International Journal of Computer Theory and Engineering, Vol. 2, No. 3, June, 2010 1793-8201 459 A Novel Genetic Algorithm approach for Network Design with Robust Fitness Function 1 Abstract—This paper presents a novel genetic algorithm approach for network design with a robust fitness function which finds the best least distance network for any number of nodes. A network design problem for this paper falls under the network topology category which is a minimum spanning tree. Since many researchers have tried to solve this problem for small to mid size, we have explored the use of genetic algorithm with modification but without changing the nature of genetic algorithm. A strong fitness function is developed here for solving this network optimization problem which not only reduces the number of generation rather produces the best result and follow the concept of “Survival of the fittest”. Fitness function is the backbone of the concept of genetic algorithm which directly affects the performance; so one of the main focus of this paper is fitness function. Since this is NP problem and traditional heuristics have had only limited success in solving small to mid size problems, in this paper we have tried to show that genetic algorithm is an alternative solution for this NP problem where conventional deterministic methods are not able to provide the optimal solution. Index Terms—Genetic Algorithm, Network design, Minimum spanning tree. I. INTRODUCTION A genetic algorithm approach to design the network is one of the ultimate solutions because traditional heuristics has the limited success. Researchers in operation research have examined this problem under the broad category of ‘minimum cost flow problem’ [1]. A simple GA approach is applied by many researchers [2],[3],[4] but we have modified the genetic algorithm approach because of its uncertain nature and found the good result. Genetic Algorithms are being used extensively in optimization problem as an alternative to traditional heuristics. It is an appealing idea that the natural concepts of evolution may be borrowed for use as a computational optimization technique, which is based on the principle “Survival of the fittest” given by “Darwin”. In this paper various size of network (10 node to 100 node) is considered which is not considered by other researchers. A strong robust fitness is developed and applied which is working in all the size of network. The fitness function consists of many functions which is required according to the nature of problem. We Manuscript received October 24, 2009. Anand kumar is with AMC Engineering College, Bangalore INDIA (email : kumaranandkumar@gmail.com). Dr N.N. Jani is with Kadi Sarva Vishwa yidyalya, Gandhinagar INDIA. (e-mail: drnnjanicsd@gmail.com). have tried to show that the impact of robust fitness function and the little variation in genetic algorithm approach is very effective. A. Network Design In this paper, network design is considered as a network topology which is a spanning tree, consists of various nodes and these nodes are represented as vertex. A tree is a connected graph containing no cycles. A tree of a general undirected graph G = (V,E) with a node (or vertex) set V and edge set E is a connected subgraph T = (V’,E’) containing no cycles with (n-1) edges where n is total no of node. In this study undirected networks are considered with the weight (distance) associated with each node. For a given connected, undirected graph G with n nodes, a minimum spanning tree T is a sub graph of a G that connects all of G’s nodes and contains no cycles [5]. When every edge (i, j) is associated with a distance cij , a minimum spanning tree is a spanning tree of the smallest possible total edge cost C = c ij (1) Where (i, j). ∈ T B. Genetic Algorithm Genetic algorithms (GA) is a powerful, robust search and optimization tool, which work on the natural concept of evolution, based on natural genetics and natural selection.. The simple genetic algorithm has following steps: Simple Genetic Algorithm { initialize population; evaluate population; While TerminationCriteriaNotSatisfied { Select parents for reproduction; Perform recombination and mutation; Evaluate population; } } This is traditional approach of Genetic algorithm, where evaluation is performed after the initialization of population. The next step is the selection of child population on the basis of fitness and application of genetic operators. Genetic algorithm is very uncertain also. It may be possible that the initial parent population has the best result and after so many generation we could not find the better result as it has been found before. At the same time application of genetic Anand Kumar and Dr. N. N. Jani, Member IAENG