混合粒子群算法 - 360文档中心

求解非线性规划问题的混合粒子群算法

维普资讯
ＣｍｕｒＥｇｎｅｉｎｐｌａｉｓ算机工程与应用ｏｐｔｎｉｅｒｇａｄＡｐｉｔｎ计ｅｎｃｏ
求解非线性规划问题的混合粒子群算法
廖锋，兴宝高
ＬＩＡＯＦｎＧＡＯＸｉｇａｅｇ，ｎ —ｂｏ
摘
要：用粒子群算法求解非线性规划问题时不可避免的会产生不可行点，处理好不可行点是粒子群算法取得良好优化结果的关
键。依据粒子的目标函数值与违反约束的程度提出了一种处理不可行点的合理选择方案，并运用融合差分演化的混合粒子群算法求解约束优化问题，数值实验表明该算法的有效性。
ｄｇｅ，ｎｐｌｎｙｒｐｒｉｌｗｒｏｔｚｔｎａｇｒｈｅｒｅａｄａｐｙａｈｂｉａｃｅｓａｍｐｉａｉｌｏｔｍｃｍｂｎｄｉｅｅｔｌｅｏｕｉｎｏｓｌｅｏｓｒｅｐｉｚｔｎｄｔｍｉｏｉｏｉｅｄｆｒｎｉｖｌｔｔｏｖｃｎｔｉｄｏｔａｏｎｍｉａｉｏ
ｒｕｔｈｕｈｒｐｏｏｅａｅｓｎｂｅｓｌｔｍｔｏｏｄａｗｔｉｆｓｌｐｉｓｂｓｄｏｂｅｔｆｎｔｎｖｌｅａｄｖｌｅｅｌｅａｔｏｓｒｓｎｒｏａｌｅｅｅｄｔｅｌｉｎｅｉｅｏｔａｅｎｏｊｃｕｃｏａｎｉａｓ．Ｔｐａｃｈｈａｂｎｉｕｏｔ
陕西师范大学数学与信息科学学院，西安７６０２１０
ＣｌｇｆＭａｈｍａｉｓａｄＩｆｒｔｎＳｉｎｅＳａｎｉｏｍａｉｅｓｔ， ’ｎ７０２，ｉａｏｌｅｏｔｅｔｎｎｍａｉｃｅｃ，ｈｎｘＮｒｌＵｎｖｒｉＸｉａ６Ｃｈｎｅｃｏｏｙ１０

混合三群粒子群优化算法求解min-max-min问题

ｎｅｉｇａｄＡｐｌａｉｎ。００，６３：１－２．ｅｒｎｎｐｉｔｓ２１４（５）２９２１ｃｏ
ＡｂｔａｔｈｔｎａｄＰｒｃｅＳｒＯｐｉｚｒＳＳｓｒｃ：ＴｅＳａｄｒａｔｌｗａｍｔｅ（ＰＯ）ｍａｅｄｔｒｍａｕｅｃｎｅｇｎｅｗｈｎｏｔｚｎｏｌｘｏｔｉｍｉｙｌａｏｐｅｔｒｏｖｒｅｃｅｐｉｉｇｃｍｐｅｐｉｍｉ —
ｃｎｔｍｐｏｅｅｉｐｅｆｒａｅｏｖｒｈｔａｉｉｎａＰＳ０ＳＦｕｔｒｏｅ．ｔＰＳＯｍｅｈｏａｉｒｖｍｎｔｎｒｏｍｎｃｅｔｅｒｄｔｏｌ．ｒｈｅｍｒｈｅｔｄｉａｐｌｅｔｓｖａｃａｓｏｆＳｐｉｄｏｏｌｅｌｓａｎ．ｘ— ｎｒｉｍａｍｉｐｒｂｌｍｓｎｄｈｅｕｍｅｉａｘａｐｅａｅｏｅａｔｎｒｃｌｅｍｌｓｒｐｒｐｏｓｄ．ｏｅ
子群分为３协同优化的子群，持迭代后期粒子群的多样性。在４经典测试函数上的仿真实验表明，算法较传统Ｐ０算法个保个新ｓ收敛更快，度更高。将粒子群算法应用于求解一类ｒｉ．ｘｍｉ精ａｎｍａ．ｎ问题，并给出了数值算例。关键词：粒子群优化算法；子群协同；ｉ．ｘｍｉ三ａｒｎｍａ — ｎ问题Ｄ：０３７０ｉｎ１０ —３１００３．３文章编ｇ：０２８３（００３－２９０文献标识码：中图分类号：Ｐ９ＯＩ１．８．ｓ．２８３．１，５０７ｓ０２６－１０ —３ｌ２１）５０１－３ＡＴ３

