Standard Error Dynamic Resampling for Preference-based Evolutionary Multi-objective Optimization

In Preference-based Evolutionary Multi-objective Optimization, the decision maker is looking for alternative solutions in a limited area of the objective space. In this area, which is of special interest to the decision maker, the goal is to find a diverse, but locally focused non-dominated front. The preference information allows to focus the optimization efforts on this most relevant part of the Pareto-front, and thereby achieve a better optimization result. Simulation-based optimization is often used to model stochastic systems, and a popular method of handling their objective noise is Dynamic Resampling. The given preference information allows for better Dynamic Resampling strategies to be defined, which further improve the optimization result. In our previous work, we proposed hybrid Dynamic Resampling strategies that base their sampling allocation on multiple resampling criteria. These criteria can be, for example, the elapsed optimization time, the Pareto-rank of a solution, or its distance to the decision maker’s area of interest. In this article, the standard error of the mean objective values of solutions is introduced as a resampling criterion for multi-objective optimization, and several variance-based, hybrid Dynamic Resampling algorithms are proposed and compared with results of non-variance-based Dynamic Resampling algorithms, presented by the authors in [20, 21, 22]. For this purpose, a multi-objective extension of the Standard Error Dynamic Resampling algorithm [11] is proposed. The new variance-based hybrid Dynamic Resampling strategies are evaluated together with the Reference point-guided NSGA-II optimization algorithm (R-NSGAII) on variants of a multi-objective benchmark function with stochastic objectives. The noise strength of these new multi-objective benchmark problems varies throughout the objective space; a function property called Noise Landscape. The algorithm performance is evaluated on noise landscapes with different types of challenges.

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