Machine learning (ML) techniques have been proposed to automatically select the best solver from a portfolio of solvers, based on predicted performance. These techniques have been applied to various problems, such as Boolean Satisfiability, Traveling Salesperson, Graph Coloring, and others. These methods, known as meta-solvers, take an instance of a problem and a portfolio of solvers as input. They then predict the best-performing solver and execute it to deliver a solution. Typically, the quality of the solution improves with a longer computational time. This has led to the development of anytime selectors, which consider both the instance and a user-prescribed computational time limit. Anytime meta-solvers predict the best-performing solver within the specified time limit. Constructing an anytime meta-solver is considerably more challenging than building a meta-solver without the "anytime" feature. In this study, we focus on the task of designing anytime meta-solvers for the NP-hard optimization problem of Pseudo-Boolean Optimization (PBO), which generalizes Satisfiability and Maximum Satisfiability problems. The effectiveness of our approach is demonstrated via extensive empirical study in which our anytime meta-solver improves dramatically on the performance of Mixed Integer Programming solver Gurobi, which is the best-performing single solver in the portfolio. For example, out of all instances and time limits for which Gurobi failed to find feasible solutions, our meta-solver identified feasible solutions for 47% of these.

翻译：机器学习（ML）技术已被提出用于根据预测性能，从求解器组合中自动选择最佳求解器。这些技术已应用于各种问题，例如布尔可满足性问题、旅行商问题、图着色问题等。这些方法被称为元求解器，它们以问题实例和求解器组合作为输入，然后预测性能最佳的求解器并执行它以提供解决方案。通常，求解质量随着计算时间的延长而提高。这导致了随时选择器的发展，这种选择器同时考虑实例和用户指定的计算时间限制。随时元求解器能在指定时间限制内预测性能最佳的求解器。构建随时元求解器比构建不具备“随时”特性的元求解器要困难得多。在本研究中，我们专注于为NP难的伪布尔优化问题设计随时元求解器，该问题是可满足性问题和最大可满足性问题的推广。通过广泛的实证研究，我们展示了方法的有效性：我们的随时元求解器在性能上显著优于混合整数规划求解器Gurobi——该组合中性能最佳的单求解器。例如，在所有Gurobi未能找到可行解的实例和时间限制中，我们的元求解器为其中47%的实例找到了可行解。