In this paper, we develop a novel evolutionary interactive method called interactive K-RVEA, which is suitable for computationally expensive problems. We use surrogate models to replace the original expensive objective functions to reduce the computation time. Typically, in interactive methods, a decision maker provides some preferences iteratively and the optimization algorithm narrows the search according to those preferences. However, working with surrogate models will introduce some inaccuracy to the preferences, and therefore, it would be desirable that the decision maker can work with the solutions that are evaluated with the original objective functions. Therefore, we propose a novel model management strategy to incorporate the decision maker’s preferences to select some of the solutions for both updating the surrogate models (to improve their accuracy) and to show them to the decision maker. Moreover, we solve a simulation-based computationally expensive optimization problem by finding an optimal configuration for an energy system of a heterogeneous business building complex. We demonstrate how a decision maker can interact with the method and how the most preferred solution is chosen. Finally, we compare our method with another interactive method, which does not have any model management strategy, and shows how our model management strategy can help the algorithm to follow the decision maker’s preferences.
Interactive methods support decision makers in finding the most preferred solution in multiobjective optimization problems. They iteratively incorporate the decision maker's preference information to find the best balance among conflicting objectives. Several interactive methods have been developed in the literature. However, choosing the most suitable interactive method for a given problem can prove challenging and appropriate indicators are needed to compare interactive methods. Some indicators exist for a priori methods, where preferences are provided at the beginning of the solution process. We present some numerical experiments that illustrate why these indicators are not suitable for interactive methods. As the main contribution of this paper, we propose a set of desirable properties of indicators for assessing interactive methods as the first step of filling a gap in the literature. We discuss each property in detail and provide simple examples to illustrate their behavior.
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