Explainable Interactive Evolutionary Multiobjective Optimization

We present a new interactive procedure for evolutionary multiobjective optimization involving the decision rule preference model in the search for the best compromise solution. As usual in the interactive multiobjective optimization, preference elicitation phases alternate with optimization phases, however, in this evolutionary procedure, one preference elicitation phase falls into many iterations of the evolutionary multiobjective optimization. In the preference elicitation phase, the Decision Maker (DM) is asked to select those solutions she considers relatively good in the current population. Using the Dominance-based Rough Set Approach (DRSA) this information is represented in terms of ``if ..., then ..." decision rules which represent DM’s preferences. They are used in the next phases of the evolutionary multiobjective optimization to iteratively 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 choices. In this way, the proposed method implements the postulate of transparency and explainability expected from interactive procedures, because the DM has a chance to understand how her answers given in the preference elicitation phase are translated into guidelines for the algorithm in the optimization phase, i.e., what is the impact of the answers on newly proposed compromise solutions. This can be considered the distinctive aspect of what we define explainable multiobjective optimization evolutionary approach (XIMEA). In particular, the method proposed in this paper is called XIMEA-DRSA. From the decision psychology point of view, in line with the main results of behavioral sciences, the decision rules support the DM to construct and learn her preferences during the decision process. For its explanatory feature resulting from the conjunction of evolutionary multiobjective optimization with DRSA, the method has been called XIMEA-DRSA. The computational effectiveness of the method has been tested on both continuous and discrete multiobjective optimization problems. In the latter case, the XIMEA-DRSA method has been applied to the multiobjective knapsack problem