Research And Application Of A Hybrid Optimization Algorithm Based On Black Hole And Differential Evolution Algorithm

In the design of power generation,transmission,and transformation equipments with characteristics of ultra high voltage and large capacity,it is necessary to consider the overheating caused by eddy current,magnetic hysteresis and eddy current loss resulted from magnetic materials,vibration problems and so on.Furthermore,in order to improve the market competitiveness of industrial products,the uneven properties of material and the dimensional errors in practical applications should be considered in the design of electrical equipments.The above situations make design problems of electrical equipments multivariable,multi-constraint,multi-modal,multi-target and strong nonlinear.To solve such complex design problems,some classical intelligent optimization algorithms are trapped into premature and low precision in searching for optimum.Based on this background,it is urgent to investigate and develop a new optimal design algorithm suitable for complex high-dimensional engineering problems.In this paper,to solve the aforementioned complex engineering problems,a hybrid optimization algorithm based on the black hole and the differential evolution techniques has been proposed.The proposed algorithm combines advantages of both the black-hole based optimization algorithm and the differential evolution algorithm,which owns a better performance than its counterparts.Firstly,based on the standard differential evolution algorithm,the concept of black hole has been introduced.As it is well known,for the black hole phenomenon in the universe,the surrounding stars accelerate to move towards the black hole by its gravitational force.Similar to this phenomenon,the algorithm convergence speed is improved.Besides,a step of correction operation has been proposed,which aims to modify the target vectors out of the design boundaries.Meanwhile,the vectors very close to the black hole will be absorbed.To guarantee a constant number of vectors in the design space,a new vector will be randomly generated once a vector is absorbed.The proposed correction operation can greatly increase diversity of the optimization algorithm.At first,the low-dimensional single-peak benchmark function and multi-peak benchmark functions have been used to validate the basic optimization ability of the proposed algorithm.Then complex high-dimensional benchmark functions have been chosen to test the high dimensional searching ability by gradually increasing the dimensions of the benchmark functions.The test results have proved the good performance of the proposed algorithm in the optimization of numerical experiments.Besides,in the engineering test experiments,two benchmark problems(optimal design of the magnetic field aligning device for anisotropic bonded permanent magnets and optimal design of the superconducting magnetic energy storage system)have been applied to further test the optimization ability of the algorithm.Through the test results,the effectiveness of the proposed algorithm has been validated again.Finally,the proposed algorithm has been applied to optimize the cogging torque of a surface mounted permanent magnet synchronous motor with 4-pole and 24-slot.Firstly,the surrogate model of the objective function was constructed by Kriging.Then the proposed hybrid algorithm was used to optimize the structure of the motor,and obtained an optimum solution.The optimum design was validated by the finite element simulation.The optimization of the cogging torque has been finished.