A new solution for solving a multi-objective integer programming problem with probabilistic multi-objective optimization

Abstract

Introduction/purpose: In this paper, a new solution for solving a multiobjective integer programming problem with probabilistic multi – objective optimization is formulated. Furthermore, discretization by means of the good lattice point and sequential optimization are employed for a successive simplifying treatment and deep optimization. Methods: In probabilistic multi – objective optimization, a new concept of preferable probability has been introduced to describe the preference degree of each performance utility of a candidate; each performance utility of a candidate contributes a partial preferable probability and the product of all partial preferable probabilities deduces the total preferable probability of a candidate; the total preferable probability thus transfers a multi-objective problem into a single-objective one. Discretization by means of the good lattice point is employed to conduct discrete sampling for a continuous objective function and sequential optimization is used to perform deep optimization. At first, the requirements of integers in the treatment could be given up so as to simply conduct above procedures. Finally, the optimal solutions of the input variables must be rounded to the nearest integers. Results: This new scheme is used to deal with two production problems, i.e., maximizing profit while minimizing pollution and determining a purchasing plan for spending as little money as possible while getting as large amount of raw materials as possible. Promising results are obtained for the above two problems from the viewpoint of the probability theory for simultaneous optimization of multiple objectives. Conclusion: This method properly considers simultaneous optimization of multiple objectives in multi-objective integer programming, which naturally reflects the essence of multi-objective programming, and opens a new way of solving multi-objective problems.

Keywords

• multi-objective optimization
• integer programming problem
• preferable probability
• discrete sampling
• sequential optimization