Evolutionary Algorithm For Multi-objective Problems Research Articles

An experimental analysis of a new two-stage crossover operator for multiobjective optimization

Evolutionary algorithms for multiobjective problems utilize three types of operations for progressing toward the higher fitness regions of the search space. Each type of operator contributes in a different way toward the achievement of the common goal. The mutation operation is responsible for diversity maintenance, while the selection operation favors the survival of the fittest. In this paper we focus our attention on the crossover operator. The crossover operator by default is responsible for the search effort and as such deserves our special attention. In particular, we propose a two-stage crossover (TSX) operator for more efficient exploration of the search space. The performance of the proposed TSX operator is assessed in comparison with the simulated binary crossover operator with the assistance of three well-known multiobjective evolutionary algorithms, namely the NSGAII, the SPEA2 and the MOCELL, for the solution of the DTLZ1---7 set of test functions. We also compare the proposed TSX with other popular reproduction operators like the differential evolution and the particle swarm optimization. Finally, we examine the efficacy of the TSX operator in handling problems having five objectives. It is shown with the assistance of the Deb, Thiele, Laumanns and Zitzler set of test functions that the TSX operator can substantially improve the results generated by three popular performance metrics for most of the cases.

Multiplicative Approximations, Optimal Hypervolume Distributions, and the Choice of the Reference Point

Many optimization problems arising in applications have to consider several objective functions at the same time. Evolutionary algorithms seem to be a very natural choice for dealing with multi-objective problems as the population of such an algorithm can be used to represent the trade-offs with respect to the given objective functions. In this paper, we contribute to the theoretical understanding of evolutionary algorithms for multi-objective problems. We consider indicator-based algorithms whose goal is to maximize the hypervolume for a given problem by distributing [Formula: see text] points on the Pareto front. To gain new theoretical insights into the behavior of hypervolume-based algorithms, we compare their optimization goal to the goal of achieving an optimal multiplicative approximation ratio. Our studies are carried out for different Pareto front shapes of bi-objective problems. For the class of linear fronts and a class of convex fronts, we prove that maximizing the hypervolume gives the best possible approximation ratio when assuming that the extreme points have to be included in both distributions of the points on the Pareto front. Furthermore, we investigate the choice of the reference point on the approximation behavior of hypervolume-based approaches and examine Pareto fronts of different shapes by numerical calculations.

Plateaus can be harder in multi-objective optimization

In recent years a lot of progress has been made in understanding the behavior of evolutionary computation methods for single- and multi-objective problems. Our aim is to analyze the diversity mechanisms that are implicitly used in evolutionary algorithms for multi-objective problems by rigorous runtime analyses. We show that, even if the population size is small, the runtime can be exponential where corresponding single-objective problems are optimized within polynomial time. To illustrate this behavior we analyze a simple plateau function in a first step and extend our result to a class of instances of the well-known SetCover problem.

PSFGA: Parallel processing and evolutionary computation for multiobjective optimisation

This paper deals with the study of the cooperation between parallel processing and evolutionary computation to obtain efficient procedures for solving multiobjective optimisation problems. We propose a new algorithm called PSFGA (parallel single front genetic algorithm), an elitist evolutionary algorithm for multiobjective problems with a clearing procedure that uses a grid in the objective space for diversity maintaining purposes. Thus, PSFGA is a parallel genetic algorithm with a structured population in the form of a set of islands. The performance analysis of PSFGA has been carried out in a cluster system and experimental results show that our parallel algorithm provides adequate results in both, the quality of the solutions found and the time to obtain them. It has been shown that its sequential version also outperforms other previously proposed sequential procedures for multiobjective optimisation in the cases studied.

PSFGA: Parallel processing and evolutionary computation for multiobjective optimisation

This paper deals with the study of the cooperation between parallel processing and evolutionary computation to obtain efficient procedures for solving multiobjective optimisation problems. We propose a new algorithm called PSFGA (parallel single front genetic algorithm), an elitist evolutionary algorithm for multiobjective problems with a clearing procedure that uses a grid in the objective space for diversity maintaining purposes. Thus, PSFGA is a parallel genetic algorithm with a structured population in the form of a set of islands. The performance analysis of PSFGA has been carried out in a cluster system and experimental results show that our parallel algorithm provides adequate results in both, the quality of the solutions found and the time to obtain them. It has been shown that its sequential version also outperforms other previously proposed sequential procedures for multiobjective optimisation in the cases studied.