An iterative error-free algorithm to solve Vandermonde systems
Applied Mathematics and Computation
Evolutionary Computation
The Density of States - A Measure of the Difficulty of Optimisation Problems
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
Computing the density of states of Boolean formulas
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Exact computation of the expectation curves for uniform crossover
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Fitness function distributions over generalized search neighborhoods in the q-ary hypercube
Evolutionary Computation
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The distribution of fitness values across a set of states sharply influences the dynamics of evolutionary processes and heuristic search in combinatorial optimization. In this paper we present a method for approximating the distribution of fitness values over Hamming regions by solving a linear programming problem that incorporates low order moments of the target function. These moments can be retrieved in polynomial time for select problems such as MAX-k-SAT using Walsh analysis. The method is applicable to any real function on binary strings that is epistatically bounded and discrete with asymptotic bounds on the cardinality of its codomain. We perform several studies on the ONE-MAX and MAX-k-SAT domains to assess the accuracy of the approximation and its dependence on various factors. We show that the approximation can accurately predict the number of states within a Hamming region that have an improving fitness value.