PUB - Publikationen an der Universität Bielefeld

For tackling an multi-objective optimization problem (MOP), evolutionary computation (EC) gathers much attention due to its population-based approach where several solutions can be obtained simultaneously. Since genetic algorithm (GA) and evolution strategy (ES) are often used in EC, we discuss only GA and ES in this chapter. Although both of them have global and local search capability, theoretical/empirical analysis reveals that GA is rather global search and ES is rather local search on MOP. These facts are related to how to generate offspring, i.e. crossover in GA and mutation in ES. On MOP, the crossover in GA and the mutation in ES generate differently distributed offspring. If mating in the crossover is not restricted, the crossover in GA can generate new offspring globally due to combination of parents which converge different points. Oppositely, the mutation in ES can generate the similar offspring with parent, i.e. locally distributed new offspring, because the offspring is generated by adding normally distributed random values to the parent. Recently, memetic algorithm, which combines GA with local search algorithm, is popular due to its performance. Since ES on MOP works as local search, we combine GA with ES as one of memetic algorithms in this chapter. This algorithm is called as hybrid representation. Several issues caused by the combination of GA and ES are discussed, e.g. the discretization error, self-adaptation and adaptive switching. Experiments are conducted on five well-known test functions using six different performance indices. The results show that the hybrid representation exhibits better and more stable performance than the original GA/ES.