复合形法解决多维非线性有约束优化问题

由于实际工程中的优化问题大多为多维非线性有约束优化问题 ,本文针对问题考虑了搜索方向和约束条件 ,提出较为实用而且简便的复合形法来确定搜索区间。用其解决了一些实际问题 。

连续负梯度方向获得共轭方向的六寻优化方法

连续两次沿负梯度方向寻优可获得共轭方向,对于一般二次目标函数,从两个角度对该现象进行了理论证明。鉴于为诸多研究领域优化问题的解决提供更多更有效的优化方法,将其推广于一般目标函数,提出了基于辅助方向的共轭方向法、三寻法和六寻法。连续三次沿负梯度方向寻优,然后沿所获得的两个共轭方向分别寻优,最后沿上述两个最优点连线进行第六次寻优,从而完成一轮寻优。给出了六寻法和用于三维优化问题的模块化一维盲人探路法C语言计算程序,并用解析法验证了程序的正确性。以一般的二次三维目标函数和Rosenbrock目标函数为例,验证了六寻法的有效性。其寻优效果比负梯度方向法好,两个算例的计算量分别减小28.70%、54.25%。六寻法可用于求解目标函数梯度可求的多维无约束优化问题。

基于共轭方向的半步有约束机械优化方法

有约束优化问题普遍存在于各个研究领域。有效的有约束优化方法均具有渐进寻优的特点。基于对优选可用方向法(可行方向法)的特点和局限性的分析,提出了半步法。一维寻优之后,如寻得边界最优点,则退回半步,然后以负梯度方向作为新的寻优方向,从而使算法具有渐进寻优的特点。为了有效地逼近边界极值点,增加辅助方向从而获得较好的新寻优方向。给出了寻优步骤和程序流程图。然后,总结出优选可用方向法的程序流程图。将原来的结构化一维盲人探路法进行了模块化。给出了半步法和模块化一维盲人探路法的C语言计算机程序。以二维二次目标函数的线性约束优化问题为例,验证了新算法的有效性。半步法可移植任何有效的无约束优化方法用于求解有约束优化问题。

An extended particle swarm optimization algorithm based on coarse-grained and fine-grained criteria and its application

In order to study the problem that particle swarm optimization (PSO) algorithm can easily trap into local mechanism when analyzing the high dimensional complex optimization problems, the optimization calculation using the information in the iterative process of more particles was analyzed and the optimal system of particle swarm algorithm was improved. The extended particle swarm optimization algorithm (EPSO) was proposed. The coarse-grained and fine-grained criteria that can control the selection were given to ensure the convergence of the algorithm. The two criteria considered the parameter selection mechanism under the situation of random probability. By adopting MATLAB7.1, the extended particle swarm optimization algorithm was demonstrated in the resource leveling of power project scheduling. EPSO was compared with genetic algorithm (GA) and common PSO, the result indicates that the variance of the objective function of resource leveling is decreased by 7.9%, 18.2%, respectively, certifying the effectiveness and stronger global convergence ability of the EPSO.