A parallel algorithm based on quantum annealing and double-elite spiral search for mixed-integer optimal control problems in engineering

Abstract

Many engineering processes can be summarized as mixed-integer optimal control problems (MIOCPs) owing to the needs for optimizing mixed-integer dynamic control policies. However, MIOCP is a challenging NP-hard problem with great computational complexity, resulting in slow convergence or premature convergence by most current heuristics. Accordingly, this study explores a new and effective hybrid Quantum Annealing-Double-Elite Spiral Search (QA-DESS) algorithm to address this issue. To be specific, QA algorithm specializes in solving integer optimization with high efficiency due to the unique quantum-tunnelling-based annealing mechanism. For the optimization of continuous decisions, a DESS algorithm which adopts adaptive Cauchy mutation and double-elite evolutionary mechanism to enhance global searching is designed. The hybrid QA-DESS algorithm integrates the strengths of such algorithms to better balance the exploration and exploitation abilities. The overall evolution performs to find the optimal mixed-integer decisions by interactive parallel computing of QA and DESS. Simulation results on benchmark functions and practical engineering MIOCPs verify that the proposed optimization algorithm is more excel at finding promising results than other 7 heuristics (including traditional and state-of-the-art algorithms).