A hybrid method for solving multi-objective global optimization problems

Real optimization problems often involve not one, but multiple objectives, usually in conflict. In single-objective optimization there exists a global optimum, while in the multi-objective case no optimal solution is clearly defined but rather a set of optimums, which constitute the so called Pareto-optimal front. Thus, the goal of multi-objective strategies is to generate a set of non-dominated solutions as an approximation to this front. However, most problems of this kind cannot be solved exactly because they have very large and highly complex search spaces. The objective of this work is to compare the performance of a new hybrid method here proposed, with several well-known multi-objective evolutionary algorithms (MOEA). The main attraction of these methods is the integration of selection and diversity maintenance. Since it is very difficult to describe exactly what a good approximation is in terms of a number of criteria, the performance is quantified with adequate metrics that evaluate the proximity to the global Pareto-front. In addition, this work is also one of the few empirical studies that solves three-objective optimization problems using the concept of global Pareto-optimality.