Improving Full Strong Branching Decisions by Incorporating Additional Information

TL;DR

This paper enhances the full strong branching rule by addressing its overestimation of LP gains and myopic decision-making, incorporating global asymmetry trends and primal bounds, leading to significantly smaller branch-and-bound trees.

Contribution

The paper introduces modifications to FSB that incorporate primal bounds and global asymmetry detection, improving branching decisions and reducing tree sizes.

Findings

22-35% reduction in mean tree sizes on benchmark instances

3.6-5.6% decrease in remaining gap for unsolved instances

5-13% reduction in tree sizes for reliability branching

Abstract

The full strong branching (FSB) rule is well known to produce extremely small branch-and-bound trees. This rule guides branching decisions based exclusively on the information regarding local gains in the linear programming (LP) bounds. We identify and correct two key shortcomings in FSB. First, the LP gains may be overestimations of the improvement in global dual bounds whenever pruning is possible. We propose a modification to address this issue, that incorporates primal bounds and readjusts the relative importance of the larger and smaller LP gains. Second, FSB decisions may be myopic as they consider only local LP gains and cannot foresee the impact of branching decisions on feasibility or integrality beyond immediate children. To address this weakness, we present an approach that detects global asymmetry trends in infeasibility and integrality due to 0 and 1 assignments and incorporates them into the FSB score function. We further extend this approach to achieve more balanced trees even when the branch-and-bound tree prunes primarily by bounds. Using randomly generated problem instances with known structures, we derive insights and fine-tune our modified scores. Evaluation on MIPLIB 2017 Benchmark instances shows a 22-35\% reduction in mean tree sizes for solved cases and a 3.6-5.6\% decrease in the remaining gap for unsolved ones. Our approach extends to reliability branching (RB), where improved scores reduce mean tree sizes by 5-13\% on solved instances and lower the mean gap by 2.6-4.3\% on unsolved instances, depending on primal bound quality.