Artificial Intelligence: Search

The use of a policy and a heuristic function for guiding search can be quite effective in adversarial problems, as demonstrated by AlphaGo and its successors, which are based on the PUCT search algorithm. While PUCT can also be used to solve single-agent deterministic problems, it lacks guarantees on its search effort and it can be computationally inefficient in practice. Combining the A* algorithm with a learned heuristic function tends to work better in these domains, but A* and its variants do not use a policy. Moreover, the purpose of using A* is to find solutions of minimum cost, while we seek instead to minimize the search loss (e.g., the number of search steps). LevinTS is guided by a policy and provides guarantees on the number of search steps that relate to the quality of the policy, but it does not make use of a heuristic function. In this work we introduce Policy-guided Heuristic Search (PHS), a novel search algorithm that uses both a heuristic function and a policy and has theoretical guarantees on the search loss that relates to both the quality of the heuristic and of the policy. We show empirically on the sliding-tile puzzle, Sokoban, and a puzzle from the commercial game `The Witness' that PHS enables the rapid learning of both a policy and a heuristic function and compares favorably with A*, Weighted A*, Greedy Best-First Search, LevinTS, and PUCT in terms of number of problems solved and search time in all three domains tested.

Chapter 4 - Intelligent graph search basics

Generative models for grid-based and image-based pathfinding

Comparing heuristics has been a major issue from the early days of heuristic search. From the very beginning, measures of the accuracy of heuristic functions were strongly based on the number of nodes generated, and they are often still based on it. In this work, an alternative approach is suggested: to model the accuracy of admissible heuristic functions as the probability of the heuristic hill-climbing search algorithm to find the goal state in a number of steps that equals the heuristic value of an arbitrary node. The resulting method serves to assess on the accuracy of both consistent and inconsistent heuristic functions. Comparisons with different sizes of the sliding-tile puzzle show that the model suggested predicts the accuracy of the heuristic function with a good precision. The resulting procedure is used to derive figures on the accuracy of a large number of heuristics for the 15-Puzzle with different variants of the search algorithm IDA?.

Traveling Salesman Problem (TSP) is a classic NP-hard problem in Combinatorial Optimization (CO), which has been widely studied. Traveling Officer Problem (TOP) derived from illegal parking in urban areas is a variant of TSP. Its solution aims to capture as many illegally parked vehicles as possible in a limited time. However, traditional methods of solving TSP cannot be applied to TOP because the illegally parked vehicle may leave before the officer arrives. Existing methods to solve TOP include heuristic search and deep learning algorithms such as ant colony optimization and feed-forward neural network. However, the performance based on capture rate and traveling distance of these algorithms is still comparably low. Hence, in this paper, we propose the heterogeneous pointer network to address this problem by modifying the encoder of the traditional pointer network to suit the spatial-temporal features of TOP. We conduct experiments using real-world datasets from Melbourne open data platform to show that our method achieves significant improvement and outperforms the existing algorithms based on capture rate and traveling distance.

The performance of heuristic search-based planners depends heavily on the quality of the heuristic function used to focus the search. These algorithms work fast and generate high-quality solutions, even for high-dimensional problems, as long as they are given a well-designed heuristic function. On the other hand, their performance can degrade considerably if there are large heuristic depression regions, i.e. regions in the search space where heuristic values do not correlate well with the actual cost-to-goal values. Consequently, the research in developing an efficient planner for a specific domain becomes the design of a good heuristic function. However, for many domains, it is hard to design a single heuristic function that captures all of the complexities of the problem. Furthermore, it is hard to ensure that heuristics are admissible (provide lower bounds on the cost-to-goal) and consistent, which is necessary for A* like searches to provide guarantees on completeness and bounds on sub-optimality. In this paper, we develop a novel heuristic search, called Multi-Heuristic A* (MHA*), that takes in multiple, arbitrarily inadmissible heuristic functions in addition to a single consistent heuristic, and uses all of them simultaneously to search in a way that preserves guarantees on completeness and bounds on sub-optimality. This enables the search to combine very effectively the guiding powers of different heuristic functions and simplifies dramatically the process of designing heuristic functions by a user because these functions no longer need to be admissible or consistent. We support these claims with experimental analysis on several domains ranging from inherently continuous domains such as full-body manipulation and navigation to inherently discrete domains such as the sliding tile puzzle.

