关键词: 非线性约束, 扩展拉格朗日乘子法, 粒子群算法, 全局最优解, 优化设计

Abstract: The problems of engineering optimization, such as the optimization design of vessel, bellow and plate-fin exchanger, are usually the one of nonlinear constrained programming. In general, the penalty function approach is used to deal with the constrained conditions, in which a reasonable initial penalty factor must be given and the infinity dynamic penalty factors are needed to obtain the optimal solution. Augmented Lagrange approach is an improved penalty function approach, which can overcome the shortcoming of penalty function approach and the optimal solution can be obtained easily; but most of current studies have not given the operable process to combine the Augmented Lagrange approach with particle swarm optimization. So Augmented Lagrange particle swarm optimization (ALPSO) is studied to deal with the problem of nonlinear constrained programming; a new scheme of updating penalty factor r is proposed to improve the performance of approach, a reasonable operator is determined. The validity of the proposed approach is examined by benchmark numerical examples, and the global optimal solution is obtained. The engineering optimization designs of vessel and bellows are performed, global optimal solution or approximate optimal solution are acquired, the results further prove that the proposed approach and scheme are feasible, and operator runs stably and reliably, the proposed approach can be used to solve the engineering nonlinear constrained problems.

Key words: Augmented Lagrange, Global optimal solution, Non-linear constraints, Optimization design, Particle swarm algorithm