A Min-Max Strategy to Aid Decision Making in a Bi-Objective Discrete Optimization Problem Using an Improved Ant Colony Algorithm

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.

Optimization of Innovation and Entrepreneurship Education and Training System in Colleges and Universities Based on OpenStack Cloud Computing

“…where P busy j and P idle j represent the power usage of server j under full and no-load conditions, respectively. U cpu j represents the CPU utilization on physical node j [22]. Next, this paper analyzes the optimization problem of virtual machine initialization deployment.…”

Bi-Objective Optimization: A Pareto Method with Analytical Solutions

“…Studies in bi-objective optimization constitute a non-trivial part in multi-objective analyses. For instance, Zhou et al [1], Kukkonen and Deb [2], Pinto-Varela et al [3], Lath et al [4], Pereyra et al [5], Garg [6], Futrell et al [7], Hirpa et al [8], Liu et al [9], Wang et al [10], Cheraghalipour et al [11], Ho-Huu et al [12], Yeh [13], Liu et al [14], Nagamanjula and Pethalakshmi [15], Xu et al [16], Diao et al [17], Mohammadi et al [18], Kparib et al [19], Kparib et al [20], Gulben and Orhan [21], Zaninudin and Paputungan [22], and Stutzle and Hoos [23]. Studies proposing multi-objective optimization techniques and solution can be found in Messac [24], Das and Dennis [25], Deb [26], Messac et al [27], Messac and Mattson [28], Kim and Weck [29], Zhang and Li [30], Chinchuluun and Pardalos [31], Mueller-Gritschneder et al [32], Pereyra et al [5], Pérez-Fernández et al [33], Marler and Arora [34], Gunantara [35], Orths et al [36], Collette and Siarry [37], Ehrgott [38], Eskelinen et al [39], Fonseca and Fleming [40], Alaa et al…”