Solve Optimization Problems with Unknown Constraint Networks

TL;DR

Learn&Optimize is a novel method that combines active constraint acquisition with optimization to solve problems with unknown constraints, enabling users to find optimal solutions without fully modeling the constraints.

Contribution

It introduces a new approach that integrates constraint learning into optimization, reducing the need for expert knowledge in constraint modeling.

Findings

Successfully learns unknown constraints during optimization

Computes boundaries for optimal solutions in the learning process

Enables solving problems without full constraint network knowledge

Abstract

In most optimization problems, users have a clear understanding of the function to optimize (e.g., minimize the makespan for scheduling problems). However, the constraints may be difficult to state and their modelling often requires expertise in Constraint Programming. Active constraint acquisition has been successfully used to support non-experienced users in learning constraint networks through the generation of a sequence of queries. In this paper, we propose Learn&Optimize, a method to solve optimization problems with known objective function and unknown constraint network. It uses an active constraint acquisition algorithm which learns the unknown constraints and computes boundaries for the optimal solution during the learning process. As a result, our method allows users to solve optimization problems without learning the overall constraint network.