Pareto Set Extrapolation method: an efficient solving technique for multi-objective optimization problems

Abstract

When considering techniques for producing the Pareto front of a Multi-Objective Optimization Problem (MOOP), there exists a trade-off between the effectiveness of the method in obtaining the Pareto front and the computational cost required to achieve that. For a method to be effective, the generated solutions must result in a true representation of the Pareto front. Frequently used techniques are the Genetic Algorithms (GAs). These methods are designed to be effective but are known to be computationally expensive. This is problematic when applied to also expensive MOOPs, which is often the case in engineering applications, as it makes them impractical to use. To solve expensive MOOPs, the applied method should be both effective and computational cost-efficient. Depending on its use, multiple run (MR) methods have been proven to achieve an appropriate level of effectiveness at a significantly lower computational cost compared to GAs. In this paper we present the \textit{Pareto Set Extrapolation} (PSE) method, which is a modification of the general MR technique and is designed to be more effective and cost-efficient than the existing MR method. In this first phase of its development, the approach is limited to solving constrained bi-Objective Optimization Problems (BOOPs) with a continuous P_f as its solution, but could be extended to MOOPs with relatively small effort and has possible use in solving discontinuous problems. The PSE method is proven to perform favorably over multiple test problems on both effectiveness and cost-efficiency, compared to the Non-dominated Sorting Genetic Algorithm (NSGA-II) and Normal Constraint (NC) method, representing the GAs and MR techniques, respectively.