O problema do Hiker Dice em tabuleiro compacto: um estudo algorítmico

Abstract

The Hiker Dice was a game recently proposed in a software designed by Mara Kuzmich and Leonardo Goldbarg. In the game a dice is responsible for building a trail on an n x m board. As the dice waits upon a cell on the board, it prints the side that touches the surface. The game shows the Hamiltonian Path Problem Simple Maximum Hiker Dice (Hidi-CHS) in trays Compact Nth , this problem is then characterized by looking for a Hamiltonian Path that maximize the sum of marked sides on the board. The research now related, models the problem through Graphs, and proposes two classes of solution algorithms. The first class, belonging to the exact algorithms, is formed by a backtracking algorithm planed with a return through logical rules and limiting the best found solution. The second class of algorithms is composed by metaheuristics type Evolutionary Computing, Local Ramdomized search and GRASP (Greed Randomized Adaptative Search). Three specific operators for the algorithms were created as follows: restructuring, recombination with two solutions and random greedy constructive.The exact algorithm was teste on 4x4 to 8x8 boards exhausting the possibility of higher computational treatment of cases due to the explosion in processing time. The heuristics algorithms were tested on 5x5 to 14x14 boards. According to the applied methodology for evaluation, the results acheived by the heuristics algorithms suggests a better performance for the GRASP algorithm