Quantifying Variable Interactions in Continuous Optimization Problems

Interactions between decision variables typically make an optimization problem challenging for an evolutionary algorithm (EA) to solve. Exploratory landscape analysis (ELA) techniques can be used to quantify the level of variable interactions in an optimization problem. However, many studies using ELA techniques to investigate interactions have been limited to combinatorial problems, with very few studies focused on continuous variables. In this paper, we propose a novel ELA measure to quantify the level of variable interactions in continuous optimization problems. We evaluated the efficacy of this measure using a suite of benchmark problems, consisting of 24 multidimensional continuous optimization functions with differing levels of variable interactions. Significantly, the results reveal that our measure is robust and can accurately identify variable interactions. We show that the solution quality found by an EA is correlated with the level of variable interaction in a given problem. Finally, we present the results from simulation experiments illustrating that when our measure is embedded into an algorithm design framework, the enhanced algorithm achieves equal or better results on the benchmark functions.