Mixed-Integer Programming Formulation of a Data-Driven Solver in Computational Elasticity

TL;DR

This paper introduces a mixed-integer quadratic programming formulation for a data-driven computational elasticity approach, enabling the use of standard solvers to find global optima and establish benchmark solutions.

Contribution

It presents a novel MIP formulation of a data-driven elasticity method, allowing for global optimization and benchmarking against heuristic approaches.

Findings

The MIP formulation successfully finds global solutions.

Preliminary experiments show competitive solution quality.

The method provides benchmark instances for future algorithms.

Abstract

This paper presents a mixed-integer quadratic programming formulation of an existing data-driven approach to computational elasticity. This formulation is suitable for application of a standard mixed-integer programming solver, which finds a global optimal solution. Therefore, the results obtained by the presented method can be used as benchmark instances for any other algorithm. Preliminary numerical experiments are performed to compare quality of solutions obtained by the proposed method and a heuristic used in the data-driven computational mechanics.