A quantum entanglement-based optimization method for complex expensive engineering problems

Abstract

Due to the computational costliness and time-consuming nature of complex and expensive engineering (CEE) problems, this paper proposes a genetic algorithm based on quantum entanglement to address these challenges. This method encodes individuals into quantum genes, where each gene bit stores not 0 or 1, but a superposition state of both. By leveraging the uncertainty of the superposition state during the collapse, this method effectively preserves population diversity even with a very small population size. A smaller population size implies fewer calls to time-consuming simulations. Additionally, quantum entangled states are created for parts of an individual's gene, utilizing the characteristic that entangled states instantly affect each other upon collapse, to achieve parallel evolution of parts of the genes in multiple individuals. This parallel evolution significantly increases the search speed of the algorithm, thereby reducing the number of iterations. Fewer iterations also mean fewer calls to simulations. Benchmark function experiments demonstrate that the proposed method is significantly superior to other similar algorithms in a 30D solution space with a population size of 20 and also has certain advantages in a 100D solution space.