扩展拉格朗日乘子粒子群算法解决工程优化问题

工程上很多优化问题，如容器设计、波纹管、板翅式换热器的结构优化设计等，皆为非线性约束优化设计问题，常采用惩罚函数法处理约束条件；为获得问题最优解，该方法需要合理确定初始惩罚因子，且需要动态惩罚因子无穷大。扩展拉格朗日乘子法是一种改进的惩罚函数法，可以克服惩罚函数法的不足，获得全局最优解，但目前对其研究和应用有限。对拉格朗日乘子法与粒子群算法相结合处理非线性约束问题进行研究，提出惩罚因子更新策略，确定扩展拉格朗日乘子粒子群算法合理的操作过程。标准测试函数结果显示：提出的方法及策略实现了扩展拉格朗日乘子粒子群算法解决非线性约束问题，并得到了问题的全局最优解；其在容器及波纹管系列优化设计中的应用进一步显示，提出的方法在处理非线性约束工程实际问题时，运行稳定可靠，可快捷获得问题的全局最优解或近似最优解。

Solving Engineering Optimization Problem by Augmented Lagrange Particle Swarm Optimization

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.