Feature-based offline algorithm selection has shown its effectiveness in a wide range of optimization problems, including the black-box optimization problem. An algorithm selection system selects the most promising optimizer from an algorithm portfolio, which is a set of pre-defined optimizers. Thus, algorithm selection requires a well-constructed algorithm portfolio consisting of efficient optimizers complementary to each other. Although construction methods for the fixed-target setting have been well studied, those for the fixed-budget setting have received less attention. Here, the fixed-budget setting is generally used for computationally expensive optimization, where a budget of function evaluations is small. In this context, first, this paper points out some undesirable properties of experimental setups in previous studies. Then, this paper argues the importance of considering the number of function evaluations used in the sampling phase when constructing algorithm portfolios, whereas the previous studies ignored that. The results show that algorithm portfolios constructed by our approach perform significantly better than those by the previous approach.

The algorithm selection problem is to choose the most suitable algorithm for solving a given problem instance and thus, it leverages the complementarity between different approaches that is present in many areas of AI. We report on the state of the art in algorithm selection, as defined by the Algorithm Selection Competition series 2015 to 2017. The results of these competitions show how the state of the art improved over the years. Although performance in some cases is very promising, there is still room for improvement in other cases. Finally, we provide insights into why some scenarios are hard, and pose challenges to the community on how to advance the current state of the art. Keywords: 1. Introduction Algorithm Selection, Meta-Learning, Competition Analysis In many areas of AI, there are different algorithms to solve the same type of problem. Often, these algorithms are complementary in the sense that one algorithm works well when others fail and vice versa. For example in propositional satisfiability solving (SAT), there are complete tree-based solvers aimed at structured, industrial-like problems, and local search solvers aimed at randomly generated problems. In many practical cases, the performance difference between algorithms can be very large, for example as shown by Xu et al. (2012) for SAT. Per-instance algorithm selection (Rice, 1976) is a way to leverage this complementarity between different algorithms.

It has become especially relevant in the last decade, with researchers increasingly investigating how to identify the most suitable existing algorithm for solving a problem instance instead of developing new algorithms. This survey presents an overview of this work focusing on the contributions made in the area of combinatorial search problems, where algorithm selection techniques have achieved significant performance improvements. We unify and organise the vast literature according to criteria that determine algorithm selection systems in practice. The comprehensive classification of approaches identifies and analyzes the different directions from which algorithm selection has been approached. This article contrasts and compares different methods for solving the problem as well as ways of using these solutions.

The algorithm selection problem is concerned with selecting the best algorithm to solve a given problem instance on a case-by-case basis. It has become especially relevant in the last decade, with researchers increasingly investigating how to identify the most suitable existing algorithm for solving a problem instance instead of developing new algorithms. This survey presents an overview of this work focusing on the contributions made in the area of combinatorial search problems, where algorithm selection techniques have achieved significant performance improvements. We unify and organise the vast literature according to criteria that determine algorithm selection systems in practice. The comprehensive classification of approaches identifies and analyses the different directions from which algorithm selection has been approached. This article contrasts and compares different methods for solving the problem as well as ways of using these solutions.