Particle Swarm Optimization And Its Application To Electromagnetic Design Problems

The history of the study of electromagnetic inverse problems exceeds more than one century.The electromagnetic inverse problem,in general,often refers to the optimal design of electrical and magnetic devices which naturally arise from many real-world and engineering problems.The current trend in dealing with an electromagnetic inverse problem is to divide it into a series of direct problems and then to solve it in an iterative way by using an optimal algorithm.It follows,then,that optimal algorithms and numerical methods for direct problems constitute the two primary branches of the study of electromagnetic inverse problems.As high fidelity models,such as the finite element method,are generally required at each iteration,the computation cost of applying such an algorithm to an inverse problem is often extremely high when compared to that of a direct problem.To address the aforementioned issues,in the current century there have been substantial efforts to develop a general frame work for solving such inverse problems.Indeed,many practical electromagnetic inverse problems have been solved by using numerical methods.The significant advancement of electronic computers and engineering technologies allows for the accelerated application of various new numerical methods to this research field.As explained previously,the general methodology to solve an inverse problem is to convert it into a series of direct counterparts and then to solve it,iteratively,by using an optimizer.As a consequence,the study of optimization algorithms constitutes one major issue in inverse problem studies.In this direction,the population based algorithms have become a trend over the last two decades and have been accepted as indispensable tools in the arsenal of optimization techniques.In this thesis,we investigate as well as analyze the development of a global stochastic search algorithm-the Particle Swarm Optimization(PSO)algorithm.The central idea of our proposed work can be summarized as follows.We introduced three new adaptive mutation operators,new best particles by using tournament selection strategy,and the selection of the best particles by using a mutation mechanism.We also proposed new strategies for the basic parameters of the conventional PSOs.In our first improvement of the PSO,the mutation operators are operated on both the personal best particle and the global best particle adaptively by using a special selection ratio.The main goal of this new method is to avoid a premature convergence.In our second improvement,we introduced a new global best particle into the basic PSO in order to preserve the diversity of the swarm and to explore more search spaces during the evolution process.Furthermore,we developed some novel strategies for the basic parameters which will maintain a good balance between the global and local searches.For the third improvement,we selected a new best particle from the current population by using a mutation mechanism with the purpose of improving the search process and to control the diversity of the swarm at the final stages of the optimization process.We also proposed dynamic strategies for the basic parameters of PSO to maintain a proper balance between the exploration and exploitation searches.All of the new strategies improve the performance of the traditional PSO algorithm and control the premature convergence in PSO process.The proposed algorithms(three modified models)were examined by using some standard mathematical test functions and an electromagnetic design problem:TEAM workshop problem 22,and its performances were then compared with existing methods.The numerical results and statistical analysis show the merits and superiority of the proposed models compared with other well developed stochastic PSO counterparts.