An efficient heuristic for reliability design optimization problems

This paper develops an efficient heuristic to solve two typical combinatorial optimization problems frequently met when designing highly reliable systems. The first one is the redundancy allocation problem (RAP) of series-parallel binary-state systems. The design goal of the RAP is to select the optimal combination of elements and redundancy levels to maximize system reliability subject to the system budget and to the system weight. The second problem is the expansion-scheduling problem (ESP) of multi-state series-parallel systems. In this problem, the study period is divided into several stages. At each stage, the demand is represented as a piecewise cumulative load curve. During the system lifetime, the demand can increase and the total productivity may become insufficient to assume the demand. To increase the total system productivity, elements are added to the existing system. The objective in the ESP is to minimize the sum of costs of the investments over the study period while satisfying availability constraints at each stage. The heuristic approach developed to solve the RAP and the ESP is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected subspace. Numerical results for the test problems from previous research are reported and compared. The results show the advantages of the proposed approach for solving both problems.