Evolutionary Multi-Objective Optimization On the Distribution of Offspring in Parameter and Fitness Space


Many real-world optimization problems have more than one objective. Frequently, these multiple optimization criteria cannot be satisfied at the same time. Therefore, a good performance with respect to one objective might correspond to a particularly poor performance with respect to another objective. As a result the target of multi-objective optimization is a set of trade-off solutions which are not dominated by any other solutions. This set is usually called the Pareto optimal solution set of the multi-objective optimization problem. Since the target of the optimization is not a single solution but a set of solutions, evolutionary algorithms seem to be inherently suitable for this type of task due to their population based approach. Although first applications of evolutionary algorithms to multi-objective optimization were carried out in the middle of the 1980's, evolutionary multi-objective optimization has gathered much attention since the end of the 1990's. Unfortunately, the analysis of evolutionary multi-objective optimization algorithms is much harder than for their single objective counterparts. Even the evaluation of the result of the algorithm is difficult and not fully solved, many performance measures, so called performance indices, have been suggested in the literature. The dynamics of the optimization process on the three spaces, i.e., the genotype space, the parameter space (the phenotype space) and the fitness space, is far from being understood. This work contributes towards understanding the dynamics of evolutionary multi-objective optimization algorithms. Besides understanding phenomena observed in existing algorithms, the knowledge which we have gained from the theoretical analysis has directly been exploited to propose new algorithms which show better performance than the existing ones. Based on the theoretical analysis, the framework for generating benchmark problems with controlled difficulties has been proposed. Finally, different multi-objective optimization algorithms have been applied to a complex "real-world" optimization task. The main contributions of this work can be summarized as follows: (1) Analysis of dynamics of multi-objective evolutionary algorithms (2) Theoretical framework for estimating offspring distribution (3) New algorithm called "Hybrid Representation (HR)" (4) New algorithm called "Voronoi-based Estimation of Distribution Algorithm (VEDA)" (5) Framework for designing "Distribution Controlled" test functions (6) Multi-objective optimization of a micro heat exchanger Due to the population-based approach of evolutionary algorithms, their application to multi-objective optimization problems seems to be natural. Although many questions about evolutionary multi-objective optimization algorithms remain, the contribution of this work will help to improve our understanding of their dynamics and with the new proposed algorithms they might also help to gain better optimization results.