Automated Algorithm Selection: Survey and Perspectives (1811.11597v1)

Abstract: It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems, where in most cases, no single algorithm defines the state of the art; instead, there is a set of algorithms with complementary strengths. This performance complementarity can be exploited in various ways, one of which is based on the idea of selecting, from a set of given algorithms, for each problem instance to be solved the one expected to perform best. The task of automatically selecting an algorithm from a given set is known as the per-instance algorithm selection problem and has been intensely studied over the past 15 years, leading to major improvements in the state of the art in solving a growing number of discrete combinatorial problems, including propositional satisfiability and AI planning. Per-instance algorithm selection also shows much promise for boosting performance in solving continuous and mixed discrete/continuous optimisation problems. This survey provides an overview of research in automated algorithm selection, ranging from early and seminal works to recent and promising application areas. Different from earlier work, it covers applications to discrete and continuous problems, and discusses algorithm selection in context with conceptually related approaches, such as algorithm configuration, scheduling or portfolio selection. Since informative and cheaply computable problem instance features provide the basis for effective per-instance algorithm selection systems, we also provide an overview of such features for discrete and continuous problems. Finally, we provide perspectives on future work in the area and discuss a number of open research challenges.

• The paper presents a comprehensive review of per-instance algorithm selection, highlighting performance complementarity across diverse optimization problems.
• It details effective methodologies including feature extraction and selector performance measurement, with selectors closing 25% to 96% of the VBS-SBS gap.
• The study outlines future challenges in algorithm selection, emphasizing improved feature efficiency and exploration of emerging problem domains.

Overview of Automated Algorithm Selection: Survey and Perspectives

The paper "Automated Algorithm Selection: Survey and Perspectives," authored by Kerschke, Hoos, Neumann, and Trautmann, provides a comprehensive examination of the automated algorithm selection problem. It offers an in-depth review of the field, exploring both the foundational and recent advances in algorithm selection for discrete and continuous optimization problems.

The paper begins by detailing the per-instance algorithm selection problem, a scenario common across numerous computationally challenging tasks. Here, the authors emphasize that performance complementarity is key—a concept where different algorithms excel at different problem instances, depending on their inherent characteristics. This nurtures the groundwork for algorithm selection, challenging the applicability of the no-free-lunch (NFL) theorem when well-structured problems occupy our interest domain.

The paper also differentiates well between related concepts: per-set algorithm selection, algorithm configuration, scheduling, and algorithm portfolios. The authors explicate the distinctions, similarities, and potential synergies across these domains, while reinforcing their focus on pure per-instance selection.

In highlighting the requisites for effective algorithm selection, the paper acknowledges problem instance features as fundamental. It provides detailed accounts of informative and economically computable instance features and their critical roles. For example, SAT, AI Planning, and TSP problems are discussed with an emphasis on existing feature sets and their contributions to advance selector performance.

Strong numerical results mentioned in the paper reveal that per-instance algorithm selectors have achieved substantial performance improvements. This is evidenced by reports where selectors closed between 25% and 96% of the VBS-SBS gap, offering significant case studies in problems like SAT and TSP.

The paper explores application perspectives, detailing exemplar algorithm selectors such as SATzilla and AutoFolio. SATzilla, in particular, is recognized for its success in harnessing decision tree-based techniques to excel in SAT Competitions, setting benchmark standards in algorithmic problem-solving.

Moving into continuous problems, the survey reviews work in fields previously less explored by algorithm selectors, such as single-objective and constrained optimization problems. The field for multi-objective continuous problems is still evolving, alongside notions like online algorithm selection.

The authors conclude by identifying research challenges and prospects in algorithm selection. These range from improving feature cost and efficiency, creating evolving problem instance sets tailored for specific solvers, to speculative exploration using novel algorithm selection techniques for emerging problems like streaming data or mixed problem classes.

Overall, this paper positions itself as a definitive resource for understanding the facets of algorithm selection across various problem domains and suggests a comprehensive pathway for future research endeavors.