A Stochastic Continuous Optimization Backend for MiniZinc with Applications to Geometrical Placement Problems

Abstract

MiniZinc is a solver-independent constraint modeling language which is increasingly used in the constraint programming community. It can be used to compare different solvers which are currently based on either Constraint Programming, Boolean satisfiability, Mixed Integer Linear Programming, and recently Local Search. In this paper we present a stochastic continuous optimization backend for MiniZinc models over real numbers. More specifically, we describe the translation of FlatZinc models into objective functions over the reals, and their use as fitness functions for the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) solver. We illustrate this approach with the declarative modeling and solving of hard geometrical placement problems, motivated by packing applications in logistics involving mixed square-curved shapes and complex shapes defined by Bézier curves.

Panorama of real-life applications in logistics embedding bin packing optimization algorithms, robotics and cloud computing technologies

“…These packing problems are encountered in automotive and perfume industries. The results are promising and details are in [4,5].…”

“…The project Net-WMS2, lead by the team Lifeware at INRIA, aims to carry out many studies for complex objects, amongst which solving curve shapes. In addition to packing problems for squares, circles, triangles and polygons [5], we consider continuous packing problems with curve shapes [4]; mixing various shapes and mixing three dimensional packing problems, mixing boxes, spheres and cylinders. On square packing problems, exact methods have been used to find optimal solutions and prove optimality.…”