2023
DOI: 10.3390/computers12010011
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The Fifteen Puzzle—A New Approach through Hybridizing Three Heuristics Methods

Abstract: The Fifteen Puzzle problem is one of the most classical problems that has captivated mathematics enthusiasts for centuries. This is mainly because of the huge size of the state space with approximately 1013 states that have to be explored, and several algorithms have been applied to solve the Fifteen Puzzle instances. In this paper, to manage this large state space, the bidirectional A* (BA*) search algorithm with three heuristics, such as Manhattan distance (MD), linear conflict (LC), and walking distance (WD… Show more

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Cited by 4 publications
(3 citation statements)
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“…Several research studies by heuristic suggest that large-scale structural optimization, modified to evaluate several strategies pooled with programming techniques, can be used for quantitative appraisal in compliance with enforcement learning [104][105][106]. As a result, LPX might be used for evaluating time-scales in heuristic game problems such as A* or (BA*) search algorithms [107].…”
Section: Discussionmentioning
confidence: 99%
“…Several research studies by heuristic suggest that large-scale structural optimization, modified to evaluate several strategies pooled with programming techniques, can be used for quantitative appraisal in compliance with enforcement learning [104][105][106]. As a result, LPX might be used for evaluating time-scales in heuristic game problems such as A* or (BA*) search algorithms [107].…”
Section: Discussionmentioning
confidence: 99%
“…In computer science, it is commonly used in algorithms like the A-star search algorithm for pathfinding, where it serves as a specific heuristic function H(z) to estimate the cost of reaching a goal state. Its simplicity makes it a valuable tool for solving problems related to route planning, logistics, and optimization in grid-like settings, thereby contributing to its widespread adoption in practical applications [38][39][40].…”
Section: Manhattan Distancementioning
confidence: 99%
“…For this important perspective, some complex machine learning features, such as decision trees [71], long short-term memory [72] might be used to evaluate data. Furthermore, our data must be harmonically optimized to find a global solution in utilizing current optimization algorithms or neural network algorithms such as the colony predation algorithm (CPA) [73], learner performance-based behavioral algorithm (LPB) [74], fitness dependent optimizer (FDO) [75], heuristic optimization [76], etc. We make it clear that COVID-19, just as the financial crisis [77], influenced the IT field [78], the liquidity of entities [79], and banks [80] as well as the behavior of taxpayers [81,82].…”
Section: Limitations and Suggestions For Further Studiesmentioning
confidence: 99%