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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.

Evolutionary algorithms have been successfully applied for exploring both converged and diversified approximate Pareto-optimal fronts in multiobjective optimization problems, two-or three-objective in general. However, when solving problems with many objectives, nearly all algorithms perform poorly due to the loss of selection pressure in fitness evaluation. An extremely large objective space could inadvertently deteriorate the effect of an evolutionary operator. In this paper, we propose a new approach to directly handle the challenges to solve many-objective optimization problems. This novel design includes two stages: first, the whole population quickly approaches a small number of "target" points near the true Pareto front; then, the proposed diversity improvement strategy is applied to facilitate these individuals to spread and distribute well. As a case study, the proposed algorithm based on this design is compared with five state-of-the-art algorithms. Experimental results show that the proposed method exhibits improved performance in both convergence and diversity for solving many-objective optimization problems. IndexTerms-Objective space reduction, diversity improvement strategy, many-objective optimization problems, many-objective evolutionary algorithms 1089-778X (c)

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