Adaptive operator probabilities in a genetic algorithm that applies three operators

The probabilities with which a genetic algorithm applies its operators have sometimes been set adaptively; information derived from the algorithm's performance has been used to revise the probabilities as the GA runs. This paper reviews one such mechanism, which assigns probabilities to crossover and mutation, and extends it to assign probabilities to three or more operators. The extension guarantees that no operator will be excluded, even if it has recently been ineffective. Several versions of the extended mechanism are tested in a steady-state GA for the rectilinear Steiner problem, in which we seek a tree of minimum length, made up of horizontal and vertical line segments, that connects a set of given points. The coding chosen for the trees gives rise to three genetic operators, a crossover and two mutations. The operator probabilities develop in interesting ways, but the algorithm itself never identifies trees shorter than those found by the same GA with fixed operator probabilities. This raises questions about how information available to a GA as it runs can be used to adjust its parameters and improve its performance. 1. I N T R O D U C T I O N The probabilities with which a genetic algorithm applies its operators have sometimes been set adaptively; information derived from the algorithm's performance has been used to revise the probabilities as the GA runs [1, 2, 9, 10]. This paper reviews and extends one such mechanism, called Adaptive Operator Probabilities (ADOPP) [7]. As originally described, ADOPP assigns operator probabilities in a steady-state GA that applies "Pcrn3ission to make digital or hard copies of part or all of this work for ~crsonal or classroom use is granted without fee provided that copies are not nade or distributed tbr profit or commercial advantage and that copies bear his notice and the full citation on the first page. Copyrights for components ffthis work owned by others than ACM must bc honored. Abstracting with ;redit is permitted. To copy otherwise, to republish, to post on servers or to -edistribute to lists, requires prior specific permission and/or a fee. " 1997 ACM 0-89791-850-9 97 0002 3.50 exactly two operators (conventionally crossover and mutation). The extension applies ADOPP to more than two operators, and it guarantees that no operator will ever be shut out. In the rectilinear Steiner problem, we seek a tree of minimum length, made up of horizontal and vertical line segments, that connects a set of given points. A particular coding of such trees gives rise in a natural way to three genetic operators, a crossover and two mutations; a GA for this problem is thus an appropriate test bed for the extended ADOPP mechanism. The GA, with several versions of ADOPP, was run repeatedly on several randomly generated problems of 50 given points. These trials revealed interesting developments of the operator probabilities, but none of the versions identified shorter trees in general than did the GA with the operator probabilities fixed at plausible values. This raises questions about the information available as a GA runs; these must be answered to make an effective ADOPP-like mechanism. In what follows, this paper (1) reviews the ADOPP mechanism and extends it to three or more operators; (2) summarizes the rectilinear Steiner problem; (3) describes a steady-state genetic algorithm for the rectilinear Steiner problem; (4) describes the performance of the GA, with several versions of ADOPP, on a test problem; and (5) discusses issues the tests raise. 2. A D A P T I V E O P E R A T O R P R O B A B I L I T I E S The ADOPP mechanism sets the probabilities with which a steady-state genetic algorithm applies its operators. ADOPP has been described for GAs that apply two operators [7, 8]. Under ADOPP, each operator's probability is always proportional to the contribution it has recently made to building chromosomes more fit than the population median; such chromosomes are called ira. proved. ADOPP updates the operator probabilities after the generation of every new chromosome, improved or not. When the GA applies an operator to build a new chromosome, the operators that created it and its