Efficient exact optimization of multi‐objective redundancy allocation problems in series‐parallel systems

This paper proposes a decomposition‐based approach to exactly solve the multi‐objective Redundancy Allocation Problem for series‐parallel systems. Redundancy allocation problem is a form of reliability optimization and has been the subject of many prior studies. The majority of these earlier studies treat redundancy allocation problem as a single objective problem maximizing the system reliability or minimizing the cost given certain constraints. The few studies that treated redundancy allocation problem as a multi‐objective optimization problem relied on meta‐heuristic solution approaches. However, meta‐heuristic approaches have significant limitations: they do not guarantee that Pareto points are optimal and, more importantly, they may not identify all the Pareto‐optimal points. In this paper, we treat redundancy allocation problem as a multi‐objective problem, as is typical in practice. We decompose the original problem into several multi‐objective sub‐problems, efficiently and exactly solve sub‐problems, and then systematically combine the solutions. The decomposition‐based approach can efficiently generate all the Pareto‐optimal solutions for redundancy allocation problems. Experimental results demonstrate the effectiveness and efficiency of the proposed method over meta‐heuristic methods on a numerical example taken from the literature.