Modeling and Optimization of Reliability Reallocation for Modified Systems
针对改进系统（如航空、航天领域）的可靠性再分配问题，提出一种考虑一次性成本的非连续非线性优化模型，并设计差分进化算法求解，以最小化成本。
Complex systems, particularly in industries such as aviation and aerospace, are characterized by high technical challenges, extended development cycles, and substantial capital investments. Consequently, manufacturers in these fields often adopt modification strategies, leveraging the success of existing systems to minimize risks and costs. Traditional reliability-cost optimization models and associated techniques are primarily designed to address reliability allocation challenges in the development of entirely new systems. However, these models face significant limitations when applied to modified systems, as they fail to accurately represent the unique reliability-cost dynamics associated with one-time costs inherent in modifications. Based on the classical binary reliability-cost function, this paper analyzes the reliability-cost decomposition of the modified system, thus establishes a discontinuous nonlinear optimization model applicable to both continuous and discrete reliability cases. Among the cost decomposition, the gradually increasing term in the objective function represents the reliability improvement cost such as reliability design and manufacture, and the one-time term represents the cost such as verification and certification. Then, a differential evolution algorithm is designed to suit both continuous and discrete reliability cases within a unified framework, aiming to find the feasible reliability reallocation solution and to minimize the cost. Finally, two numerical examples utilizing three common cost functions, namely logarithmic, exponential, and power-law types, are conducted to validate the rationality of the proposed model and to demonstrate the effectiveness of the algorithm. Some comparisons with genetic algorithm and particle swarm optimization algorithm are also presented in view of optimality, mean value and deviation in this paper.