A particle swarm optimization (PSO) based algorithm for finding the Pareto solutions of multiobjective design problems is proposed. To enhance the global searching ability of the available PSOs, a novel formula for updating the particles' velocity and position, as well as the introduction of craziness, are reported. To handle a multiobjective design problem using the improved PSO, a new fitness assignment mechanism is proposed. Moreover, two repositories, together with the age variables for their members, are introduced for storing and selecting the previous best positions of the particle as well as that of its companions. Besides, the use of age variables to enhance the diversity of the solutions is also described. The proposed method is tested on two numerical examples with promising results.Index Terms-Inverse problem, multiobjective optimal algorithm, optimal design, particle swarm optimization (PSO).

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Abstract-An improved meshless method is presented with an emphasis on the detailed description of this new computational technique and its numerical implementations by investigating the usefulness of a commonly neglected parameter in this paper. Two approaches to enforce essential boundary conditions are also thoroughly investigated. Numerical tests on a mathematical function is carried out as a means of validating the proposed method. It will be seen that the proposed method is more robust than the conventional ones. Applications in solving electromagnetic problems are also presented.Index Terms-Lagrange multiplier method, least squares method, meshless method, moving-least square approximants.

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