Objective Coefficient Rounding and Almost Symmetries in Binary Programs

TL;DR

This paper explores how rounding objective coefficients in binary programs can increase almost symmetries, making instances easier to solve and providing good approximations, with effects varying by problem type and solver.

Contribution

It empirically demonstrates that rounding coefficients can improve solver performance by exploiting almost symmetries across various binary problem instances.

Findings

Rounding reduces problem complexity and speeds up solving.

Increased almost symmetries facilitate solver efficiency.

Effectiveness varies with instance type and solver used.

Abstract

This article investigates the interplay of rounding objective coefficients in binary programs and almost symmetries. Empirically, reducing the number of significant bits through rounding often leads to instances that are easier to solve. One reason can be that the amount of symmetries increases, which enables solvers to be more effective when they are exploited. This can signify that the original instance contains 'almost symmetries'. Furthermore, solving the rounded problems provides approximations to the original objective values. We empirically investigate these relations on instances of the capacitated facility location problem, the knapsack problem and a diverse collection of additional instances, using the solvers SCIP and CP-SAT. For all investigated problem classes, we show empirically that this yields faster algorithms with guaranteed solution quality. The influence of symmetry depends on the instance type and solver.