A Study of Fixed-Length Subset Recombination.
Kelly D. Crawford, Cory J. Hoelting, Roger L. Wainwright, Dale A. Schoenefeld · 1996
While bit-based, order-based and real-valued genetic algorithms have been wellstudied in the literature, the fixed-length subset representation has received relatively little attention. We discuss various crossover operators for this representation and the pitfalls associated with each. In particular, we explore the ratio of the subset size to the set size. This important ratio is a major contributor to the rate of convergence. 1 INTRODUCTION Given a set, S, of the integers from 1 to N inclusive, a fixed-length subset is defined to be any subset of S of cardinality n. For example, if N = 4 and n = 2, then S = f1; 2; 3; 4g, and the fixed-length subsets of size n are f1,2g, f1,3g, f1,4g, f2,3g, f2,4g, and f3,4g. A fixed-length subset problem is one where candidate solutions are represented by fixedlength subsets. There are numerous examples of fixed-length subset problems in the literature. Radcliffe (1991, 1993) described improved crossover operators for fixed-length subsets. Ra...