Very greedy crossover in a genetic algorithm for the traveling salesman problem
SAC '95 Proceedings of the 1995 ACM symposium on Applied computing
Weight-biased edge-crossover in evolutionary algorithms for two graph problems
Proceedings of the 2001 ACM symposium on Applied computing
A new evolutionary approach to the degree-constrained minimumspanning tree problem
IEEE Transactions on Evolutionary Computation
Seeking global edges for traveling salesman problem in multi-start search
Journal of Global Optimization
Finding pareto-optimal set by merging attractors for a bi-objective traveling salesmen problem
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
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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 predominate in optimal solutions to these problems, and the performance of evolutionary algorithms for them is often improved by biasing their operators to favor these edges. From the distributions of edges' ranks in optimal solutions to these two problems, we identify probabilities for edges that minimize the average expected time until mutation chooses them for inclusion in a solution. On instances of the degree-constrained minimum spanning tree problem, an evolutionary algorithm performs better with this operator than with alternative mutations. These results are not replicated on instances of the traveling salesman problem, where the inclusion of one edge in a tour requires the inclusion of another dependant edge.