Quantum-inspired algorithm with fitness landscape approximation in reduced dimensional spaces for numerical function optimization

Abstract

In realistic numerical optimization problems, the efficiency of the algorithm is a crucial consideration. Fitness landscape approximation is beneficial for improving the search efficiency in evolutionary algorithms, but this method increases the computational cost significantly with an increase in the dimension. This paper proposes a quantum-inspired algorithm with dimension decomposition and fitness landscape approximation. The high-dimensional problem space is transformed into a low-dimensional projection space for fitness landscape approximation through mapping transformation. Linear approximation for the fitness landscape is performed in the transformed multiple 1D projected spaces. In accordance with two different diversity-retaining strategies, reference sampling points with different characteristics are selected to perform two-point linear approximation. Candidate points in the projection space are estimated and then synthesized as candidate solutions in the problem space. Then, candidate solutions are used in an appropriate population reconstruction mechanism to improve the performance of the algorithm. The proposed algorithms are implemented on benchmark functions abstracted from real-world optimization problems and compared with several algorithms. Experimental results on errors, success rates, and their rankings show the superiority of the proposed approach with the solution diversity priority with regard to effectiveness, adaptability, and stability.