GoNDEF: an exact method to generate all non-dominated points of multi-objective mixed-integer linear programs
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Most real-world problems involve multiple conflicting criteria. These problems are called multi-criteria/multi-objective optimization problems (MOOP). The main task in solving MOOPs is to find the non-dominated (ND) points in the objective space or efficient solutions in the decision space. A ND point is a point in the objective space with objective function values that cannot be improved without worsening another objective function. In this paper, we present a new method that generates the set of ND points for a multi-objective mixed-integer linear program (MOMILP). The Generator of ND and Efficient Frontier (GoNDEF) for MOMILPs finds that the ND points represented as points, line segments, and facets consist of every type of ND point. First, the GoNDEF sets integer variables to the values that result in ND points. Fixing integer variables to specific values results in a multi-objective linear program (MOLP). This MOLP has its own set of ND points. A subset of this set establishes a subset of the ND points set of the MOMILP. In this paper, we present an extensive theoretical analysis of the GoNDEF and illustrate its effectiveness on a set of instance problems.
KeywordsMulti-objective optimization Mixed-integer linear programming Non-dominated point Exact method
Financial support for this work by TUPRAS under grant OS.00054 is gratefully acknowledged. MT gratefully acknowledges the computational infrastructure support provided by the IBM Corporation through the IBM SUR award. The authors acknowledge valuable comments and suggestions provided by Emre Alper Yıldırım, Emre Mengi, Seyed Mojtaba Hosseini, Ali Fattahi, Matthias Ehrgott, and referees of Optimization and Engineering journal.
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