Learning Objective Boundaries for Constraint Optimization Problems

TL;DR

This paper introduces Bion, a machine learning-based method to estimate objective boundaries in constraint optimization problems, improving search space pruning and solver efficiency across multiple problem types.

Contribution

Bion is a problem-specific, solver-independent approach that learns from past instances to accurately estimate objective boundaries, aiding in more efficient problem solving.

Findings

Bion can prune objective domains by over 80%.

Estimated boundaries can improve solver performance on some problems.

The effectiveness of boundary estimation is problem-dependent.

Abstract

Constraint Optimization Problems (COP) are often considered without sufficient knowledge on the boundaries of the objective variable to optimize. When available, tight boundaries are helpful to prune the search space or estimate problem characteristics. Finding close boundaries, that correctly under- and overestimate the optimum, is almost impossible without actually solving the COP. This paper introduces Bion, a novel approach for boundary estimation by learning from previously solved instances of the COP. Based on supervised machine learning, Bion is problem-specific and solver-independent and can be applied to any COP which is repeatedly solved with different data inputs. An experimental evaluation over seven realistic COPs shows that an estimation model can be trained to prune the objective variables' domains by over 80%. By evaluating the estimated boundaries with various COP solvers, we find that Bion improves the solving process for some problems, although the effect of closer bounds is generally problem-dependent.