A Propose of Genetic Operators for Quantum Algorithms with Real Representation

In the literature, there are many Quantum Inspired Evolutionary Algorithms (QIEA) that proved good performance and results when applied to solving a myriad of problems. However, the real quantum representation increases precision for numerical optimisation problems and reduces the memory storage need, alternatively to the binary representation. On the other hand, evolutionary algorithms' performance mainly depends on the crossover and mutation operators, reaching equilibrium between the explorative and exploitative features of evolutionary algorithms. This paper proposes new quantum genetic operators for real quantum representation, instead of the 1/5 rule present in AEIQ-R, to improve the performance of the quantum genetic algorithm with real representation. Three crossover and two mutation operators are proposed and tested to optimise four functions with different dimensions. Friedman's test indicated a significant difference between the combinations, and that combination composed of quantum arithmetic crossover and quantum creep mutation have the best performance.