On Using Decision Maker Preferences with ParEGO

In this paper, an interactive version of the ParEGO algorithm is introduced for identifying most preferred solutions for computationally expensive multiobjective optimization problems. It enables a decision maker to guide the search with her preferences and change them in case new insight is gained about the feasibility of the preferences. At each interaction, the decision maker is shown a subset of non-dominated solutions and she is assumed to provide her preferences in the form of preferred ranges for each objective. Internally, the algorithm samples reference points within the hyperbox defined by the preferred ranges in the objective space and uses a DACE model to approximate an achievement (scalarizing) function as a single objective to scalarize the problem. The resulting solution is then evaluated with the real objective functions and used to improve the DACE model in further iterations. The potential of the proposed algorithm is illustrated via a four-objective optimization problem related to water management with promising results.