Exact solution algorithms for biobjective mixed integer programming problems

Abstract

In this thesis, objective space based exact solution algorithms for biobjective mixed integer programming problems are proposed. The algorithms solve scalarization models in order to explore predetermined regions of the objective space called boxes, defined by two nondominated points. The initial box is defined by the two extreme nondominated points of the Pareto frontier, which includes all nondominated points. At each iteration of the algorithms, a box is explored either by a weighted sum or a Pascoletti-Serafini scalarization to determine nondominated line segments and points. The first algorithm creates new boxes immediately when it finds a nondominated point by solving Pascoletti-Serafini scalarization, whereas the second algorithm conducts additional operations after obtaining a nondominated point by this scalarization. Our computational experiments demonstrate the computational feasibility of the algorithms.