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.

构建适用于 NP-Hard 的 Pseudo-Boolean 优化问题的任意时刻元求解器，明显提高了性能，并改进了在组合求解器组合中性能表现最好的单个求解器 Gurobi 的成功率。