Designing Competent Mutation Operators via Probabilistic Model Building of Neighborhoods

TL;DR

This paper introduces a probabilistic model-based mutation operator for genetic algorithms that efficiently identifies key problem components, leading to faster and more reliable solutions for certain separable problems.

Contribution

It presents a novel mutation operator using probabilistic linkage models, improving efficiency and effectiveness over traditional methods in solving additively separable problems.

Findings

Scales as O(2^km^{1.5}) for additively separable problems

Requires fewer function evaluations than selectorecombinative algorithms

Successfully solves bounded difficulty problems with subquadratic evaluations

Abstract

This paper presents a competent selectomutative genetic algorithm (GA), that adapts linkage and solves hard problems quickly, reliably, and accurately. A probabilistic model building process is used to automatically identify key building blocks (BBs) of the search problem. The mutation operator uses the probabilistic model of linkage groups to find the best among competing building blocks. The competent selectomutative GA successfully solves additively separable problems of bounded difficulty, requiring only subquadratic number of function evaluations. The results show that for additively separable problems the probabilistic model building BB-wise mutation scales as O(2^km^{1.5}), and requires O(k^{0.5}logm) less function evaluations than its selectorecombinative counterpart, confirming theoretical results reported elsewhere (Sastry & Goldberg, 2004).