New Variants of Genetic Algorithms Applied to Problems of Combinatorial Optimization

Problems of Combinatorial Optimization distinguish themselves by their well-structured problem description as well as by their huge number of possible action alternatives. Especially in the area of production and operational logistics these problems frequently occur. Their advantage lies in their subjective understanding of action alternatives and their objective functions. The use of classical optimization methods for problems of combinatorial optimization often fails because of the exponentially growing computational effort. Therefore, even if they are not able to ensure a global solution, heuristic methods like Genetic Algorithms (GAs) or Evolution Strategies (ESs) are massively utilized in practice because of their significant lower computational effort. Both, GAs and ESs have a number of drawbacks that reduce their applicability to that kind of problems. During the last decades plenty of work has been investigated in order to introduce new coding standards and operators especially for Genetic Algorithms. All these approaches have one thing in common: They are rather problem specific and often they do not challenge the basic principle of Genetic Algorithms. In the present paper we take a different approach and look upon the concepts of a Standard Genetic Algorithm (SGA) as an artificial self organizing process in order to overcome some of the fundamental problems Genetic Algorithms are concerned with in almost all areas of application. With the purpose of providing concepts which make the algorithm more open for scalability on the one hand, and which fight premature convergence on the other hand, this paper presents an extension of the SGA that does not introduce any problem specific knowledge: On the basis of an Evolution-Strategy-like selective pressure handling a concept of dynamically dealing with multiple crossover operators in parallel is introduced. In contrast to contributions in the field of Genetic Algorithms that introduce new coding standards and operators for certain problems, the introduced approach should be considered as a novel heuristic appliable to multiple problems of Combinatorial Optimization using exactly the same coding standards and operators for crossover and mutation as done when treating a certain problem with a SGA. Furthermore, the corresponding Genetic Algorithm is unrestrictedly included in all of the newly proposed hybrid variants under especial parameter settings. In the present paper the new algorithm is discussed for the Traveling Salesman Problem (TSP) as a well documented instance of a multimodal combinatorial optimization problem. Even if we did not presuppose any information about the quality of the involved operators we were able to achieve results superior to the results obtained with a corresponding Genetic Algorithm for all considered benchmark problems and operators.