Robust Truss Topology Optimization via Semidefinite Programming with Complementarity Constraints: A Difference-of-Convex Programming Approach

TL;DR

This paper introduces a new heuristic method for robust truss topology optimization under load uncertainties, using semidefinite programming with complementarity constraints and a difference-of-convex programming approach to improve computational efficiency.

Contribution

It proposes a novel formulation and an efficient heuristic based on DC programming for robust truss optimization, reducing computational time compared to traditional methods.

Findings

The method can find practical truss designs within reasonable computational costs.

It often requires solving only a dozen convex optimization subproblems.

The approach offers a viable alternative to time-consuming global optimization techniques.

Abstract

The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very time-consuming. This paper presents an alternative formulation, semidefinite programming with complementarity constraints, and proposes an efficient heuristic. The proposed method is based upon the convex-concave procedure for DC (difference-of-convex) programming. It is shown that the method can often find a practically reasonable truss design within the computational cost of solving some dozen of convex optimization subproblems.