Solving algorithm design for the cost minimization reliability optimization model driven by a novel cost-based importance measure

Cost-based importance measures (CIMs) enable efficient prioritization of system components and cost-effective strategies for reliable operation of complex systems with minimized expenses. However, existing CIMs are limited to scenarios with well-defined partial derivatives of total improvement cost concerning component reliability. Furthermore, in the cost minimization reliability optimization model (ROM), these CIMs only assess the effect of varying component reliability on overall cost, ignoring the comprehensive impact of constraints on component ranking. To bridge this gap, we propose a novel cost-based importance measure tailored for the cost minimization ROM, called the cost minimization ROM-based importance measure (CMRIM). This measure offers a comprehensive assessment of how variations in component reliability impact both the objective function and constraints, irrespective of the existence of partial derivatives of total improvement cost concerning component reliability. The CMRIM mechanism is subsequently examined to guide the formulation of optimization rules. Theoretical analysis confirms CMRIM's effectiveness in guiding reliability optimization strategies. Additionally, a CMRIM-based genetic algorithm (CMGA) is developed for the cost minimization ROM. Empirical results across various system scales demonstrate CMGA's ability to pinpoint optimal solutions with minimal cost. Moreover, CMGA exhibits accelerated convergence, heightened robustness, and superior computational efficiency compared to alternative optimization methods.