Redundancy Optimization of Finite-Dimensional Structures: A Concept and a Derivative-Free Algorithm

TL;DR

This paper introduces a new concept for redundancy optimization in finite-dimensional structures, linking it with robust optimization and information-gap theory, and proposes a derivative-free algorithm to find optimal solutions.

Contribution

It presents a novel, widely-applicable redundancy optimization concept and a derivative-free algorithm based on SQP with adaptive finite differences.

Findings

Optimal solutions may have multiple worst-case scenarios

The proposed algorithm effectively handles derivative-free optimization

Redundancy measure aligns with information-gap theory

Abstract

Redundancy is related to the amount of functionality that the structure can sustain in the worst-case scenario of structural degradation. This paper proposes a widely-applicable concept of redundancy optimization of finite-dimensional structures. The concept is consistent with the robust structural optimization, as well as the quantitative measure of structural redundancy based on the information-gap theory. A derivative-free algorithm is proposed based on the sequential quadratic programming (SQP) method, where we use the finite-difference method with adaptively varying the difference increment. Preliminary numerical experiments show that an optimal solution of the redundancy optimization problem possibly has multiple worst-case scenarios.