Quantum behaved particle swarm optimization (QPSO) has been one of the most widely used algorithm in engineering world. Since its debut in 2004, QPSO has been used for resolving numerous complicated multimodal problems. Moreover, considering the adaptability and versatility, it has resolved a variety of real-world and test problems. To tackle numerical and engineering optimization problems, we introduce novel hybrid algorithm QPSODE. The novel hybrid algorithm integrates Quantum behaved particle swarm optimization (QPSO) with differential evolution (DE) strategy. A crossover and selection (influenced by DE) is used in the QPSODE’s position updating mechanism. During the selection process, the Boltzmann operator is applied to the position vectors of two randomly chosen particles, not to their individual optimum placements. Therefore, unlike the QPSO, a particle is only relocated to a new position if it has a higher fitness value, implying the application of a selection strategy across the whole search space. Additionally, the hybrid algorithm is improved by introducing proper parameters tuning, control parameter, path disparity. The hybrid algorithm enhances the algorithm’s performance by speeding up the convergence and avoiding the premature convergence, the main flaw in the earlier algorithms. The proposed algorithm is put to test, by using 19 well-known benchmark test functions and the engineering optimization problem for superconducting magnetic energy storage (SMES). In terms of the quality of the resulting outputs, QPSODE outperforms various state-of-the-art approaches.

Electromagnetic design problems are generally formulated as nonlinear programming problems with multimodal objective functions and continuous variables. These can be solved by either a deterministic or a stochastic optimization algorithm. Recently, many intelligent optimization algorithms, such as particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC), have been proposed and applied to electromagnetic design problems with promising results. However, there is no universal algorithm which can be used to solve engineering design problems. In this paper, a stochastic smart quantum particle swarm optimization (SQPSO) algorithm is introduced. In the proposed SQPSO, to tackle the premature convergence problem in order to improve the global search ability, a smart particle and a memory archive are adopted instead of mutation operations. Moreover, to enhance the exploration searching ability, a new set of random numbers and control parameters are introduced. Experimental results validate that the adopted control policy in this work can achieve a good balance between exploration and exploitation. Finally, the SQPSO has been tested on well-known optimization benchmark functions and implemented on the electromagnetic TEAM workshop problem 22. The simulation result shows an outstanding capability of the proposed algorithm in speeding convergence compared to other algorithms.

Particle Swarm Optimization (PSO) is a member of the swarm intelligence-based on a metaheuristic approach which is inspired by the natural deeds of bird flocking and fish schooling. In comparison to other traditional methods, the model of PSO is widely recognized as a simple algorithm and easy to implement. However, the traditional PSO’s have two primary issues: premature convergence and loss of diversity. These problems arise at the latter stages of the evolution process when dealing with high-dimensional, complex and electromagnetic inverse problems. To address these types of issues in the PSO approach, we proposed an Improved PSO (IPSO) which employs a dynamic control parameter as well as an adaptive mutation mechanism. The main proposal of the novel adaptive mutation operator is to prevent the diversity loss of the optimization process while the dynamic factor comprises the balance between exploration and exploitation in the search domain. The experimental outcomes achieved by solving complicated and extremely high-dimensional optimization problems were also validated on superconducting magnetic energy storage devices (SMES). According to numerical and experimental analysis, the IPSO delivers a better optimal solution than the other solutions described, particularly in the early computational evaluation of the generation.

Many versatile and promising swarm intelligence evolutionary algorithms are being developed to solve engineering optimization problems. Although evolutionary algorithms have been implemented in various optimization fields, there is still potential for enhancement in the domain of complex, electromagnetic, and multimodal objective problems. To effectively address the shortcomings and slow convergence speed observed in both smart quantum particle swarm optimization (QPSO) and differential evolution (DE), a hybrid strategy is proposed. In the proposed QPSODE, apart from the smart strategy of QPSO for improving the exploration as a whole, more additional features such as non-linear adaptive control parameter, the partition of the swarm to apply smart and gaussian mutation mechanism, crossover and selection of best particle using Boltzmann strategy to avoid premature convergence are introduced. Consequently, applying the new design algorithm to several benchmark-constrained, mostly non-convex, and superconducting magnetic energy storage (SMES) electromagnetic problems shows a marked performance improvement. The performances of the QPSODE is compared with those of many other widely recognized population-based swarm intelligence optimizers. Experimental results and statistical analysis using Friedman test show that the search accuracy and the convergence of the hybrid QPSODE strategy are advantageous over other optimization approaches.