Multiobjective Optimization via Parametric Programming: Algorithms and Applications

In this talk we highlight the relations between multiobjective optimization, where several conflicting objectives are simultaneously optimized subject to constraints, and parametric programming that is used to solve such problems. Solution to a multiobjective problem is a set of Pareto efficient points, known in the literature as Pareto efficient surface. It turns out that using weighting or hierarchical method for solving multiobjective optimization models we can formulate them as parametric programming problems and compute their efficient solution set numerically. We present a methodology that allows tracing the Pareto efficient surface for conic linear optimization problems without discretization of the objective space and without solving the optimization problem at each discretization point. Our methodology is illustrated by financial applications from portfolio and risk management, and health care applications.

Joint work with Tamas Terlaky, Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA, Alireza Ghaffari-Hadigheh, Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran