Abstract
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.
Highlights
A ratio min-max strategy is incorporated 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 as the criteria was solved by an improved Ant Colony System algorithm developed by the authors
Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making
Summary
Optimization is defined as a process for finding the best solution to a problem, referred to as the global optimal solution from a given set of possible (feasible). In today’s business environment, where cost of production is high coupled with a lot of competitions due to globalization, single-objective optimization problems have become less popular. Much attention has been shifted to multi-objective optimization problems. A multi-objective optimization problem has a set of objectives that are usually in competition or conflict; the appreciation of one objective results in the depreciation of the other [2]. It is very difficult or impossible to obtain a solution that is optimal for each of the objectives. The best way is to find a solution that will be adjudged the best compromise one
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