抛物型方程反问题的混合粒子群算法

西安理工大学理学院，安７０５西１０４
ＳｈｏｆＳｉｎｅＸｉａｉｅｓｔｆＴｅｈｏｏｙ， ’ ｌ７０５Ｃｉａｃｏｌｏｃｅｃ， ’ ｌＵｎｖｒｉｏｃｎｌｇＸｉａｌ１０４，ｈｎｌｙ
摘要：粒子群优化算法（Ｓ是一种新兴的优化技术，ＰＯ）它的思想来源于人工生命和演化计算理论。ＰＯ通过粒子追随自己找到Ｓ
的最好解和整个群的最好解来完成优化。粒子群算法简单容易实现，可调参数少，已经得到了广泛研究和应用。提出了一种结合有限元方法求解偏微分方程反问题的混合粒子群算法，在对多个抛物型方程反问题模型测试的数值模拟中都得到了较好的结
ａｙｏｕａｉｎＴｅｌｏｉｍｃｍｐｅｅｔｅｐｉｚｔｏｔｒｕｈｏｌｗｉｇｔｅ－ｅｓｎｌｂｓｓｌｔｎｏａｈｐｒｉｌｄｒｃｍｐｔｏ．ｈａｇｒｈｔｔｏｌｔｓｈｏｔｍｉａｉｎｈｏｇｆｌｏｎｈｐｒｏａｅｔｏｕｉｆｅｃａｔｅａｏｃｎｈｇｏａｅｔｖｌｅｆｔｗｈｌｓｒ１Ｏａｅｍｐｅｎｅｔａｅｎｅｐｒｍｅｅｓｅｄｔｅｔｍｅ．ａｔｅｌｂｌｂｓａｕ０ｅｈｏｅｗａｎ．ＰＳｃｎｂｉｌｍｅｔｄｗｉｅｓａｄｆｗａａｔｒｎｅｏｂｕｈｄＩｈｓｔ
ｂｅｓｃｅｓｕｌａｐｉｄｉａｙｒａ．ａｅｒｆｒｂｅｒｓｌｉｓｍｅｉｖｒｅｐｏｌｍｓｏａａｏｉｑａｉｎｍｏｅ ’ ｅｎｕｃｓｆｌｙｐｌｅｎｍｎａｅｓＩｃｎｇｔｐｅｅａｌｅｕｔｎｏｎｅｓｒｂｅｆｐｂｌｅｕｔｏｄｌＳｔｓｒｃ

新型混合粒子群算法在核动力设备优化设计中的应用

ｔｈｃｌｐｉｍ．Ａｎｉｒｖｄｃｍｐｅｌｏｔｍｓｅｌｙｄｆｒｏｔｉｉｇｂｔｒｒｓｌｅｃｉｖｎｅ — ｏｔｅｌａｔｏｏｍｕｍｐｏｅｏｌｘａｇｒｈｗａｍｐｏｅｂａｎｎｅｔｕｔｗｈｎａｈｅｉｇｉｒｉｏｅｅｓｔａｉｎｔｓｉｒｅｍｐｏｅｔｅａｃｒｃｆｔｅｏｔｌｅｕｔｅｔｇｔｅｂｎｈｒｕｃｉｎｔｒｕｈｔｅｏｔｔｍｅｏｄｒｔｉｒｖｈｃｕａｙｏｐｉｏｉｎｏｈｍａｒｓｌ．Ｔｓｎｅｃｍａｋｆｎｔｏｇｈｐｉｉｈｏｈ —
合形法产生初始可行群体，加快粒子群收敛速度；引入遗传算法的交叉和变异策略，避免粒子群陷入局部最优；在迭代末期的优解附近，进行改进复合形算法的寻优，提高最优解的精度．过算法测试基准函数的优化计算，通结果显示，型混新合粒子群算法有较好的优化性能，并在核动力设备优化设计中有很好的应用．关键词：粒子群算法；复合形算法；遗传算法；核动力设备；优化设计
（ｏｅｅｏｕｌｒｃｎｅａｄＴｃｎｌｇ，ａｂｎＥｇｅｒｇＵｉｒｉ，ａｂｎ１００，Ｃｉ）ＣｌｇｆｃａｉｃｎｅｈｏｏｙＨｒｉｎｉｅｉｎｖｓｙＨｒｉ５０１ｈｎｌＮｅＳｅｎｎｅｔａ
ＡｂｓｒｃＴｈｔｎａｄｐａｔｃｅｓｒｌｏｔｍｉａｉｎｈｓｔｅｓｏｔｏｎｓｏｌｗｏｖｒｅｃｐｅｄａｄｐｏｃｕｔａｔ：ｅｓａｄｒｒｉｌｗａｎｐｉｚｔｏａｈｈｒｃｍｉｇｆｓｏｃｎｅｇｎｅｓｅｎｏｒａｃ－ｒｃｆｃｎｅｇｎｃａｙｏｏｖｒｅｅ，ｗｈｌａｉａｌｎｎｏｔｅｌｃｌｏｔｍｕｍｅｅｉｇｗｉｈｎｎｉｅｒｃｎｓｒｉｔｏｔｍｉａｉｎｉｅｅｓｌｆｌｇｉｔｈｏａｐｉｙｉｗｈｎｄａｎｔｏｌｎａｏｔａｎｐｉｚｔｏｌｐｏｌｍｓｒｂｅ．Ｔｏｏｅｃｍｅｔｓｉｉｕｔｓｅｋｎｆｙｒａｔｌｗａｌｐｔｚｔｏｌｏｔｍｓｄｓｇｅｖｒｏｈｅｅｄｆｃｌｉ，ａｎｗｉｄｏｂｄｐｒｉｅｓＦｌｆｅｈｉｃｌｏｉａｉｎａｇｒｈｗａｅｉｎｄ；ｍｉｉ

