Abstract: A hybrid algorithm based on modified augmented Lagrange function and PSO is proposed for solving constrained optimization problems. The general constrained optimization problem is converted into a bound constrained optimization problem. The basic steps off the proposed hybrid algorithm comprise an outer iteration and an inner iteration. The inner iteration, in which a nonlinear bound constrained minimization sub-problem of the modified augmented Lagrange multiplier, is solved by improved PSO algorithm. The outer iteration is performed to update the Lagrange multipliers and penalty parameters using a first-order update scheme, check for convergence and accordingly reinitiate another bound constrained minimization or declare convergence. The proposed algorithm is tested on 8 well-known benchmark constrained optimization problems, and the results show that it is very suitable and steadier than other algorithms from the literature for different constrained optimization problems.

Key words: augmented Lagrange function, constrained optimization problems, Particle Swarm Optimization

摘要： 提出一种基于修改增广Lagrange函数和PSO的混合算法用于求解约束优化问题。将约束优化问题转化为界约束优化问题，混合算法由两层迭代结构组成，在内层迭代中，利用改进PSO算法求解界约束优化问题得到下一个迭代点。外层迭代主要修正Lagrange乘子和罚参数，检查收敛准则是否满足，重构下次迭代的界约束优化子问题，检查收敛准则是否满足。数值实验结果表明该混合算法的有效性。

关键词: 增广Lagrange函数, 约束优化问题, 粒子群优化