Analyzing Adaptive Parameter Landscapes in Parameter Adaptation Methods for Differential Evolution

TL;DR

This paper introduces the concept of adaptive parameter landscapes in differential evolution, providing a new way to analyze how parameter adaptation methods influence the optimization process and offering insights into their working principles.

Contribution

It proposes a novel concept of adaptive parameter landscapes and a method for analyzing them, enhancing understanding of parameter adaptation methods in differential evolution.

Findings

Insightful analysis of PAMs in DE

Identification of characteristics of adaptive parameter landscapes

Enhanced understanding of parameter adaptation effects

Abstract

Since the scale factor and the crossover rate significantly influence the performance of differential evolution (DE), parameter adaptation methods (PAMs) for the two parameters have been well studied in the DE community. Although PAMs can sufficiently improve the effectiveness of DE, PAMs are poorly understood (e.g., the working principle of PAMs). One of the difficulties in understanding PAMs comes from the unclarity of the parameter space that consists of the scale factor and the crossover rate. This paper addresses this issue by analyzing adaptive parameter landscapes in PAMs for DE. First, we propose a concept of an adaptive parameter landscape, which captures a moment in a parameter adaptation process. For each iteration, each individual in the population has its adaptive parameter landscape. Second, we propose a method of analyzing adaptive parameter landscapes using a 1-step-lookahead greedy improvement metric. Third, we examine adaptive parameter landscapes in PAMs by using the proposed method. Results provide insightful information about PAMs in DE.