The N-Queen problem is a classical combinatorial optimization and constraint satisfaction problem that involves placing N queens on an N × N chessboard such that no two queens threaten each other. Due to its exponential search space and increasing computational complexity with larger board sizes, the problem serves as an important benchmark for evaluating the efficiency of heuristic and metaheuristic optimization techniques. This study presents a comprehensive performance analysis of the Simulated Annealing (SA) optimization approach for solving the N-Queen problem across varying board dimensions. The proposed methodology models the N-Queen problem as an optimization task by defining an objective function that minimizes the number of conflicting queen pairs. Simulated Annealing is employed to iteratively explore the solution space, allowing probabilistic acceptance of suboptimal solutions to escape local minima. Key parameters, including initial temperature, cooling schedule, and termination criteria, are systematically tuned to evaluate their impact on convergence speed and solution quality. Experimental results demonstrate that the SA-based approach effectively finds valid solutions for large values of N with high success rates and reduced computational effort compared to exhaustive and deterministic methods. Performance metrics such as solution accuracy, convergence time, number of iterations, and conflict reduction rate are analyzed and discussed. The results indicate that Simulated Annealing offers a robust and scalable solution for the N-Queen problem, particularly for higher-dimensional instances where traditional methods become impractical. Overall, this study highlights the suitability of Simulated Annealing as an efficient metaheuristic for solving complex combinatorial optimization problems and provides insights into its performance characteristics when applied to the N-Queen problem.

Quantum cooperative search algorithm for 3-SAT

The paper introduces three extensions of the A* search algorithm which improve the search efficiency by relaxing the admissibility condition. 1) A* employs an admissible heuristic function but invokes quicker termination conditions while still guaranteeing that the cost of the solution found will not exceed the optimal cost by a factor greater than 1 + . 2) R¿* may employ heuristic functions which occasionally violate the admissibility condition, but guarantees that at termination the risk of missing the opportunity for further cost reduction is at most ¿. 3) R¿*,* is a speedup version of R¿*, combining the termination condition of A* with the risk-admissibility condition of R¿*. The Traveling Salesman problem was used as a test vehicle to examine the performances of the algorithms A* and R¿*. The advantages of A* are shown to be significant in difficult problems, i.e., problems requiring a large number of expansions due to the presence of many subtours of roughly equal costs. The use of R¿* is shown to produce a 4:1 reduction in search time with only a minor increase in final solution cost.

Tree search is a common technique for solving constraint satisfaction and combinatorial optimization problems. The most popular strategies are depth-first search and limited discrepancy search. Aside from pruning or ordering the children of each node, these algorithms do not adapt their search order to take advantage of information that becomes available during search, such as heuristic scores or leaf costs. We present a framework called best-leaf-first search (BLFS) that uses this additional information to estimate the cost of taking discrepancies in the search tree and then attempts to visit leaves in a best-first order. In this way, BLFS brings the idea of best-first search from shortest path problems to the areas of constraint satisfaction and combinatorial optimization. Empirical results demonstrate that this new dynamic approach results in better search performance than previous static search strategies on two very different domains: structured CSPs and the traveling salesman problem.

The performance and efficiency of A* search algorithm heavily depends on the quality of the heuristic function. Therefore, designing an optimal heuristic function becomes the primary goal of developing a search algorithm for specific domains in artificial intelligence. However, it is difficult to design a well-constructed heuristic function without careful consideration and trial-and-error, especially for complex pathfinding problems. The complexity of a heuristic function increases and becomes unmanageable to design when an increasing number of parameters are involved. Existing approaches often avoid complex heuristic function design: they either trade-off the accuracy for faster computation or taking advantage of the parallelism for better performance. The objective of this paper is to reduce the difficulty of complex heuristic function design for A* search algorithm. We aim to design an algorithm that can be automatically optimized to achieve rapid search with high accuracy and low computational cost. In this paper, we present a novel design and optimization method for a Multi-Weighted-Heuristics function (MWH) named Evolutionary Heuristic A* search (EHA*) to: (1) minimize the effort on heuristic function design via Genetic Algorithm (GA), (2) optimize the performance of A* search and its variants including but not limited to WA* and MHA*, and (3) guarantee the completeness and optimality. EHA* algorithm enables high performance searches and significantly simplifies the processing of heuristic design. We apply EHA* to multiple grid-based pathfinding benchmarks to evaluate the performance. Our experiment result shows that EHA* (1) is capable of choosing an accurate heuristic function that provides an optimal solution, (2) can identify and eliminate inefficient heuristics, (3) is able to automatically design multi-heuristics function, and (4) minimizes both the time and space complexity.

