Abstract: A discrete partcle swarm optimization (PSO) is proposed to solve the problem of nonlinear constraints discrete optimization design in engineering, in which the penalty function is employed to transform discrete design variables to continuous design variables. An augment function is constructed and a new scheme of penalty parameter is proposed. The validity of proposed approach is examined by the famous benchmark-vessel design, the comparison results show that the proposed discrete particle swarm optimization is superior to the other algorithms from literatures and has better convergence performances. The proposed approach is applied further in the optimal design of bellows, the global optimums are obtained, the objective function value of maximum bellows movement per weight unit is 79.9% improved than that of products in-service and it nears to theoretical solution. Therefore, the validity of the proposed approach is been examined, and the proposed discrete particle swarm optimization and scheme can be used to solve the problem of nonlinear constraints discrete optimization design in engineering.

Key words: Discrete design variables, Engineering optimization design, Global optimum solution, Particle swarm optimization, Penalty factor, Penalty function