Theoretical Analysis and Experimental Evidence of Opposite-Center Learning

The main motivation of this paper is to discuss some theoretical details of opposite-center learning (OCL) and further validate its effectiveness for the optimization problems. In order to reveal the strong flexibility of its definition, two analytical solutions of opposite-center point are deduced for 1-D case. In order to reduce its computational complexity for higher dimensions, several termination criterion of iterative process are discussed thoughtfully and then a simple and efficient criterion is found when considering both the algorithm performance and computation cost. Moreover, a uniform evaluation approach to compute an evaluation function is proposed and then different opposition strategies can be compared easily by means of the mathematical expectation of these functions. To further verify its practical performance, OCL mechanism is embedded into differential evolution (DE) for population initialization and generation jumping and opposite-center DE is proposed. Simulation results demonstrate the strong exploitation ability of OCL. The obtained results also confirm a good tradeoff of solution accuracy and convergence speed in solving various function optimizations.