Differential evolution for noisy multiobjective optimization

Abstract

We propose an extension of multiobjective optimization realized with the differential evolution algorithm to handle the effect of noise in objective functions. The proposed extension offers three merits with respect to its traditional counterpart. First, an adaptive selection of the sample size for the periodic fitness evaluation of a trial solution based on the fitness variance in its local neighborhood is proposed. This avoids the computational complexity associated with the unnecessary reevaluation of quality solutions without disregarding the necessary evaluations for relatively poor solutions to ensure accuracy in fitness estimates. The second strategy is concerned with determining the expected value of the noisy fitness samples on the basis of their distribution, instead of their conventional averaging, as the fitness measure of the trial solutions. Finally, a new crowding-distance-induced probabilistic selection criterion is devised to promote quality solutions from the same rank candidate pool to the next generation, ensuring the population quality and diversity in the objective spaces. Computer simulations performed on a noisy version of a well-known set of 23 benchmark functions reveal that the proposed algorithm outperforms its competitors with respect to inverted generational distance, spacing, error ratio, and hypervolume ratio metrics.

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