超越方程的优化解法

针对粒子群算法局部搜索能力差,后期收敛速度慢等缺点,提出了一种改进的粒子群算法,该算法是在粒子群算法后期加入拟牛顿方法,充分发挥了粒子群算法的全局搜索性和拟牛顿法的局部精细搜索性,从而克服了粒子群算法的不足,把超越方程转化为函数优化的问题,利用该算法求解,数值实验结果表明,算法有较高的收敛速度和求解精度。     

非线性约束优化的光滑化平方根罚函数

介绍一种非线性约束优化的不可微平方根罚函数,为这种非光滑罚函数提出了一个新的光滑化函数和对应的罚优化问题,获得了原问题与光滑化罚优化问题目标之间的误差估计. 基于这种罚函数,提出了一个算法和收敛性证明,数值例子表明算法对解决非线性约束优化具有有效性.     

带等式约束的光滑优化问题的一类新的精确罚函数

罚函数方法是将约束优化问题转化为无约束优化问题的主要方法之一. 不包含目标函数和约束函数梯度信息的罚函数, 称为简单罚函数. 对传统精确罚函数而言, 如果它是简单的就一定是非光滑的; 如果它是光滑的, 就一定不是简单的. 针对等式约束优化问题, 提出一类新的简单罚函数, 该罚函数通过增加一个新的变量来控制罚项. 证明了此罚函数的光滑性和精确性, 并给出了一种解决等式约束优化问题的罚函数算法. 数值结果表明, 该算法对于求解等式约束优化问题是可行的.     

群零模正则化问题的等价Lipschitz优化模型

针对群零模正则化问题, 从零模函数的变分刻画入手, 将其等价地表示为带有 互补约束的数学规划问题(简称MPCC问题), 然后证明将互补约束直接罚到MPCC的目标函数而得到的罚问题是MPCC问题的全局精确罚. 此精确罚问题的目标函数不仅在可行集上全局Lipschitz连续而且还具有满意的双线性结构, 为设计群零模正则化问题的序列凸松弛算法提供了满意的等价Lipschitz优化模型.     

基于粒子群算法的大型网络计划资源优化

现有求解网络计划资源优化的方法中,解析法不能解决大型复杂网络优化问题,启发式方法过多依赖具体问题、求解效率低,遗传算法生成新一代优化解种群依据的三个算子的实现参数选择,大部分依靠经验并严重影响解的品质,粒子群算法存在大型网络计划资源优化计算量过大和缺少大型网络计划资源优化算例问题.借助设计网络计划时间参数的计算机算法、建立评价函数、设计进化方程等基础工作,选择与工作开始时间相关的变量作为粒子空间位置,用蒙特卡洛方法和限制条件优化初始粒子群,设置可行解范围,用二维动态数组解决大型网络计划资源优化运行image超限问题,通过粒子群算法进化,寻求大型网络计划资源优化解,算例表明基于粒子群算法的大型网络计划资源优化效果明显,粒子群算法参数分析表明:粒子群算法的参数会影响网络计划资源优化结果,而且初始粒子群限制条件和优化目标设置的影响程度较大.     

非线性约束最优化问题中的一种光滑精确罚函数算法（英文）

针对非线性不等式约束优化问题提出一种新的光滑精确罚函数,并证明这种类型的光滑罚函数对求解非线性约束优化问题具有好的性质.基于这个光滑精确罚函数,文中设计罚函数算法,并证明在一些较弱的条件下,算法具有全局收敛性.最后,一些数值算例说明算法的有效性.     

改进的二进制粒子群算法求解车辆路径问题

设计了一种改进的二进制粒子群优化算法来求解车辆路径问题,算法基于粒子群算法的寻优模式充分考虑粒子之间的导向作用,改进二进制粒子群算法的位取值方式,减小了在进化过程中停滞于局部最优解的概率,并通过构造辅助函数处理优化问题的约束条件,基于分层次实现多个目标的思路来寻优,提高了算法的搜索效率和计算速度.实验测试结果验证了该算法对求解车辆路径问题的适用性和有效性.     

非线性约束优化问题的混合粒子群算法

把处理约束条件的一个外点方法和改进的粒子群优化算法相结合,提出了一种求解非线性约束优化问题的混合粒子群优化算法.该方法兼顾了粒子群优化和外点法的优点,对算法迭代过程中出现不可行粒子,利用外点法处理后产生可行粒子.数值实验表明了提出的新算法具有有效性、通用性和稳健性.     

一个新的目标罚函数算法

提出了求解约束优化问题的一种新的目标罚函数算法,这种目标罚函数的形式借助于目标罚函数、障碍函数、外部罚函数三种思想构成,提出了一个算法,并证明了算法的收敛性.新算法的一个特点是可以任意选择开始点进行迭代,数值实验结果表明了算法对于不同的初始点的有效性.     

