Analysing Multiobjective Optimization Using Evolutionary Path Length Correlation

Recently, a number of studies have attempted to characterize the interaction between objectives and decision variables in multiobjective problems. In this paper, we continue this line of research by focusing specifically on quantifying observable differences in the ease of optimizing extreme solutions (i.e. solutions on the limits of the Pareto front). We propose an evolutionary path length correlation (EPLC) measurement in the decision variable space that is computed by tracing the evolutionary history of solutions on the Pareto front. We draw on the length scale measure and extend the well-known fitness distance correlation to multiobjective optimization problems. Here, the overarching goal is to investigate the emergent dynamics of specific problem–algorithm combinations, rather than the characterization of the search landscape per se. We evaluate the efficacy of the EPLC using benchmark continuous multiobjective problems and combinatorial problems with controllable objective interactions and known Pareto optima. In some problems, observable differences in the convergence to extreme solutions in each objective can be captured using the EPLC. Our results go some way towards furthering our understanding of how specific algorithms traverse the landscape, given interactions between both decision variables and objectives.