The Fifteen Puzzle- A New Approach through Hybridizing Three Heuristics Methods

TL;DR

This paper introduces a hybridized heuristic approach using Bidirectional A* search with Manhattan distance, linear conflict, and walking distance heuristics to efficiently solve the Fifteen Puzzle by reducing state space exploration.

Contribution

It presents a novel hybrid heuristic method that significantly decreases the number of generated states in solving the Fifteen Puzzle, improving space efficiency and solution optimality.

Findings

Reduces the number of generated states dramatically.

Uses only 25KB storage for heuristics.

Achieves optimal or near-optimal solutions.

Abstract

Fifteen Puzzle problem is one of the most classical problems that have captivated mathematical 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 deal with this large state space, Bidirectional A* (BA*) search algorithm with three heuristics, such as Manhattan distance (MD), linear conflict (LC), and walking distance (WD) has been used to solve the Fifteen Puzzle problems. The three mentioned heuristics will be hybridized in a way that can dramatically reduce the number of generated states by the algorithm. Moreover, all those heuristics require only 25KB of storage but help the algorithm effectively reduce the number of generated states and expand fewer nodes. Our implementation of BA* search can significantly reduce the space complexity, and guarantee either optimal or near-optimal solutions.1