Multiobjective Bilevel Optimization: A Survey of the State-of-the-Art

Optimization makes processes, systems, or products more efficient, reliable, and with better outcomes. A popular topic on optimization today is multiobjective bilevel optimization (MOBO). In MOBO, an upper level problem is constrained by the solution of a lower level one. The problem at each level can include multiple conflicting objective functions and its own constraints. This survey aims to study the solution approaches proposed to solve MOBO problems, including exact methods and approximate techniques such as metaheuristics (MHs). This work explores classical literature to investigate why most classical methods, theories, and algorithms focus on linear and some convex MOBO problems to solve the optimistic MOBO. Moreover, we study and propose a taxonomy of MH-based frameworks for solving some MOBO instances, highlighting the pros and cons of five main approaches. Finally, a growing interest in MOBO has been detected in the optimization community. A significant number of possible applications and solution approaches establish an early research line to find solutions to these types of problems.