Random Matrix-Based Genetic Algorithm: An Efficient Yet Privacy-Preserving Optimization Method

TL;DR: Random matrix-based genetic algorithm (RMGA) is an efficient yet privacy-preserving optimization method that effectively solves privacy-preserving optimization problems (PPOPs) based on a limited number of fitness-preserving evaluations.

Abstract: As a kind of advanced computational intelligence and artificial intelligence algorithm, evolutionary computation (EC) has achieved considerable success in solving various real-world optimization problems. However, EC algorithms still encounter two significant challenges when solving privacy-preserving optimization problems (PPOPs). First, as the exact fitness information cannot be accessed in PPOPs, EC algorithms are required to find the global optimum solely relying on fitness-preserving evaluation. Second, as the access number of fitness-preserving evaluations is limited to avoid privacy attacks, EC algorithms need to obtain satisfactory solutions within a limited access number of fitness-preserving evaluations, which is difficult. To address these issues, this paper proposes a random matrix-based genetic algorithm (RMGA), together with two novel methods. The first is a random matrix-based crossover (RMC) method and the second is a random matrix-based mutation (RMM) method, both of which leverage random matrices and matrix-based operations to enhance optimization efficiency. By integrating the RMC and RMM, the RMGA can efficiently solve PPOPs based on a limited number of fitness-preserving evaluations. To investigate the proposed algorithm, experiments are conducted on 13 PPOPs, where state-of-the-art algorithms are used for comparison. The experimental results validate the superiority of the RMGA over the compared algorithms.