An intuitive distance-based explanation of opposition-based sampling

The impact of the opposition concept can be observed in many areas around us. This concept has sometimes been called by different names, such as, opposite particles in physics, complement of an event in probability, absolute or relative complement in set theory, and theses and antitheses in dialectic. Recently, opposition-based learning (OBL) was proposed and has been utilized in different soft computing areas. The main idea behind OBL is the simultaneous consideration of a candidate and its corresponding opposite candidate in order to achieve a better approximation for the current solution. OBL has been employed to introduce opposition-based optimization, opposition-based reinforcement learning, and opposition-based neural networks, as some examples among others. This work proposes an Euclidean distance-to-optimal solution proof that shows intuitively why considering the opposite of a candidate solution is more beneficial than another random solution. The proposed intuitive view is generalized to N-dimensional search spaces for black-box problems.

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