Abstract
Multi-objective integer nonlinear programming (MOINLP) problems are multi-objective integer programming problems with at least one nonlinear objective function or constraint. To date, MOINLP problem has not been exactly solved. Although traditional ε-constraint method can be used to solve MOINLP problem, the obtained solution may not be Pareto-optimal. To overcome this shortcoming, a basic ε-constraint method (BEM) is proposed to solve MOINLP problem exactly. However, the time complexity of BEM is as high as O ( ( p − 1 ) M 2 N ) , where p, M, and N are the numbers of objectives, Pareto-optimal solutions, and feasible solutions, respectively. For this reason, an improved BEM (IBEM) is developed whose time complexity is O ( M 2 N ) . That is, the time complexity of IBEM for solving MOINLP problem is equal to solving the single-objective one. Finally, to avoid using all the feasible solutions (N) in obtaining each Pareto-optimal solution, three methods to eliminate dominated solutions effectively are used before performing IBEM. The test results illustrate that our method can not only solve MOINLP problem exactly but also has high efficiency.
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