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arXiv:2001.06079 · Quantum Machine Intelligence

Optimizing the optimizer: decomposition techniques for quantum annealing

Gideon Bass, Maxwell Henderson, Joshua Heath, Joseph Stephen Dulny

Published Mar 26, 2021• 20 citations
arXivHTMLPDF
DOI
10.1007/s42484-021-00039-9

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During recent years, quantum computers have received increasing attention, primarily due to their ability to significantly increase computational performance for specific problems. Computational performance could be improved for mathematical optimization by quantum annealers. This special type of quantum computer can solve quadratic unconstrained binary optimization problems. However, multi-energy systems optimization commonly involves integer and continuous decision variables. Due to their mixed-integer problem structure, quantum annealers cannot be directly used for multi-energy system optimization. To solve multi-energy system optimization problems, we present a hybrid Benders decomposition approach combining optimization on quantum and classical computers. In our approach, the quantum computer solves the master problem, which involves only the integer variables from the original energy system optimization problem. The subproblem includes the continuous variables and is solved by a classical computer. For better performance, we apply improvement techniques to the Benders decomposition. We test the approach on a case study to design a cost-optimal multi-energy system. While we provide a proof of concept that our Benders decomposition approach is applicable for the design of multi-energy systems, the computational time is still higher than for approaches using classical computers only. We therefore estimate the potential improvement of our approach to be expected for larger and fault-tolerant quantum computers.
Quantum Annealing (QA) is a metaheuristic designed to enhance Simulated Annealing by leveraging concepts from quantum mechanics, improving parallelization on classical computers. Studies have shown promising results for this technique in the field of NP-hard problems and constrained optimization. In this article, we examine Path Integral Quantum Annealing (PIQA), a well-known technique for simulating QA on conventional computers. We then propose optimizations to the algorithm, offering hardware software developers a suite of parallelization techniques evaluated for their effectiveness in enhancing quality and speed. The proposed approach encompasses four distinct degrees of optimization, leveraging techniques based on multiple-trial parallelism and a novel pre-optimization method. The article further proposes a methodology for handling multiple instances within the search space, whereby problem data is replicated into slices and allocated to concurrent processes during the simulation. Through empirical trials, we evaluate the impact of our optimization techniques on the convergence speed of the algorithm compared to unoptimized PIQA, using the Multidimensional Knapsack Problem as a benchmark. Our findings show that these optimizations, applied individually or collectively, enable the algorithm to achieve equal or superior results with fewer simulation steps. Overall, the results highlight the potential for future implementations of optimized PIQA on dedicated hardware.