PROS-C: Accelerating Random Orthogonal Search for Global Optimization Using Crossover

Pure Random Orthogonal Search (PROS) is a parameterless evolutionary algorithm (EA) that has shown superior performance when compared to many existing EAs on well-known benchmark functions with limited search budgets. Its implementation simplicity, computational efficiency, and lack of hyperparameters make it attractive to both researchers and practitioners. However, PROS can be inefficient when the error requirement becomes stringent. In this paper, we propose an extension to PROS, called Pure Random Orthogonal Search with Crossover (PROS-C), which aims to improve the convergence rate of PROS while maintaining its simplicity. We analyze the performance of PROS-C on a class of functions that are monotonically increasing in each single dimension. Our numerical experiments demonstrate that, with the addition of a simple crossover operation, PROS-C consistently and significantly reduces the errors of the obtained solutions on a wide range of benchmark functions. Moreover, PROS-C converges faster than Genetic Algorithms (GA) on benchmark functions when the search budget is tight. The results suggest that PROS-C is a promising algorithm for optimization problems that require high computational efficiency and with a limited search budget.