Probabilistic Dominance in Robust Multi-Objective Optimization

Real-world problems often require the simultaneous optimization of multiple, often conflicting, criteria called objectives. Additionally, many of these problems carry on top a wide range of uncertainties in their fitness functions and decision variables, rendering the optimization task even more complex. Several robust optimization techniques do exist to address uncertainty in different aspects of such problems. However, they typically fail to investigate the actual uncertainty distributions while comparing candidate solutions. This paper presents a novel histogram-based approach that enables to compare candidate solutions with arbitrarily distributed uncertain objectives. The proposed comparison operator receives the uncertainty distribution of each objective of two candidate solutions to be compared, and accurately calculates the probability that one objective is greater than the other. Thereby, it enables to determine whether one solution dominates the other. We employ this comparison operator in an existing multi-objective optimization algorithm to allow for finding robust solutions to problems with uncertain objectives. We also extend a well-known multi-objective benchmark suite with various uncertainties, and integrate it together with the proposed comparison operator into an existing framework that incorporates several multi-objective optimization problems and algorithms. Our experiments show that the proposed comparison operator enables achieving better optimization quality and higher robustness compared to the state-of-the-art.