# Threshold shift method for reliability-based design optimization

## TL;DR

The paper introduces the threshold shift method (TSM), a new approach for reliability-based design optimization that shifts constraint thresholds to improve efficiency and handle highly non-linear probabilistic constraints, outperforming existing methods.

## Contribution

The paper proposes the threshold shift method (TSM), which shifts constraint thresholds instead of variables and uses surrogate models for scalable, efficient RBDO with non-linear constraints.

## Key findings

- TSM outperforms existing RBDO methods on benchmark problems.
- TSM effectively handles highly non-linear probabilistic constraints.
- The method is computationally efficient and scalable.

## Abstract

We present a novel approach, referred to as the 'threshold shift method' (TSM), for reliability based design optimization (RBDO). The proposed approach is similar in spirit with the sequential optimization and reliability analysis (SORA) method where the RBDO problem is decoupled into an optimization and a reliability analysis problem. However, unlike SORA that utilizes shift-vector to shift the design variables within a constraint (independently), in TSM we propose to shift the threshold of the constraints. We argue that modifying a constraint, either by shifting the design variables (SORA) or by shifting the threshold of the constraints (TSM), influences the other constraints of the system. Therefore, we propose to determine the thresholds for all the constraints by solving a single optimization problem. Additionally, the proposed TSM is equipped with an active-constraint determination scheme. To make the method scalable, a practical algorithm for TSM that utilizes two surrogate models is proposed. Unlike the conventional RBDO methods, the proposed approach has the ability to handle highly non-linear probabilistic constraints. The performance of the proposed approach is examined on six benchmark problems selected from the literature. The proposed approach yields excellent results outperforming other popular methods in literature. As for the computational efficiency, the proposed approach is found to be highly efficient, indicating it's future application to other real-life problems.