Avoiding Redundant Restarts in Multimodal Global Optimization

TL;DR

This paper investigates the inefficiency of naive restart strategies in multimodal global optimization, quantifies the redundancy potential of benchmark functions, and proposes a repelling mechanism to improve restart efficiency.

Contribution

It introduces a method to measure redundancy potential in landscapes and proposes a repelling restart mechanism for CMA-ES to reduce wasted evaluations.

Findings

The redundancy potential varies across benchmark functions.

The repelling mechanism reduces duplicate restarts.

Improved efficiency over standard restart methods.

Abstract

Na\"ive restarts of global optimization solvers when operating on multimodal search landscapes may resemble the Coupon's Collector Problem, with a potential to waste significant function evaluations budget on revisiting the same basins of attractions. In this paper, we assess the degree to which such ``duplicate restarts'' occur on standard multimodal benchmark functions, which defines the \textit{redundancy potential} of each particular landscape. We then propose a repelling mechanism to avoid such wasted restarts with the CMA-ES and investigate its efficacy on test cases with high redundancy potential compared to the standard restart mechanism.