Engineering optimization problems usually contain various constraints and mixed integer-discrete-continuous types of design variables. We propose an efficient particle swarm optimization (PSO) algorithm for such problems. First, we transform the constrained optimization problem into an unconstrained problem without introducing problem-dependent or user-defined parameters such as penalty factors or Lagrange multipliers (such parameters are usually required in general optimization algorithms). Then, we extend the above PSO method to handle integer, discrete, and continuous design variables in a simple manner with a high degree of precision. The proposed PSO scheme is fairly simple and therefore easy to implement. To demonstrate the effectiveness of our method, several mechanical design optimization problems are solved, and the numerical results are compared with results reported in the literature.
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