Multicriteria–multistage planning for the optimal path selection using hybrid genetic algorithms

Abstract

The problem of the competence set expansion involves determining the optimal expansion path under the minimum cost and time. As we know, the conventional competence set model only considers the problems of the static situation and the single objective. However, the dynamic situation and the multicriteria should also be simultaneously considered in practice. In this paper, a multicriteria and multistage competence set model is proposed. In order to efficiently obtain an optimal expansion path, hybrid genetic algorithms (HGA) are employed. In addition, a numerical example is used to demonstrate the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide a sound competence set model by simultaneously considering the multicriteria and multistage situations.

Introduction

Making good decisions involve the successive accumulation of the particular skills, ideas, information and knowledge. In order to efficiently and effectively acquire these abilities, competence set analysis was proposed [1], [2]. Using the method of searching the optimal expansion path such as the minimum spanning tree [3] or the mathematical programming [4], we can obtain the optimal expansion path (e.g. the minimum cost or time) to acquire the required competence.

In conventional competence set analysis, one criterion such as cost or benefit function is used to determine the optimal expansion path. However, in practice we usually determine the optimal expansion path by considering multicriteria (e.g. cost, time, efficient, benefit, and so on). Additionally, since the decision problems usually involve the time frame, the problem of multistage should also be considered in competence set analysis.

In order to deal with multicriteria problems, many methods such as goal programming [5], [6], min–max optimization [7], [8] and the ε—constraint method [9], [10] have been proposed. However, these methods are only suitable for simple multicriteria problems and usually fall into local optimum while dealing with complex multicriteria mathematical programming problems. On the other hand, the dynamic programming method [11] is usually employed to deal with the multistage mathematical programming problem. As we know, however, the dynamic programming method can only deal with small scaling problems for the problem of “the course of dimensionality” [12]. That is, when the network is complex, it is hard for the decision-maker to obtain the optimal solution.

Recently, evolutionary algorithms, including genetic algorithms [13], [14], [15], [16], [17], and genetic programming [18], have been widely employed to deal with the complex and large scaling problems [19], [20]. The advantage of evolutionary algorithms is its stochastic global search method to obtain the global optimum even in a complex system. In this paper, hybrid genetic algorithms (HGA) [21] are employed to deal with the multicriteria and multistage competence set problems simultaneously. In addition, a numerical example is used to illustrate the procedures of the proposed method. On the basis of the numerical example, we can conclude that the proposed method can provide a sound competence set model by simultaneously considering the multicriteria and multistage situations.

The rest of this paper is organized as follows. The basic concepts of competence set analysis are reviewed in Section 2. In Section 3, a multicriteria and multistage HGA model is presented. A numerical example, which is given to demonstrate the proposed method, is proposed in Section 4. Discussions are presented in Section 5 and conclusions are in the last section.