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Multi-objective integer programming: a general approach for generating all non-dominated solutions. (English) Zbl 1176.90554
Summary: 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.

##### MSC:
 90C29 Multi-objective and goal programming 90C10 Integer programming
##### Keywords:
multiple objective programming; integer programming
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##### References:
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