Quantum-based optimization methods for the linear redundancy allocation problem: A comparative analysis

The redundancy allocation problem (RAP) aims to efficiently assign multiple parallel components to maximize overall system reliability while adhering to budget constraints. This non-linear and NP-hard combinatorial optimization (CO) problem has been tackled through the development and application of exact methods and meta-heuristics. Moreover, recent advancements in quantum computing have opened up new avenues for addressing CO problems, often formulated as quadratic unconstrained binary optimization (QUBO) models. Our paper contributes by modeling RAP as a binary linear problem, translating it into a QUBO model, and solving it using exhaustive, exact, and quantum optimization approaches. To date, this is the first application of quantum methods to RAP. Initially, among the quantum algorithms explored, we focus on gate-based models utilizing noiseless quantum simulators. Specifically, we delve into the Quantum Approximative Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE). Additionally, we investigate Quantum Annealing using the D-Wave computer. Computational experiments were conducted on fifteen small-scale instances. Given the limitations of current quantum hardware and simulators, these simplified cases provide a controlled environment to assess algorithmic performance and define the study’s scope. While the gate-based models generally require more configuration trials to yield viable solutions, the D-Wave computer consistently achieves optimal results at a faster rate. These results underscore the potential of quantum optimization in addressing challenges within reliability engineering. By integrating quantum computing into the research agenda, we can effectively navigate future advancements in this field.