混合变异粒子群优化算法及其应用

为改善粒子群优化算法在解决复杂优化问题时收敛质量不高的不足,提出了一种改进的粒子群优化算法,即混合变异粒子群优化算法(HMPSO).HMPSO算法采用了带有随机因子的惯性权重取值更新策略,降低了标准粒子群优化算法中由于粒子飞行速度过大而错过最优解的概率,从而加速了算法的收敛速度.此外,通过混合变异进化环节的引入,缓解了粒子种群在进化过程中的多样性与收敛性这一矛盾,使得算法的全局探索与局部开发得到有效平衡.利用经典的基准测试函数和平面冗余机械臂逆运动学问题的求解来验证提出算法的有效性,试验结果表明:与其他算法相比,HMPSO算法具有更快的收敛速度、更高的收敛精度、更强的收敛稳定性以及更低的计算成本.     

On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization

In this paper we propose two methods for smoothing a nonsmooth square-root exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. We develop an algorithm for solving the optimization problem based on the smoothed penalty function and prove the convergence of the algorithm. The efficiency of the smoothed penalty function is illustrated with some numerical examples, which show that the algorithm seems efficient.     

On Smoothing l1 Exact Penalty Function for Constrained Optimization Problems

This article introduces a smoothing technique to the l₁ exact penalty function. An application of the technique yields a twice continuously differentiable penalty function and a smoothed penalty problem. Under some mild conditions, the optimal solution to the smoothed penalty problem becomes an approximate optimal solution to the original constrained optimization problem. Based on the smoothed penalty problem, we propose an algorithm to solve the constrained optimization problem. Every limit point of the sequence generated by the algorithm is an optimal solution. Several numerical examples are presented to illustrate the performance of the proposed algorithm.     

Exactness and algorithm of an objective penalty function

Penalty function is an important tool in solving many constrained optimization problems in areas such as industrial design and management. In this paper, we study exactness and algorithm of an objective penalty function for inequality constrained optimization. In terms of exactness, this objective penalty function is at least as good as traditional exact penalty functions. Especially, in the case of a global solution, the exactness of the proposed objective penalty function shows a significant advantage. The sufficient and necessary stability condition used to determine whether the objective penalty function is exact for a global solution is proved. Based on the objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the objective penalty function is proved for a local solution. An algorithm is presented in the paper in finding a local solution, with its convergence proved under some conditions. Finally, numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm.     

Augmented Lagrangian Objective Penalty Function

Augmented Lagrangian function is one of the most important tools used in solving some constrained optimization problems. In this article, we study an augmented Lagrangian objective penalty function and a modified augmented Lagrangian objective penalty function for inequality constrained optimization problems. First, we prove the dual properties of the augmented Lagrangian objective penalty function, which are at least as good as the traditional Lagrangian function's. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker condition. This is especially so when the Karush-Kuhn-Tucker condition holds for convex programming of its saddle point existence. Second, we prove the dual properties of the modified augmented Lagrangian objective penalty function. For a global optimal solution, when the exactness of the modified augmented Lagrangian objective penalty function holds, its saddle point exists. The sufficient and necessary stability conditions used to determine whether the modified augmented Lagrangian objective penalty function is exact for a global solution is proved. Based on the modified augmented Lagrangian objective penalty function, an algorithm is developed to find a global solution to an inequality constrained optimization problem, and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the modified augmented Lagrangian objective penalty function is proved for a local solution. An algorithm is presented in finding a local solution, with its convergence proved under some conditions.     

Algorithm of Barrier Objective Penalty Function

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm.     

A solution method for semivectorial bilevel programming problem via penalty method

In this paper, we address a class of semivectorial bilevel programming problem in which the upper level is a scalar optimization problem and the lower level is a linear multi-objective optimization problem. Then, we present a new penalty function method, which includes two different penalty parameters, for solving such a problem. Furthermore, we give a simple algorithm. Numerical examples show that the proposed algorithm is feasible.     

遗传算法求解约束非线性规划及Matlab实现

对于约束非线性规划问题,传统的方法:可行方向法、惩罚函数法计算烦琐且精度不高.用新兴的遗传算法来解决约束非线性规划,核心是惩罚函数的构造.以前的惩罚函数遗传算法有的精度较低,有的过于复杂.本文在两个定义的基础上构造了新的惩罚函数,并在新的惩罚函数的基础上,提出了一种解决约束非线性最优化问题的方法.通过两个例子应用Matlab说明了这个算法的可行性.     

A penalty function-based differential evolution algorithm for constrained global optimization

We propose a differential evolution-based algorithm for constrained global optimization. Although differential evolution has been used as the underlying global solver, central to our approach is the penalty function that we introduce. The adaptive nature of the penalty function makes the results of the algorithm mostly insensitive to low values of the penalty parameter. We have also demonstrated both empirically and theoretically that the high value of the penalty parameter is detrimental to convergence, specially for functions with multiple local minimizers. Hence, the penalty function can dispense with the penalty parameter. We have extensively tested our penalty function-based DE algorithm on a set of 24 benchmark test problems. Results obtained are compared with those of some recent algorithms.