Improved Fixed-Budget Results via Drift Analysis
This work addresses a methodological gap for researchers in theoretical computer science and optimization, though it is incremental as it adapts existing drift analysis techniques.
The paper tackled the lack of general tools in fixed-budget theory for randomized search heuristics by transferring drift theory to this perspective, resulting in more precise bounds for the LeadingOnes benchmark function than previous state-of-the-art.
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.