Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
An approach to a problem in network design using genetic algorithms
An approach to a problem in network design using genetic algorithms
A network-flow technique for finding low-weight bounded-degree spanning trees
Journal of Algorithms
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A polynomial time approximation scheme for minimum routing cost spanning trees
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A weighted coding in a genetic algorithm for the degree-constrained minimum spanning tree problem
SAC '00 Proceedings of the 2000 ACM symposium on Applied computing - Volume 1
Weight-biased edge-crossover in evolutionary algorithms for two graph problems
Proceedings of the 2001 ACM symposium on Applied computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Comparison of Algorithms for the Degree Constrained Minimum Spanning Tree
Journal of Heuristics
Network random keys: a tree representation scheme for genetic and evolutionary algorithms
Evolutionary Computation
An Effective Implementation of a Direct Spanning Tree Representation in GAs
Proceedings of the EvoWorkshops on Applications of Evolutionary Computing
A Genetic Algorithm for Survivable Network Design
Proceedings of the 5th International Conference on Genetic Algorithms
Proceedings of the 6th International Conference on Genetic Algorithms
Deterministic Polylog Approximation for Minimum Communication Spanning Trees
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Redundant representations in evolutionary computation
Evolutionary Computation
Representations for Genetic and Evolutionary Algorithms
Representations for Genetic and Evolutionary Algorithms
String coding of trees with locality and heritability
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Edge sets: an effective evolutionary coding of spanning trees
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
Biased mutation operators for subgraph-selection problems
IEEE Transactions on Evolutionary Computation
The Dandelion Code: A New Coding of Spanning Trees for Genetic Algorithms
IEEE Transactions on Evolutionary Computation
Solving OCST problems with problem-specific guided local search
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Towards an understanding of locality in genetic programming
Proceedings of the 12th annual conference on Genetic and evolutionary computation
EvoGeneSys, a new evolutionary approach to graph generation
Applied Soft Computing
Graph grammars for evolutionary 3D design
Genetic Programming and Evolvable Machines
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The edge-set encoding of trees directly represents trees as sets of their edges. Nonheuristic operators for edge-sets manipulate trees' edges without regard for their weights, while heuristic operators consider edges' weights when including or excluding them. In the latter case, the operators generally favor edges with lower weights, and they tend to generate trees that resemble minimum spanning trees. This bias is strong, which suggests that evolutionary algorithms (EAs) that employ heuristic operators will succeed when optimum solutions resemble minimum spanning trees (MSTs) but fail otherwise. The one-max tree problem is a scalable test problem for trees where the optimum solution can be predefined. Heuristic operators for edge-sets fail when optimum solutions are random trees or stars. Similarly, for the optimal communication spanning tree (OCST) problem, heuristic operators are efficient only for problem instances where optimal solutions are slightly different from MSTs. In contrast, for both problems the performance of nonheuristic operators is approximately independent of the type of the optimal solution. Therefore, heuristic operators for edge-sets should be used only if optimal solutions closely resemble MSTs. If optimal solutions have low or no bias towards MSTs, heuristic operators for edgesets fail, and nonheuristic operators should be preferred.