Multiobjective Optimization: Solution concepts and their applications

Abstract: Multiobjective Optimization Problems (MOPs) characterize an essential class of optimization problems that involve optimizing more than one objective function simultaneously. Due to a rich history and a wide range of applications, multiobjective optimization is a research area under heavy investigation within Operations Research and Economics in the last several decades.There has been a growing interest among optimizers to analyze the nature of an approximate solution to an optimization problem. It stems from the fact that most of the optimization problems cannot be solved exactly. Due to the problem structure, there are several notions of optimality of MOPs. This talk will provide a brief exposition to different solution concepts of MOPs and their approximate counterparts. We will discuss an improved notion of approximate optimality and characterize them in details. Subsequently, we will highlight future algorithmic development for these improved solutions and conclude the talk with some applications of MOPs in real-world problems.