Zeros of generalized Krawtchouk polynomials
Journal of Approximation Theory
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
SIAM Review
Evolutionary Computation
On the Choice of the Mutation Probability for the (1+1) EA
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
Walsh analysis, epistasis, and optimization problem difficulty for evolutionary algorithms
Walsh analysis, epistasis, and optimization problem difficulty for evolutionary algorithms
Optimal fixed and adaptive mutation rates for the leadingones problem
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Approximating the distribution of fitness over hamming regions
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Mutation rates of the (1+1)-EA on pseudo-boolean functions of bounded epistasis
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Exact computation of the expectation curves of the bit-flip mutation using landscapes theory
Proceedings of the 13th annual conference on Genetic and evolutionary computation
A methodology to find the elementary landscape decomposition of combinatorial optimization problems
Evolutionary Computation
Local search and the local structure of NP-complete problems
Operations Research Letters
Mutation rate matters even when optimizing monotonic functions
Evolutionary Computation
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The frequency distribution of a fitness function over regions of its domain is an important quantity for understanding the behavior of algorithms that employ randomized sampling to search the function. In general, exactly characterizing this distribution is at least as hard as the search problem, since the solutions typically live in the tails of the distribution. However, in some cases it is possible to efficiently retrieve a collection of quantities called moments that describe the distribution. In this paper, we consider functions of bounded epistasis that are defined over length-n strings from a finite alphabet of cardinality q. Many problems in combinatorial optimization can be specified as search problems over functions of this type. Employing Fourier analysis of functions over finite groups, we derive an efficient method for computing the exact moments of the frequency distribution of fitness functions over Hamming regions of the q-ary hypercube. We then use this approach to derive equations that describe the expected fitness of the offspring of any point undergoing uniform mutation. The results we present provide insight into the statistical structure of the fitness function for a number of combinatorial problems. For the graph coloring problem, we apply our results to efficiently compute the average number of constraint violations that lie within a certain number of steps of any coloring. We derive an expression for the mutation rate that maximizes the expected fitness of an offspring at each fitness level. We also apply the results to the slightly more complex frequency assignment problem, a relevant application in the domain of the telecommunications industry. As with the graph coloring problem, we provide formulas for the average value of the fitness function in Hamming regions around a solution and the expectation-optimal mutation rate.