A Systematic Way of Structuring Real-World Multiobjective Optimization Problems

Abstract

In recent decades, the benefits of applying multiobjective optimization (MOO) methods in real-world applications have rapidly increased. The MOO literature mostly focuses on problem-solving, typically assuming the problem has already been correctly formulated. The necessity of verifying the MOO problem and the potential impacts of having an incorrect problem formulation on the optimization results are not emphasized enough in the literature. However, verification is crucial since the optimization results will not be meaningful without an accurate problem formulation, not to mention the resources spent in the optimization process being wasted.

In this paper, we focus on the MOO problem structuring, which we believe deserves more attention. The novel contribution is the proposed systematic way of structuring MOO problems that leverages problem structuring approaches from the literature on multiple criteria decision analysis (MCDA). They are not directly applicable to the formulation of MOO problems since the objective functions in the MOO problem depend on decision variables and constraint functions, whereas MCDA problems have a given set of solution alternatives characterized by criterion values. Therefore, we propose to elicit expert knowledge to identify decision variables and constraint functions, in addition to the objective functions, to construct a MOO problem appropriately. Our approach also enables the verification and validation of the problem before the actual decision making process.