Handling expensive multiobjective optimization problems with evolutionary algorithms

Abstract

Multiobjective optimization problems (MOPs) with a large number of conflicting objectives are often encountered in industry. Moreover, these problem typically involve expensive evaluations (e.g. time consuming simulations or costly experiments), which pose an extra challenge in solving them. In this thesis, we first present a survey of different methods proposed in the literature to handle MOPs with expensive evaluations. We observed that most of the existing methods cannot be easily applied to problems with more than three objectives. Therefore, we propose a Kriging-assisted reference vector guided evolutionary algorithm (K-RVEA) for problems with at least three expensive objectives. The algorithm dynamically balances between convergence and diversity by using reference vectors and uncertainty information from the Kriging models. We demonstrate the practicality of K-RVEA with an air intake ventilation system in a tractor. The problem has three expensive objectives based on time consuming computational fluid dynamics simulations. We also emphasize the challenges of formulating a meaningful optimization problem reflecting the needs of the decision maker (DM) and connecting different pieces of simulation tools. Furthermore, we extend K-RVEA to handle constrained MOPs. We found out that infeasible solutions can play a vital role in the performance of the algorithm. In many real-world MOPs, the DM is usually interested in one or a small set of Pareto optimal solutions based on her/his preferences. Additionally, it has been noticed in practice that sometimes it is easier for the DM to identify non- preferable solutions instead of preferable ones. Therefore, we finally propose an interactive simple indicator-based evolutionary algorithm (I-SIBEA) to incorporate the DM’s preferences in the form of preferable and/or non-preferable solutions. Inspired by the involvement of the DM, we briefly introduce a version of K-RVEA to incorporate the DM’s preferences when using surrogates. By providing efficient algorithms and studies, this thesis will be helpful to practitioners in industry and increases their ability of solving complex real-world MOPs.