Memory-bound search algorithms may assist AI agents in determining the optimal moves in games with enormous search spaces, like Go or Chess, while taking into account the limited memory available during gaming.
• Natural Language Processing: Memory-bound search may be used for jobs when the hardware’s memory limitations are present, such as machine translation or text summarization.
• Devices with Limited Resources: Embedded systems, mobile phones, and Internet of Things devices often have little memory. Memory-bound search may let these devices work within their memory limits to complete complicated tasks like data processing or picture recognition.

AI’s memory-bound search approach is essential for effectively solving problems and making decisions when memory is scarce. Memory consumption and solution quality are balanced by these algorithms via the use of heuristic functions and smart memory management. Memory-bound search guarantees that AI can function properly even with restricted memory availability, which has useful applications in robotics, autonomous systems, and resource-constrained devices. Memory-bound search has advantages in these kinds of situations, but it also has drawbacks, such as the possibility of less-than-ideal answers and a rise in computing complexity since effective memory management is required. For certain AI applications, memory-bound search algorithms must be carefully designed taking into account the trade-offs between memory utilization and result quality. All things considered, memory-bound search increases the capacity of AI systems, increasing their versatility and adaptability in a variety of real-world situations with few memory limits.

Q. What is the process by which memory-bound search manages to explore big search spaces?

A: To direct the search toward promising regions of the search space, memory-bound search algorithms make use of informed heuristics. Even with limited memory, these heuristics enable the algorithm to efficiently concentrate its research efforts by predicting the cost or distance to the target.

Q. How does memory-bound search balance the need for memory with the quality of the solutions it finds?

A: Memory management techniques and heuristic functions are used to handle the trade-off. While memory management strategies like dynamic allocation and eviction rules guarantee that the most relevant data is kept within the memory limit, informed heuristics direct the search towards promising regions.

Q. What data structures are often used in memory-bound search implementations?

A: Commonly utilized data structures in memory-bound search are priority queues and sets. While sets effectively record visited states or nodes, priority queues assist in ranking nodes according to their heuristic values. Furthermore, g-scores and f-scores are stored in dictionaries or hash tables for constant-time lookups and changes.

Q. What are some substitute methods for AI’s memory-bound search?

A: Alternate strategies include memory-aware algorithms, which dynamically modify their behavior depending on available memory, and anytime algorithms, which provide approximation answers that become better with time. Another method is incremental heuristic search, in which answers are improved little by little as additional memory becomes available.

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With the rapid development of artificial intelligence in recent years, applying various learning techniques to solve mixed-integer linear programming (MILP) problems has emerged as a burgeoning research domain. Apart from constructing end-to-end models directly, integrating learning approaches with some modules in the traditional methods for solving MILPs is also a promising direction. The cutting plane method is one of the fundamental algorithms used in modern MILP solvers, and the selection of appropriate cuts from the candidate cuts subset is crucial for enhancing efficiency. Due to the reliance on expert knowledge and problem-specific heuristics, classical cut selection methods are not always transferable and often limit the scalability and generalizability of the cutting plane method. To provide a more efficient and generalizable strategy, we propose a reinforcement learning (RL) framework to enhance cut selection in the solving process of MILPs. Firstly, we design feature vectors to incorporate the inherent properties of MILP and computational information from the solver and represent MILP instances as bipartite graphs. Secondly, we choose the weighted metrics to approximate the proximity of feasible solutions to the convex hull and utilize the learning method to determine the weights assigned to each metric. Thirdly, a graph convolutional neural network is adopted with a self-attention mechanism to predict the value of weighting factors. Finally, we transform the cut selection process into a Markov decision process and utilize RL method to train the model. Extensive experiments are conducted based on a leading open-source MILP solver SCIP. Results on both general and specific datasets validate the effectiveness and efficiency of our proposed approach.

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Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2022YFB2403400) and National Natural Science Foundation of China (Grant Nos. 11991021 and 12021001).

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Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

Shengchao Wang, Liang Chen & Yu-Hong Dai

Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, 100190, China

Lingfeng Niu

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Wang, S., Chen, L., Niu, L. et al. Enhancing cut selection through reinforcement learning. Sci. China Math. (2024). https://doi.org/10.1007/s11425-023-2294-3

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Received : 03 August 2023

Accepted : 18 April 2024

Published : 15 May 2024

DOI : https://doi.org/10.1007/s11425-023-2294-3

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