Combining Parallel Stochastic Methods and Mixed Termination Rules in Optimization

Abstract

Parallel optimization enables faster and more efficient problem-solving by reducing computational resource consumption and time. By simultaneously combining multiple methods, such as evolutionary algorithms and swarm-based optimization, effective exploration of the search space and achievement of optimal solutions in shorter time frames are realized. In this study, a combination of termination criteria is proposed, utilizing three different criteria to end the algorithmic process. These criteria include measuring the difference between optimal values in successive iterations, calculating the mean value of the cost function in each iteration, and the so-called “DoubleBox” criterion, which is based on the relative variance of the best value of the objective cost function over a specific number of iterations. The problem is addressed through the parallel execution of three different optimization methods (PSO, Differential Evolution, and Multistart). Each method operates independently on separate computational units with the goal of faster discovery of the optimal solution and more efficient use of computational resources. The optimal solution identified in each iteration is transferred to the other computational units. The proposed enhancements were tested on a series of well-known optimization problems from the relevant literature, demonstrating significant improvements in convergence speed and solution quality compared to traditional approaches.