On approaches for solving computationally expensive multiobjective optimization problems

Abstract

In this thesis, we consider solving computationally expensive multiobjective optimization problems that take into account the preferences of a decision maker (DM). The aim is to support the DM in identifying the most preferred solution for problems that have several conflicting objectives and when the evaluation of the candidate solutions is time consuming. This is conducted by replacing computationally expensive functions with computationally inexpensive functions, known as surrogates. First, based on a literature survey, we introduce two frameworks, i.e., a sequential and an adaptive framework, based on which surrogate-based methods are classified and compared. We then identify relevant challenges that warrant more research efforts. In order to deal with the challenges, we develop two surrogate-based methods: SURROGATE-ASF and ANOVA- MOP. As an interactive method, SURROGATE-ASF has two phases: initialization and decision-making. In the first phase, the decision space is decomposed into a finite number of hyper-boxes. For each hyper-box, a single-objective surrogate problem is built. By solving an appropriate surrogate problem in the latter phase, a solution corresponding to the preferences of the DM is obtained. Numerical results support that SURROGATE- ASF can solve problems with at most 12 decision variables, 5 objective functions and nonconvex and/or disconnected sets of Pareto optimal solutions. To solve problems with high-dimensional decision and objective spaces, we develop the ANOVA-MOP method. Based on information obtained from sensitivity analysis, a problem is decomposed into a few sub-problems with low-dimensional decision and objective spaces. These sub-problems are solved, and the solutions obtained are composed to form approximated solutions for the original problem. ANOVA-MOP can be applied either as a non-interactive or an interactive method. Finally, we discuss the potential of a new metamodeling technique, called T-splines, to be incorporated into ANOVA-MOP to solve problems including non-differentiable functions. By applying the methods developed in this thesis, we extend the applicability of interactive methods to solving computationally expensive problems.