Automated Algorithm Selection on Continuous Black-Box Problems by Combining Exploratory Landscape Analysis and Machine Learning

Abstract

In this paper, we build upon previous work on designing informative and efficient Exploratory Landscape Analysis features for characterizing problems' landscapes and show their effectiveness in automatically constructing algorithm selection models in continuous black-box optimization problems. Focussing on algorithm performance results of the COCO platform of several years, we construct a representative set of high-performing complementary solvers and present an algorithm selection model that -compared to the portfolio's single best solver -on average requires less than half of the resources for solving a given problem. Therefore, there is a huge gain in efficiency compared to classical ensemble methods combined with an increased insight into problem characteristics and algorithm properties by using informative features. Acting on the assumption that the function set of the Black-Box Optimization Benchmark is representative enough for practical applications the model allows for selecting the best suited optimization algorithm within the considered set for unseen problems prior to the optimization itself based on a small sample of function evaluations. Note that such a sample can even be reused for the initial population of an evolutionary (optimization) algorithm so that even the feature costs become negligible.

Expressiveness and robustness of landscape features

“…When facing a new optimization problem to solve, insights on its characteristics can be leveraged to select a well-performing algorithm and a suitable instantiation of its parameters [4,8]. Reliable indicators that give insight on the structure of the fitness landscape are therefore at high demand.…”

Instruction-level design of local optimisers using push GP

“…There are many optimisation algorithms that can potentially be applied to a given problem, but theoretical understanding [Wolpert et al, 1997, Joyce andHerrmann, 2018] tells us that a particular optimiser will not be effective over all problems. Despite some progress [Kerschke and Trautmann, 2018], theory has not yet reached the stage where it can offer concrete guidance on which optimisers are suitable for particular problem types. This means that, in practice, it is often necessary to go through a process of trying out different optimisers to see which one is effective on a particular problem.…”

Towards dynamic algorithm selection for numerical black-box optimization

“…In theory, the instances should have very li le impact on the performance of the algorithms, as they are selected in such a way to preserve the characteristics of the functions. However, in practice there has been some debate about the impact of instances on algorithm performance, claiming that the landscapes of di erent instances of the same function can look signi cantly di erent to an algorithm [18,26,29]. In the following, we ignore this discussion and assume that performance is not signi cantly impacted by the instances.…”