EMOSOR: Evolutionary multiple objective optimization guided by interactive stochastic ordinal regression

Abstract

We propose a family of algorithms, called EMOSOR, combining Evolutionary Multiple Objective Optimization with Stochastic Ordinal Regression. The proposed methods ask the Decision Maker (DM) to holistically compare, at regular intervals, a pair of solutions, and use the Monte Carlo simulation to construct a set of preference model instances compatible with such indirect and incomplete information. The specific variants of EMOSOR are distinguished by the following three aspects. Firstly, they make use of two different preference models, i.e., either an additive value function or a Chebyshev function. Secondly, they aggregate the acceptability indices derived from the stochastic analysis in various ways, and use thus constructed indicators or relations to sort the solutions obtained in each generation. Thirdly, they incorporate different active learning strategies for selecting pairs of solutions to be critically judged by the DM. The extensive computational experiments performed on a set of benchmark optimization problems reveal that EMOSOR is able to bias an evolutionary search towards a part of the Pareto front being the most relevant to the DM, outperforming in this regard the state-of-the-art interactive evolutionary hybrids. Moreover, we demonstrate that the performance of EMOSOR improves in case the forms of a preference model used by the method and the DM’s value system align. Furthermore, we discuss how vastly incorporation of different indicators based on the stochastic acceptability indices influences the quality of both the best constructed solution and an entire population. Finally, we demonstrate that our novel questioning strategies allow to reduce a number of interactions with the DM until a high-quality solution is constructed or, alternatively, to discover a better solution after the same number of interactions.