An outer approximation bi-level framework for mixed categorical structural optimization problems

TL;DR

This paper introduces a bi-level outer approximation framework for efficiently solving large-scale mixed categorical structural optimization problems, demonstrating superior performance over existing methods.

Contribution

The paper presents a novel bi-level decomposition approach combining mixed integer linear and continuous subproblems for structural optimization.

Findings

Efficiently solves large-scale mixed categorical problems

Outperforms state-of-the-art algorithms in quality and speed

Successfully applied to a 120-bar dome truss problem

Abstract

In this paper, mixed categorical structural optimization problems are investigated. The aim is to minimize the weight of a truss structure with respect to cross-section areas, materials and cross-section type. The proposed methodology consists of using a bi-level decomposition involving two problems: master and slave. The master problem is formulated as a mixed integer linear problem where the linear constraints are incrementally augmented using outer approximations of the slave problem solution. The slave problem addresses the continuous variables of the optimization problem. The proposed methodology is tested on three different structural optimization test cases with increasing complexity. The comparison to state-of-the-art algorithms emphasizes the efficiency of the proposed methodology in terms of the optimum quality, computation cost, as well as its scalability with respect to the problem dimension. A challenging 120-bar dome truss optimization problem with 90 categorical choices per bar is also tested. The obtained results showed that our method is able to solve efficiently large scale mixed categorical structural optimization problems.