Permutation problems, genetic algorithms, and dynamic representations

Abstract

Permutation problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions. It is also common to see many different types of search spaces reduced to permutation problems as there are many heuristics and metaheuristics for them due to their popularity. This study incorporates the travelling salesman problem, bin packing problem, and graph colouring problem. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types of representations. The majority of the algorithms are built around the Recentering-Restarting Genetic Algorithm. The algorithm variations were effective on all problems examined although the variations between the different algorithms in this particular study were for the most part not statistically different. This observation led to the conclusion that algorithm success is dependent on problem instance; in order to fully explore the search space, one needs to study multiple algorithms for a given problem.