Efficient Linkage Discovery by Limited Probing

Abstract

This paper addresses the problem of discovering the structure of a fitness function from binary strings to the reals under the assumption of bounded epistasis. Two loci (string positions) are epistatically linked if the effect of changing the allele (value) at one locus depends on the allele at the other locus. Similarly, a group of loci are epistatically linked if the effect of changing the allele at one locus depends on the alleles at all other loci of the group. Under the assumption that the size of such groups of loci are bounded, and assuming that the function is given only as a “black box function”, this paper presents and analyzes a randomized algorithm that finds the complete epistatic structure of the function in the form of the Walsh coefficients of the function.

Convergence Theorems of Estimation of Distribution Algorithms

“…A learning method not based on statistical independence tests has been investigated by Heckendorn and Wright (2004). Earlier work has been reported by Munetomo and Goldberg (1999).…”

Upper Bounds on the Time and Space Complexity of Optimizing Additively Separable Functions

“…Two previous algorithms for linkaged iscoveryu sed the same randomized test for linkage asused in this paper [4,7], but instead ofusingb inary search restricted each instance of the test to detect linkage between a specific pair of positions i and j , resulting in a requirement 2 …”

“…Previous work has shown that additively separable problems of order k defined on strings of length M can be solved using Ο (2 k M 2 ) function evaluations [4,7] 1 , 2 . Empirical evidence as well as facetwise decompositional models suggest that sub-quadratic ( Ο (2 k M β ) for β < 2) performance is possible.…”

Computing the epistasis variance of large-scale traveling salesman problems

“…values of the variables one by one. These interactions among variables immanent in problems is called linkage [13,9] or epistasis [10,4,20].…”

“…In the approaches, the epistasis among variables are implicitly estimated and applied to the evolution of solutions. Recently, a number of approaches that attempt to detect independently optimizable linkage groups of a pseudo-Boolean function 1 have been proposed [13,9,23]. The Walsh transform, first introduced by Bethke [2] and popularized by Goldberg [7,8], is one of the classical methods for analyzing epistatic properties of a pseudo-Boolean function.…”