Author(s)

Douglas Yenwon Kparib, Stephen Boakye Twum, Douglas Kwasi Boah

Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, Navrongo, Ghana.

A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.

Optimization, Discrete, Bi-Objective, Ratio Min-Max, Network, Pareto Optimal

Kparib, D. , Twum, S. and Boah, D. (2019) A Min-Max Strategy to Aid Decision Making in a Bi-Objective Discrete Optimization Problem Using an Improved Ant Colony Algorithm. American Journal of Operations Research, 9, 161-174. doi: 10.4236/ajor.2019.94010.