Differential evolution algorithm with adaptive crossover and sorting mutation strategies for high-dimensional optimization

High-dimensional continuous optimization problems have arisen in many modern applications including engineering design, feature learning, and big data analytics. An efficient and scalable optimization method is required to search the solution spaces that exponentially increase in size with the number of decision variables. In this paper, we propose an adaptive differential evolution algorithm using adaptive crossover and sorting mutation strategies (DEASCSM) for solving problems of dimensions up to 1000. The adaptive crossover adapts the search to suit different problem landscapes, while the sorting mutation accelerates the convergence. We investigate the algorithm's scalability by considering both the value-to-reach and limited-budget approaches and evaluate its performance on several benchmark functions. Experimental results show that the DEASCSM algorithm can find optimal solutions for high-dimensional problems and scales differently, depending on the problem characteristics. The performance comparison with well-known methods demonstrates its superiority.