IJCSNS International Journal of Computer Science and Network Security, VOL.9 No.2, February 2009 4 Manuscript received February 5, 2009 Manuscript revised February 20, 2009 Evolutionary Optimized Networks and Their Properties Seung-Youp Shin † and Akira Namatame † , † Dept. of Computer Science, National Defense Academy of Japan, Kanagawa, 239-8686 Japan Summary Networks in the real world have a variety of structures and they are different in many respects. Among them, in both natural and artificial networks, they often show scale-free as the result of optimization of growth. An important feature of many complex networks is the structure and performance. Such networks with desirable properties become important in a variety of applications such as in supply chain networks, computer and transportation networks etc. In this paper we present a methodology of evolutionary design of optimized networks in which the structure of a network is designed to optimize various performance measurements. We propose a methodology in which a complex system optimizes its network structure in order to optimize its overall object function. Especially these in turn depend on two critical measures of the network performances, congestion and economy in terms of design cost. In this paper, we use the genetic algorithm (GA) as a tool of optimization. We also propose some methodologies to investigate the properties of evolved networks. The objective functions of GA are the combination of the congestion function which is defined by node betweenness and the density of links. We show that an evolutionary optimization process can account for the observed regularities displayed by most networks. Using a graph theoretical case study, we show that when design cost is paramount the Star network emerges and when congestion is important the dense network is found. When congestion and design cost requirements are both important to varying degrees, other classes of networks such as the network with multiples hubs including scale-free emerge. Four major types of networks are encountered: (a) sparse exponential-like networks, (b) sparse scale-free networks, (c) star networks and (d) highly dense networks. The evolutionary consequences of these results are outlined. Key words: Traffic network, Congestion, Optimal network, Genetic algorithm 1. Introduction One of the outstanding problems in complex adaptive systems found in engineering, biology, ecology, economics, sociology, and so on, is explaining and predicting the emergence of self-organized network structures with very interesting properties [1]. Recently, there have been attempts to propose mechanisms for the emergence of the scale-free topologies for such networks. Barábasi and Albert have suggested preferential attachment as a mechanism and these results provide valuable insights into the structure of the scale-free networks [2]. An important feature of many complex systems, both natural and artificial, is the structure and organization of their interaction networks with interesting properties. Such networks are found in a variety of applications such as in supply chain networks, computer and communication networks etc. Networks in the real world a variety of structures and they are different in many respects. However, the questions of why and how the different network configurations emerge, what is the significance of these different topologies, why do we find similar topologies in diverse applications, and what, if any, is the common underlying governing principle remain to be investigated further. We propose a general conceptual framework for self- organization of a network by evolutionary adaptation, modeled after Darwin, in which the system’s, i.e. the network’s (We use these terms interchangeably in this paper), objective is to maximize its chances of overall survival by adapting its configuration according to the environmental pressure. The basic premise is that networks found in nature today exhibit certain characteristic configurations and properties because the same helped them survive the test of time and natural selection. A network typically serves to transport material, energy, and/or information; thus the idea of survival, in all the discussion to follow, is a general one to mean performance towards achieving the design objectives of the network. Therefore, the novel hypothesis is that although human-engineered networks such as supply chains or communication networks have not necessarily ‘emerged’ by evolutionary adaptation, the underlying design principles that led to their creation could be very similar to those that caused natural networks to evolve to their present forms. The universality of scale-free and other features found in a variety of networks, natural or otherwise, lends support to this view. The proposed framework seeks to shed light on these principles and their guiding influence on network evolution. We will illustrate how the external environment, which imposes or demands certain survival objectives, critically determines the optimal configuration. These insights can be valuable for the study and analysis of all networks under various service environments. In this spirit, the framework applies equally to natural as well as human-engineered networks.