Network design techniques using adapted genetic algorithms Mitsuo Gen a, * , Runwei Cheng a , Shumuel S. Oren b a Department of Industrial and Information Systems Engineering, Ashikaga Institute of Technology, Ashikaga 326-8558, Japan b Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA Received 29 March 2000; revised 8 November 2000; accepted 22 November 2000 Abstract In recent years we have evidenced an extensive effort in the development of computer communication networks, which have deeply integrated in human being's everyday life. One of important aspects of the network design process is the topological design problem involved in establishing a communication network. However, with the increase of the problem scale, the conventional techniques are facing the challenge to effectively and ef®ciently solve those complicated network design problems. In this article, we summarized recent research works on network design problems by using genetic algorithms GAs), including multistage process planning MPP) problem, ®xed charge transportation problem fc-TP), minimum spanning tree problem, centralized network design, local area network LAN) design and shortest path problem. All these problems are illustrated from the point of genetic representation encoding skill and the genetic operators with hybrid strategies. Large quantities of numerical experiments show the effectiveness and ef®ciency of such kind of GA-based approach. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Genetic algorithms; Network design; Multistage process planning; Minimum spanning tree; Fixed charge transportation problems; Centralized network design; Local area network design; and Bicriteria shortest path problem 1. Introduction Genetic algorithms GAs) are one of the most powerful and broadly applicable stochastic search and optimization techniques based on principles from evolution theory [19,25]. Over the past few years, the GAs community has turned much of its attention toward the optimization of network design problems [12,13]. This paper is intended as a text covering applications of GAs to some dif®cult- to-solve network design problems inherent in industrial engineering and the computer communication network [16]. 2. Adaptation of GAs GAs were ®rst created as a kind of generic and weak method featuring in a binary encoding and binary genetic operators. This approach requires a modi®cation of an original problem into an appropriate form suitable for the GAs, as shown in Fig. 1. The approach includes a mapping between potential solutions and binary representations, taking care of decoders or repair procedures, etc. For complex problems, such an approach usually fails to provide successful applications. To overcome such problems, various non-standard implementations of the GAs have been created for particular problems. As shown in Fig. 2, this approach leaves the problem unchanged and adapts the GAs by modifying the chromosome representation of a potential solution and applying appropriate genetic operators. An encoding method can be either direct or indirect. In the direct encoding method, the whole solution for a given problem is used as a chromosome. For a complex problem, however, such a method will make almost all of conventional genetic operators unusable because large amounts of offspring will be infeasible or illegal. In general, it is not a good choice to use the whole original solution of a given problem as the chromosome representation because many real problems are too complex to have a suitable implementation with a whole solution representation. On the contrary, in the indirect encoding method, just a necessary part of a solution is used in a chromosome. A decoder is then used to produce solutions. A decoder is a problem-speci®c and determining procedure to generate solutions according to chromosomes produced by GAs. With this method, the GAs will focus their search solely on the interesting part of a solution space. A third approach is to adapt both the GAs and a given problem, as shown in Fig. 3. A common feature of Advances in Engineering Software 32 2001) 731±744 0965-9978/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S0965-997801)00007-2 www.elsevier.com/locate/advengsoft * Corresponding author. Tel.: 181-284-62-065; fax: 181-284-64-1071. E-mail addresses: gen@ashitech.ac.jp M. Gen), runweicheng@hotmail.com R. Cheng), oren@ieor.berkeley.edu S.S. Oren).