Improved Fixed-Budget Results via Drift Analysis

TL;DR

This paper extends drift analysis techniques to fixed-budget optimization, providing new bounds on achievable fitness within given evaluation limits, especially improving results for the LeadingOnes benchmark.

Contribution

It introduces a novel application of drift theory to fixed-budget analysis, offering more precise bounds than previous methods.

Findings

Derived bounds on expected function value within fixed evaluation budgets.

Applied variable drift theorem to LeadingOnes, improving accuracy of results.

Provided a general framework for fixed-budget analysis using drift theory.

Abstract

Fixed-budget theory is concerned with computing or bounding the fitness value achievable by randomized search heuristics within a given budget of fitness function evaluations. Despite recent progress in fixed-budget theory, there is a lack of general tools to derive such results. We transfer drift theory, the key tool to derive expected optimization times, to the fixed-budged perspective. A first and easy-to-use statement concerned with iterating drift in so-called greed-admitting scenarios immediately translates into bounds on the expected function value. Afterwards, we consider a more general tool based on the well-known variable drift theorem. Applications of this technique to the LeadingOnes benchmark function yield statements that are more precise than the previous state of the art.