A Generic Bet-and-run Strategy for Speeding Up Traveling Salesperson and Minimum Vertex Cover

TL;DR

This paper investigates a generic bet-and-run restart strategy for classical NP-complete problems, demonstrating significant improvements in solver performance on standard benchmarks without problem-specific tuning.

Contribution

It introduces a problem-agnostic bet-and-run approach applicable to TSP and vertex cover, showing its effectiveness without relying on problem knowledge.

Findings

Restarts significantly improve solver performance on benchmark instances.

The proposed strategy is effective across different algorithms and problems.

No problem-specific tuning is necessary for the restart approach.

Abstract

A common strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. However, while specific restart strategies have been developed for specific problems (and specific algorithms), restarts are typically not regarded as a general tool to speed up an optimization algorithm. In fact, many optimization algorithms do not employ restarts at all. Recently, "bet-and-run" was introduced in the context of mixed-integer programming, where first a number of short runs with randomized initial conditions is made, and then the most promising run of these is continued. In this article, we consider two classical NP-complete combinatorial optimization problems, traveling salesperson and minimum vertex cover, and study the effectiveness of different bet-and-run strategies. In particular, our restart strategies do not take any problem knowledge into account, nor are tailored to the optimization algorithm. Therefore, they can be used off-the-shelf. We observe that state-of-the-art solvers for these problems can benefit significantly from restarts on standard benchmark instances.