Multi-objective integer programming: a general approach for generating all non-dominated solutions.

*(English)*Zbl 1176.90554Summary: We develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical \(\epsilon \)-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical \(\epsilon \)-constraint method on the bi-objective integer programming problem for the sake of completeness and comment on its efficiency. Then present our method on tri-objective integer programming problem and then extend it to the general MOIP problem with \(k\) objectives. A numerical example considering tri-objective assignment problem is also provided.

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\textit{M. Özlen} and \textit{M. Azizoğlu}, Eur. J. Oper. Res. 199, No. 1, 25--35 (2009; Zbl 1176.90554)

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