How Far Are We From an Optimal, Adaptive DE?

TL;DR

This paper introduces a Greedy Approximate Oracle (GAO) to analyze the potential of optimal parameter adaptation in Differential Evolution (DE), comparing it with existing adaptive methods on benchmark functions to guide future improvements.

Contribution

It proposes the GAO method to approximate an optimal adaptation process and uses it to evaluate and improve existing adaptive DE mechanisms.

Findings

GAO reveals potential performance improvements in adaptive DEs.

Comparison shows current adaptive methods are below the optimal adaptation benchmark.

Insights from GAO guide future development of more effective parameter adaptation strategies.

Abstract

We consider how an (almost) optimal parameter adaptation process for an adaptive DE might behave, and compare the behavior and performance of this approximately optimal process to that of existing, adaptive mechanisms for DE. An optimal parameter adaptation process is an useful notion for analyzing the parameter adaptation methods in adaptive DE as well as other adaptive evolutionary algorithms, but it cannot be known generally. Thus, we propose a Greedy Approximate Oracle method (GAO) which approximates an optimal parameter adaptation process. We compare the behavior of GAODE, a DE algorithm with GAO, to typical adaptive DEs on six benchmark functions and the BBOB benchmarks, and show that GAO can be used to (1) explore how much room for improvement there is in the performance of the adaptive DEs, and (2) obtain hints for developing future, effective parameter adaptation methods for adaptive DEs.