Connectedness, regularity and the success of local search in evolutionary multi-objective optimization

Local search techniques have proved to be very efficient in evolutionary multi-objective optimization (MOO). However, the reasons behind the success of local search in MOO have not yet been well discussed. This paper attempts to investigate empirically the main factors that may have contributed significantly to the success of local search in MOO. It is found that for many widely used test problems, the Pareto optimal solutions are connected both in objective space and parameter space. Besides, the Pareto-optimal solutions often distribute so regularly in parameter space that they can be defined by piecewise linear functions. By constructing an approximate model using the solutions produced by an optimizer, the quality of the non-dominated solution set can be further improved. The evolutionary dynamic weighted aggregation (EDWA) method has been adopted as a local search technique in finding Pareto-optimal solutions. Its effectiveness for MOO is demonstrated on a number of two or three objective optimization problems.