Cost and Reliability Optimization by Using the Grey Wolf Algorithm

Abstract

This study shows how to use the Grey Wolf Optimizer (GWO) to create a multi-objective reliability-cost optimization framework for complex networks. The goal is to determine the optimal reliability levels for each item so that the system as a whole is as reliable as possible and stays within budget. Two cost models, quadratic and exponential, are used to look at how making things more reliable will affect the economy. This work not only improves the computer optimization process but also adds important theoretical results that strengthen the mathematical foundation of the reliability allocation problem. It is shown that system reliability always increases as component reliabilities increase, and that the associated cost functions are always increasing and convex. So, the best allocations happen at the edge of the zone where reliability is possible. A similar analytical conclusion shows that the exponential cost model has a substantially larger marginal penalty at high reliability levels, which is why it costs more. The suggested architecture is used in a complex network with 15 components. The results reveal that the GWO algorithm finds the best balance between reducing costs and improving reliability. The exponential cost model has a greater marginal penalty near high reliability levels. This makes the quadratic model better suited to systems that require very high reliability, while the exponential model may be sufficient for systems that need intermediate reliability. Combining metaheuristic optimization with rigorous theoretical analysis provides a better understanding of the trade-offs between reliability and cost, helping us make better decisions for complex engineering systems.  The results show that the Grey Wolf Optimiser (GWO) is a reasonable compromise between reliability and cost, with a system reliability of 0.9626 in a 15-component network. The analysis indicates that the exponential model is more expensive at high reliability levels than the quadratic model, and the quadratic model is more effective for high-reliability systems.