N-Queen problem is a problem which a N-Queen pawn in is place chess with n x n size. N-Queen pawn is a put in such away in chess board with under condition that the queen pawns do not attack each other. The attacking movement of N-Queen problem is similar to the way of the queen pawn attacking in chess. Commonly the queen pawn moves horizontally to left and right, forward and backward vertically and also diagonally, so there are no queen pawns in a line of horizontal, vertical and diagonal.Heuristical searching is one of the method which can be used to solve the game of N-Queen problem selectively, by giving solution of the shortest time channel efficiently in order to able the user to solve this game well, fast and relevantly. Some algorithms that use heuristic is Iterative Deepening algorithm A* (IDA*) and Branch and Bound (B&B) algorithm. The used heuristic function is by seeing the numbers of boxes which are empty and the number of queen which is not be put in board yet.The aim of making this final project to implement the solving of N-Queen problem using heuristic searching (B&B and IDA*). From this implementation could be seen that IDA* and B&B algorithm is able to give channel in solving N- Queen problem. After a repetition of test by using 19 sheet of data, it is shown the comparison of result between IDA* algorithm and B&B algorithm which IDA* algorithm result the shorter channel in solving N-Queen problem based on the node 61%, and time 41% which better than B&B algorithm.

We report for the first time on finding shortest path solutions for the travelling salesman problem (TSP) using hybrid “in materio” computation: a technique that uses search algorithms to configure materials for computation. A single-walled carbon nanotube (SWCNT) / polymer composite material deposited on a micro-electrode array is configured using static voltages so that voltage output readings determine the path order in which to visit cities in a TSP. Our initial results suggest that the hybrid computation with the SWCNT material is able to solve small instances of the TSP as efficiently as a comparable evolutionary search algorithm performing the same computation in software. Interestingly the results indicate that the hybrid system’s search performance on TSPs scales linearly rather than exponentially on these smaller instances. This exploratory work represents the first step towards building SWCNT-based electrode arrays in parallel so that they can solve much larger problems.KeywordsShort PathTravelling Salesman ProblemTravel Salesman ProblemElectrode ArraySmall InstanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We perform a comprehensive study of mappings between constraint satisfaction problems (CSPs) and propositional satisfiability (SAT). We analyse four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, we compare the impact of achieving arc-consistency on the CSP with unit propagation on the SAT problem. We then extend these results to CSP algorithms that maintain (some level of) arc-consistency during search like FC and MAC, and to the Davis-Putnam procedure (which performs unit propagation at each search node). Because of differences in the branching structure of their search, a result showing the dominance of achieving arc-consistency on the CSP over unit propagation on the SAT problem does not necessarily translate to the dominance of MAC over the Davis-Putnam procedure. These results provide insight into the relationship between propositional satisfiability and constraint satisfaction.

Heuristic search algorithm has been widely used in the fields of geographic information system, intelligent robot path planning, etc. This paper proposes a heuristic search algorithm based on artificial neural network, which is named ANN*. The architecture of the ANN* algorithm is similar to the A* algorithm, but it contains a novel heuristic function of the new design. This novel heuristic function utilizes the regression network, which is a kind of classical artificial neural network. In the ANN* algorithm, the artificial neural network is used to learn the features of massive map data and predict the path search difficulty of the map. In order to guarantee the diversity of the training data, this paper designs a random map generation framework, which is able to generate random grid maps according to the length, width and density. The experiments show that the ANN* algorithm can accomplish the task of path planning in the grid map with high quality. This paper provides a new scheme of exploring the applications of artificial neural network for heuristic search algorithm.