A quantum-based sine cosine algorithm for solving general systems of nonlinear equations

In this paper, a quantum-based sine cosine algorithm, named as Q-SCA, is proposed for solving general systems of nonlinear equations. The Q-SCA hybridizes the sine cosine algorithm (SCA) with quantum local search (QLS) for enhancing the diversity of solutions and preventing local optima entrapment. The essence of the proposed Q-SCA is to speed up the optimum searching operation and to accelerate the convergence characteristic. The proposed Q-SCA works in twofold: firstly, an improved version of SCA based on tuning the search space around the destination solution dynamically, so that the search space is shrunken gradually as the optima are attained. In addition, a new mechanism to update the solutions is introduced using bidirectional equations. Secondly, QLS is incorporated to improve the quality of the obtained solutions by the SCA phase. By this methodology, the proposed Q-SCA can achieve high levels of exploration/exploitation and precise stable convergence to high-quality solutions. The performance of the proposed algorithm is assessed by adopting twelve systems of nonlinear equations and two electrical applications. Furthermore, the proposed Q-SCA algorithm is applied on expensive large-scale problems including CEC 2017 benchmark and realistic optimal power dispatch (OPD) to confirm its scalability. Experimental results affirm that the Q-SCA is performs steadily, and it has a promising overall performance among several compared algorithms.