Quantum Algorithm for Crowding Method

Abstract

The purpose of this paper is to introduce a simple, basic, yet intuitive method to exploit Grover’s search algorithm on crowding method, a part of general evolutionary algorithm. Specifically, Grover’s algorithm’s capability of “finding multiple needles in a haystack” provides a new, quantum way to properly select a parent individual out of the population that is the closest to its child individual in each niche. We avoid meticulously analyzing the mathematical procedure; rather, we would like to provide a set of concise intuition to help further motivate quantum computing researchers to continue the work. Conclusively, we prove that Grover’s algorithm indeed reduces the upper bound of time complexity required for the crowding method operation. Although our solution does not provide a quadratic or exponential speedup, the fact that quantum adaptation brings changes to existing classical algorithm is worth noticing, and it can attract more computing algorithm researchers to the field of quantum computing.