Evolutionary Optimized Networks and Their Properties

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: