Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence
Proceedings of the 3rd International Conference on Genetic Algorithms
Epistasis in Genetic Algorithms: An Experimental Design Perspective
Proceedings of the 6th International Conference on Genetic Algorithms
Building Better Test Functions
Proceedings of the 6th International Conference on Genetic Algorithms
Genetic algorithms as function optimizers
Genetic algorithms as function optimizers
Predictive models for the breeder genetic algorithm i. continuous parameter optimization
Evolutionary Computation
Evolutionary Computation
Gene expression and scalable genetic search
Advances in evolutionary computing
Hyperplane ranking, nonlinearity and the simple genetic algorithm
Information Sciences: an International Journal - Special issue: Evolutionary computation
Walsh transforms, balanced sum theorems and partition coefficients over multary alphabets
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Gene Expression and Fast Construction of Distributed Evolutionary Representation
Evolutionary Computation
Efficient Linkage Discovery by Limited Probing
Evolutionary Computation
Properties of symmetric fitness functions
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Fluctuating crosstalk, deterministic noise, and GA scalability
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Detecting the epistatic structure of generalized embedded landscape
Genetic Programming and Evolvable Machines
Lower and upper bounds for linkage discovery
IEEE Transactions on Evolutionary Computation
Efficient linkage discovery by limited probing
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
Adapting to complexity during search in combinatorial landscapes
EvoWorkshops'03 Proceedings of the 2003 international conference on Applications of evolutionary computing
Fluctuating crosstalk as a source of deterministic noise and its effects on GA scalability
EuroGP'06 Proceedings of the 2006 international conference on Applications of Evolutionary Computing
From problems to protocols: Towards a negotiation handbook
Decision Support Systems
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Classically, epistasis is either computed exactly by Walsh coefficients or estimated by sampling. Exact computation is usually of theoretical interest since the computation typically grows exponentially with the number of bits in the domain. Given an evaluation function, epistasis also can be estimated by sampling. However this approach gives us little insight into the origin of the epistasis and is prone to sampling error. This paper presents theorems establishing the bounds of epistasis for problems that can be stated as mathematical expressions. This leads to substantial computational savings for bounding the difficulty of a problem. Furthermore, working with these theorems in a mathematical context, one can gain insight into the mathematical origins of epistasis and how a problem's epistasis might be reduced. We present several new measures for epistasis and give empirical evidence and examples to demonstrate the application of the theorems. In particular, we show that some functions display “parity” such that by picking a well-defined representation, all Walsh coefficients of either odd or even index become zero, thereby reducing the nonlinearity of the function.