Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Artificial intelligence: a modern approach
Artificial intelligence: a modern approach
A tractable Walsh analysis of SAT and its implications for genetic algorithms
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Epistasis in Genetic Algorithms: An Experimental Design Perspective
Proceedings of the 6th International Conference on Genetic Algorithms
Genetic algorithms as function optimizers
Genetic algorithms as function optimizers
Efficient Linkage Discovery by Limited Probing
Evolutionary Computation
Linkage identification by non-monotonicity detection for overlapping functions
Evolutionary Computation
New entropy-based measures of gene significance and epistasis
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
A survey on chromosomal structures and operators for exploiting topological linkages of genes
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
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The interaction among variables of an optimization problem is known as epistasis, and its degree is an important measure for the nonlinearity of the problem. We address the problem of enormous time complexity for computing Davidor's epistasis variance of the traveling salesman problem (TSP). To reduce the complexity, we introduce the concept of schema-linear problem (SLP), show that TSP is a SLP, and present a relevant lemma, called Summation Rule. Using the Summation Rule, we provide a closed formula for epistasis that reduces the time complexity from O(nn) to O(n2). Additionally, we propose a new more scalable measure of epistasis by a careful derivation from the original.