There are inherently various uncertainties in practical engineering, and reliability-based design optimization (RBDO) and robust design optimization (RDO) are two well-established methodologies when considering the uncertainties. Naturally, reliability-based robust design optimization (RBRDO) is a methodology developed recently by combining RBDO and RDO, in which the tolerances of random design variables are always assumed as constants. However, the tolerance of random design variables is a key factor for the objective robustness and manufacturing cost, and the tolerance allocation is the core problem in mechanical manufacturing. Inspired by the cost–tolerance relationship in mechanical manufacturing, this paper presents an integrated framework to simultaneously find the optimal design variable and the corresponding tolerance in the multi-objective RBRDO, with the trade-off between objective robustness and manufacturing cost. The failure mechanism of the constraint handling strategy of the constrained reference vector-guided evolutionary algorithm (C-RVEA) is discussed to solve the multi-objective optimization formulation. Then the robust repair operator and reliability-based repair operator are proposed to transform unfeasible solutions to the feasible ones under reliability constraints. Numerical results reveal that the proposed repair algorithm is effective. By solving the integrated multi-objective optimization problem, the Pareto front with the compromised solutions between the objective robustness and manufacturing cost could be obtained, from which decision makers can select the satisfying solution conveniently according to the preferred requirements.

中文翻译：

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基于可靠性的鲁棒设计优化在考虑制造公差的多目标进化优化与修复算法

实际工程中存在固有的各种不确定性，而基于可靠性的设计优化（RBDO）和稳健设计优化（RDO）是考虑不确定性时两种成熟的方法。自然，基于可靠性的稳健设计优化 (RBRDO) 是最近通过结合 RBDO 和 RDO 开发的一种方法，其中随机设计变量的容差始终假定为常数。然而，随机设计变量的公差是客观鲁棒性和制造成本的关键因素，而公差分配是机械制造中的核心问题。受机械制造中的成本公差关系的启发，本文提出了一个集成框架，可以在多目标 RBRDO 中同时找到最优设计变量和相应的公差，并在目标鲁棒性和制造成本之间进行权衡。讨论了约束参考向量引导进化算法（C-RVEA）的约束处理策略的失效机制，以求解多目标优化公式。然后提出了鲁棒修复算子和基于可靠性的修复算子，在可靠性约束下将不可行解转化为可行解。数值结果表明所提出的修复算法是有效的。通过求解集成多目标优化问题，可以得到目标鲁棒性和制造成本之间折衷解的帕累托前沿，