Convergence properties of quantum evolutionary algorithms on high dimension problems

We propose and investigate new rotation gates for two modified Quantum Inspired Evolutionary methods for solving high dimension optimisation problems. The Quantum Inspired Evolutionary Algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to high dimension problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding respectively, while keeping close to the original quantum computing metaphor. We introduce five performance metrics and use them to evaluate the proposed approaches against sets of multimodal mathematical test functions and real world problems of high dimensionality. We report issues found while implementing some of the published real QIEA techniques which were the motivation for developing our real algorithm modifications. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (particularly with high dimension problems), demonstrating faster convergence and accuracy.