A hybrid approach for biobjective optimization

• Published in: Discrete optimization Vol. 28; pp. 89 - 114
• Main Authors: Stidsen, Thomas, Andersen, Kim Allan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2018
• Subjects: Biobjective optimization; Branch-and-cut algorithm; Mixed integer programming; Traveling salesman problem; Mixed integer programming; Traveling salesman problem; Biobjective optimization; Branch-and-cut algorithm
• ISSN: 1572-5286; 1873-636X
• DOI: 10.1016/j.disopt.2018.02.001

A large number of the real world planning problems which are today solved using Operations Research methods are actually multiobjective planning problems, but most of them are solved using singleobjective methods. The reason for converting, i.e. simplifying, multiobjective problems to singleobjective problems is that no standard multiobjective solvers exist and specialized algorithms need to be programmed from scratch. In this article we will present a hybrid approach, which operates both in decision space and in objective space. The approach enables massive efficient parallelization and can be used to a wide variety of biobjective Mixed Integer Programming models. We test the approach on the biobjective extension of the classic traveling salesman problem, on the standard datasets, and determine the full set of nondominated points. This has only been done once before (Florios and Mavrotas, 2014), and in our approach we do it in a fraction of the time.