Exact algorithms for multi-objective integer non-linear programming by cutting solution space

Multi-objective integer non-linear programming (MINP) problems are ubiquitous in real life, however, only the epsilon-constraint method can be used to solve MINP problems. To improve the computation time of the epsilon-constraint method, we propose improved exact algorithms to obtain all the Pareto-optimal solutions for MINP. Our contribution is to cut most non-Pareto-optimal solutions by several specific Pareto-optimal solutions before performing epsilon-constraint method. Thus, the computation time can be significantly saved. The performance of these exact algorithms are evaluated by the general instances of the multi-objective assignment problem. The computational results show that the performance of the proposed exact algorithms are better than the epsilon-constraint method.