Explainable interactive evolutionary multiobjective optimization

We present a new approach to Interactive Evolutionary Multiobjective Optimization (IEMO) guided by a preference elicitation procedure inspired by artificial intelligence and designed in line with decision psychology. For a conflicting nature of objectives, a solution optimizing all objectives simultaneously does not exist and thus the best compromise solution is searched for. In the interactive search, preference elicitation phases alternate with optimization phases. In the IEMO procedure proposed in this paper, during the preference elicitation phase, the Decision Maker (DM) gets a sample of solutions from the current population and is asked to indicate relatively good solutions in this sample. Using the Dominance-based Rough Set Approach (DRSA), this information is summarized by "if ..., then ... " decision rules which represent DM's preferences. They are used in the next optimization phases of the IEMO to influence the crossover so as to converge towards the part of the Pareto front containing the best compromise solution. Besides guiding the search process, the decision rules can be read as arguments explaining the DM's preferences. In this way, the proposed method implements the postulate of transparency and explainability expected from interactive procedures. The DM has a chance to understand how their answers given in the preference elicitation phase are translated into guidelines for the algorithm in the optimization phase. This is a distinctive aspect of what we call eXplainable Interactive Multiobjective Evolutionary optimization Approach (XIMEA). The presented XIMEA-DRSA method implements this approach. From the viewpoint of behavioral psychology, the decision rules support the DM to construct and learn their preferences in the course of evolutionary optimization. To check the efficiency of XIMEA-DRSA, we performed several experiments on continuous as well as combinatorial test problems, assuming the existence of an artificial DM that iteratively provides its preferences according to a known value function. The results prove that XIMEA-DRSA is converging to the most interesting part of the Pareto front, similar to an evolutionary algorithm that optimizes the value function of the artificial DM and, therefore, the latter is used as a benchmark.