Are Two Opposite Points Better Than One?

Various opposition-based learning (OBL) strategies were proposed to further improve solution quality since 2005. However, in all existing OBLs, only one opposite point is generated for a given candidate solution in population. There is the old saying that there is strength in numbers. The purpose of this study is to examine the feasibility and effectiveness of double-points opposition-based learning (DOBL). The basic concept of DOBL is first proposed and then some viable forms are introduced in this paper. In addition, previous evaluation function and calculation method are highly complex, which block its application in DOBL. Based on a new evaluation function, another approach is presented to calculate its mathematical expectation more easily. The results by theoretical analysis and simulation experiment over sampling problems indicate that DOBL is better than the conventional OBL. In engineering application, double-points opposition-based learning differential evolution (DODE) is first developed to accelerate its convergence speed. Experiment results over 58 optimization problems show that DODE has an eclectic convergence speed in a fair competitive environment. Furthermore, the contribution of opposite points and the effect of jumping rate are also discussed in detail. When both considering algorithm convergence and reliability, a small jumping rate is generally recommended for an unknown optimization problem.