To Combine or not to Combine Graybox Crossover and Local Search?

Specialized graybox local search and crossover have been successfully combined within the framework of the so-called Drils (Deterministic recombination and iterated local search) algorithm. As for any evolutionary algorithm, the initial design framework, and the underlying high-level choices and parameters, are crucially important. The Drils algorithm is no exception, and recent enhanced variants exist in the literature. In this paper, we aim at: (i) improving the performance of the latest variants of Drils, and (ii) providing a better principled understanding of graybox search behavior and dynamics. On the basis of a preliminary analysis using Local Optima Networks of small-size NKQ-landscapes, we first highlight the difference of using local search with and without crossover. We then propose to pipeline these two techniques in a simple two-phase like iterated local search scheme which is shown to provide substantial improvements over the latest Drils+ variant for large-size NKQ-landscapes. We further report a dedicated analysis in an attempt to provide new insights into the impact of local search and crossover on the phenotype and the genotype of the local optima encountered in the search trajectory.