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Optimizing a linear function over the nondominated set of multiobjective integer programs
Author(s) -
Lokman Banu
Publication year - 2021
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12627
Subject(s) - mathematical optimization , set (abstract data type) , integer (computer science) , function (biology) , linear programming , decomposition , algorithm , computer science , mathematics , feasible region , integer programming , multi objective optimization , evolutionary biology , biology , programming language , ecology
In this paper, we develop two algorithms to optimize a linear function over the nondominated set of multiobjective integer programs. The algorithms iteratively generate nondominated points and converge to the optimal solution reducing the feasible set. The first algorithm proposes improvements to an existing algorithm employing a decomposition and search procedure in finding a new point. Differently, the second algorithm maximizes one of the criteria throughout the algorithm and generates new points by setting bounds on the linear function value. The decomposition and search procedure in the algorithms is accompanied by problem‐specific mechanisms in order to explore the objective function space efficiently. The algorithms are designed to produce solutions that meet a prespecified accuracy level. We conduct experiments on multiobjective combinatorial optimization problems and show that the algorithms work well.