A computational comparison of handling distance constraints in MINLP

TL;DR

This paper compares different computational methods for handling distance constraints in MINLP problems, introducing new algorithms and symmetry handling techniques, with a focus on performance evaluation.

Contribution

It develops novel algorithms for tightening bounds in MINLPs with distance constraints and introduces a symmetry handling approach using Givens rotations.

Findings

New algorithms improve bound tightening in MINLP with minDCs.

Symmetry handling via Givens rotations enhances computational efficiency.

Performance varies depending on problem scenarios.

Abstract

Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening variable bounds in general MINLPs with minDCs. Because many such problems exhibit substantial symmetry, we further introduce a practical approach for handling rotation symmetries via separation of lexicographic constraints induced by Givens rotations. In a computational study, we examine the performance of the various methods and determine the scenarios in which each approach demonstrates superiority.