A study of fractional optimization with multi objective function and vanishing constraints

Abstract

Fractional optimization refers to optimization problems where the objective function involves the ratio of two functions, often representing trade-offs between different variables. These problems are commonly encountered in various scientific, engineering, and economic applications. The complexity increases when multiple conflicting objectives are involved, leading to multi-objective optimization (MOO). Furthermore, vanishing constraints-constraints that approach zero under specific conditions-pose additional challenges to optimization methods. In this paper, we conduct an in-depth study of fractional optimization problems with multi-objective functions under vanishing constraints. We explore the formulation, theoretical properties, and solution techniques for such problems. Scalarization methods, perturbation techniques, and evolutionary algorithms are evaluated for their efficacy in solving these problems. Numerical experiments and case studies highlight the practical applicability and challenges of these methods.