Decision Diagram-Based Branch-and-Bound with Caching for Dominance and Suboptimality Detection

TL;DR

This paper enhances decision diagram-based branch-and-bound algorithms by introducing caching of dominance and suboptimality thresholds, significantly reducing node expansion and solving more complex problems faster.

Contribution

It introduces a novel caching mechanism for thresholds based on dominance relations, improving the efficiency of decision diagram-based branch-and-bound methods.

Findings

Reduced number of nodes expanded in experiments

Faster solution times for difficult problems

Ability to solve more instances with narrower diagrams

Abstract

The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width decision diagrams that can provide lower and upper bounds for any given subproblem. Eventually, every part of the search space will be either explored or pruned by the algorithm, thus proving optimality. This paper presents new ingredients to speed up the search by exploiting the structure of dynamic programming models. The key idea is to prevent the repeated expansion of nodes corresponding to the same dynamic programming states by querying expansion thresholds cached throughout the search. These thresholds are based on dominance relations between partial solutions previously found and on the pruning inequalities of the filtering techniques introduced by Gillard et al. in 2021. Computational experiments show that the pruning brought by this caching mechanism allows significantly reducing the number of nodes expanded by the algorithm. This results in more benchmark instances of difficult optimization problems being solved in less time while using narrower decision diagrams.