Solution to the maximum independent set problem with genetic algorithm

Abstract

In this study, from the problems of graph theory to the Maximum Independent set problem belonging to NP-Hard complexity class, were searched solutions close to optimal quality by using genetic algorithms from artificial intelligence techniques. Unlike most of the studies in the literature, the initial population of the genetic algorithm has not been determined at random and has been created with various heuristic approaches. In the heuristic approaches discussed, the vertex order and sum of neighborhood vertex order sequences techniques are used and the performance ratios of both are compared. These two techniques were found to be effective against different problems, and two algorithms were combined to form a much more successful initial population. It was found experimentally on the small size problems where the merging process is done, and the big size problems were obtained. In the next step, problems which have different edge densities and with large peak numbers for computational experiments were selected from randomly generated problems used in a literature study, and these problems were solved by genetic algorithm generated by intuitive approach of the initial population, and performance ratios and resolution times were investigated.