How to Speed up Optimization? Opposite-Center Learning and Its Application to Differential Evolution

This paper introduces a new sampling technique called Opposite-Center Learning (OCL) intended for convergence speed-up of meta-heuristic optimization algorithms. It comprises an extension of Opposition-Based Learning (OBL), a simple scheme that manages to boost numerous optimization methods by considering the opposite points of candidate solutions. In contrast to OBL, OCL has a theoretical foundation-the opposite center point is defined as the optimal choice in pair-wise sampling of the search space given a random starting point. A concise analytical background is provided. Computationally the opposite center point is approximated by a lightweight Monte Carlo scheme for arbitrary dimension. Empirical results up to dimension 20 confirm that OCL outperforms OBL and random sampling: the points generated by OCL have shorter expected distances to a uniformly distributed global optimum. To further test its practical performance, OCL is applied to differential evolution (DE). This novel scheme for continuous optimization named Opposite-Center DE (OCDE) employs OCL for population initialization and generation jumping. Numerical experiments on a set of benchmark functions for dimensions 10 and 30 reveal that OCDE on average improves the convergence rates by 38% and 27% compared to the original DE and the Opposition-based DE (ODE), respectively, while remaining fully robust. Most promising are the observations that the accelerations shown by OCDE and OCL increase with problem dimensionality.