Abstract
The objective functions in multiobjective optimization problems are often non-linear, noisy, or not available in a closed form and evolutionary multiobjective optimization (EMO) algorithms have been shown to be well applicable in this case. Nowadays, for example within the scope of sustainable development, many objectives are taken into account: besides classical objectives such as cost and profit, some new objectives like energy consumption, noise levels or risks have to be considered. With more and more objectives, the number of incomparable alternatives typically increases and the complexity of these problems does not make it easy for a decision maker to formalize preferences towards a specific solution or not even towards a specific but small enough portion of the search space. Moreover, also the algorithms themselves have difficulties to find a good approximation of the entire Pareto front if the number of incomparable solutions increases and the Pareto dominance relation does not indicate a good search direction anymore. In this case, combining the decision making with the search algorithm to an interactive optimization algorithm is considered as a valuable approach. While better and better solutions are found by the optimization algorithm, the DM can specify the preferences more and more precisely while learning about the problem and the objectives' inherent tradeoffs. Such an interactive approach should profit from evaluating solutions only within the interesting regions of the search space in terms of a faster convergence towards the DM's preferred solutions. In the field of EMO, interactive optimization has only been considered recently and in comparison to the vast amount of general EMO algorithms, significantly less interactive EMO algorithms exist. Although, for example, optimization algorithms based on the weighted hypervolume indicator allow to incorporate various preference types into the search, no effort has been made to use this concept within an interactive algorithm. In this report, we propose and discuss how to combine interactive decision making and weighted hypervolume based search algorithms. We focus on a basic model where the DM is asked to pick the most desirable solution among a set. Several examples on standard test problems show the working principles and the usefulness of the interactive approach, in particular with respect to the proximity of the algorithm's population to the DM's most preferred solution.