The fundamental design choices in an evolutionary algorithm are its representation of candidate solutions and the operators that will act on that representation. We propose representing spanning trees in evolutionary algorithms for network design problems directly as sets of their edges, and we describe initialization, recombination, and mutation operators for this representation. The operators offer

Many graph problems seek subgraphs of minimum weight that satisfy a set of constraints. Examples include the minimum spanning tree problem (MSTP), the degree-constrained minimum spanning tree problem (d-MSTP), and the traveling salesman problem (TSP). Low-weight edges predominate in optimum solutions to such problems, and the performance of evolutionary algorithms (EAs) is often improved by biasing variation operators to favor these edges. We investigate the impact of biased edge-exchange mutation. In a large-scale empirical investigation, we study the distributions of edges in optimum solutions of the MSTP, the d-MSTP, and the TSP in terms of the edges ’ weightbased ranks. We approximate these distributions by exponential functions and derive approximately optimal probabilities for selecting edges to be incorporated into candidate solutions during mutation. A theoretical analysis of the expected running time

Many graph problems seek subgraphs of minimum weight that satisfy the problems' constraints. Examples include the degree-constrained minimum spanning tree and traveling salesman problems. Low-weight edges