Performance Metric Ensemble for Multiobjective Evolutionary Algorithms

Abstract

Evolutionary algorithms have been successfully exploited to solve multiobjective optimization problems. In the literature, a heuristic approach is often taken. For a chosen benchmark problem with specific problem characteristics, the performance of multiobjective evolutionary algorithms (MOEAs) is evaluated via some heuristic chosen performance metrics. The conclusion is then drawn based on statistical findings given the preferable choices of performance metrics. The conclusion, if any, is often indecisive and reveals no insight pertaining to which specific problem characteristics the underlying MOEA could perform the best. In this paper, we introduce an ensemble method to compare MOEAs by combining a number of performance metrics using double elimination tournament selection. The double elimination design allows characteristically poor performance of a quality algorithm to still be able to win it all. Experimental results show that the proposed metric ensemble can provide a more comprehensive comparison among various MOEAs than what could be obtained from a single performance metric alone. The end result is a ranking order among all chosen MOEAs, but not quantifiable measures pertaining to the underlying MOEAs.Index Terms-Double elimination design, ensemble method, evolutionary algorithms (EAs), performance metrics.

Diversity Assessment in Many-Objective Optimization

“…It is well recognized that performance indicators of MOEAs should be able to account for convergence, diversity and uniformity of the solution set [22], [54], [55]. However, MaOPs may pose serious challenges to existing performance indicators in assessing convergence, diversity and uniformity.…”

Comparison of many-objective evolutionary algorithms using performance metrics ensemble

“…Fig. 1 shows the process of performance metrics ensemble proposed by [22]. The final output from the performance metrics ensemble is a ranking order of all MOEAs considered.…”

“…The process of double elimination tournament down selects the winning front out of all approximation fronts available using a series of binary tournament selections [22]. In each tournament selection, a performance metric from metrics ensemble is randomly chosen for comparison.…”

“…1. The process of Performance Metrics Ensemble [22]. problem characteristics, including nonseparable problems, deceptive problems, a truly degenerate problem, a mixed shape Pareto front problem, problems scalable in the number of position related parameters, and problems with dependencies between positionand distance-related parameters [32].…”

“…To overcome these deficiencies and arrive at a fair evaluation of MOEAs, performance metrics ensemble with double elimination tournament [22] is used in this research work. The ensemble method uses multiple metrics collectively to obtain a better assessment than what could be obtained from any single performance metric alone.…”