Omega our multi ethnic genetic algorithm

Abstract

Combinatorial optimization is a branch of optimization. Its domain is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, the goal being that of nding the best possible solution. Two fundamental aims in optimization are nding algorithms characterized by both provably good run times and provably good or even optimal solution quality. When no method to nd an optimal solution, under the given constraints (of time, space etc.) is available, heuristic approaches are typically used. A metaheuristic is a heuristic method for solving a very general class of computational problems by combining user- given black-box procedures, usually heuristics themselves, in the hope of obtaining a more e cient or more robust procedure. The genetic algorithms are one of the best metaheuristic approaches to deal with optimization problems. They are a population- based search technique that uses an ever changing neighborhood structure, based on population evolution and genetic operators, to take into account di erent points in the search space. The core of the thesis is to introduce a variant of the classic GA approach, which is referred to as OMEGA (Multi Ethnic Genetic Algorithm). The main feature of this new metaheuristic is the presence of di erent populations that evolve simultaneously, and exchange genetic material with each other. We focus our attention on four di erent optimization problems de ned on graphs. Each one is iii iv proved to be NP-HARD. We analyze each problem from di erent points of view, and for each one we de ne and implement both a genetic algorithm and our OMEGA.