一种新混合粒子群算法及其在阵列天线方向图综合中的应用

一种新混合粒子群算法及其在阵列天线方向图综合中的应用作者：姚旭曹祥玉陈沫来源：《现代电子技术》2008年第08期摘要：针对传统粒子群算法（PSO）中存在的易陷入局部最优解和后期收敛速度慢的问题，首次提出一种新混合粒子群算法（NHPSO），采用杂交粒子群算法和固定惯性权重策略，并把简化的二次插值法融入杂交粒子群算法中。

实验证明新算法大大提高了收敛速度，改善了解的质量。

对阵列天线特殊主瓣形式的波束赋形和旁瓣电平优化结果取得了非常好的效果，计算机仿真证实该新算法应用于此类问题非常有效。

关键词：粒子群算法；混合粒子群算法;二次插值法；阵列天线；波瓣赋形中图分类号：TN82文献标识码：B文章编号：1004-373X(2008)08-084-YAO Xu,CAO Xiangyu，(Laboratory of Microwave and Antennas Technology,Telecommunication College,Air ForceAbstract：A hybrid Particle Swarm Optimization(PSO) algorithm is proposed with fixed inertia weight in the hybrid particle swarm optimization algorithm,and a simplified quadratic interpolation method is integrated into this algorithm,aiming at overcoming easily trapping in the local extreme points and slow evolving speed of convergence.The experiment shows that this new algorithm improved the global search ability and the quality of optima.The results of both mainlobe shaping and sidelobe levels are very effective.The simulation results prove that the proposed hybrid new algorithm is efficieKeywords：particle swarm optimization algorithm;hybrid particle swarm optimization algorithm；quadratic interpolation method;array antennas;shaped beam在雷达、无线通信等众多领域中,常要求阵列天线具有确定的主瓣宽度、特殊形状的主瓣形状 (如余割波束、余割平方波束、扇形波束等)和低的副瓣电平。

用于约束多目标优化问题的混合粒子群算法

ｕｅｏｔｓｔｅｐｒｒｎｅｏｈｌｏｔｍ．ｘｅｍｅｔｌｒｓｌｈｗｈｔｔｅｐｏｏｅｐｒａｈｉａｆｃｎｄｏｔｓｄｔｅｔｈｅｆｍａｃｆｔｅａｇｒｈＥｐｒｎａｅｕｔｓｏｔａｈｒｐｓｄａｐｏｃｓｎｅｉｔａｕ－ｏｉｉｓｉｅｎ
域一个研究的热点。但研究更多的局限于无约束优化问题。然而，在科学研究与工程应用中，多应用问题最终都归结为许求解带有约束条件的函数优化问题，因此，研究基于粒子群优化算法求解约束优化问题是有着重要的理论意义和应用价
１引言
近年来，用粒子群算法ｎ】目标优化问题已成为优化领求解
ＭＯＰＯ一般不必进行适应度赋值，算法设计得到简化，Ｓ使但ＭＯＰＯ必须为每个粒子从外部档案中选取一个合适的全局Ｓ最好位置，这是ＭＯＡ设计中所没有的。本文在此工作基础Ｅ上提出一种混合多目标粒子群优化算法，该算法引入Ｐｒｔ支ａｏｅ配关系思想，锦标赛选择和排挤距离选择技术，引进免疫机并
ｉｎｐｏｌｍ．ｍｐｔｒＥｎｉｅｒｎｎｐｉｔｎ，０１４（５４－２ｔｏｒｂｅＣｏｕｅｇｎｅｉｇａｄＡｐｌａｏｓ２１，７１）：９５．ｃｉ
ＡｂｔａｔＡｈｂｄｐｒｃｗｒａｇｒｈｏｒｓｌｉｇｏｓａｅｌ—ｂｅｔｅｐｉｚｔｎｐｏｌｉｐｏｏｅ，ｓｃ：ｙｒａｔｌｓａｍｌｏｔｍｆｏｖｎｃｎｔｉｄｍｕｔｏｊｃｉｏｔａｉｒｂｅｓｒｐｓｄｉｒｉｉｅｉｒｎｉｖｍｉｏｍｎ

求解非线性方程组的混合粒子群算法

ＣｍｕｅＥｇｎｅｉｎＡｐｉｔｎ计算机工程与应用ｏｐｔｎｉｒｇａｄｐｌａｉｓｒｅｎｃｏ
２１，７９０１４（）
３３
求解非线性方程组的混合粒子群算法
欧阳艾嘉刘利斌乐光学，肯立，，～李
ｆｎｔｏｓＣｏｕｅｇｎｅｉｇａｄＡｐｌａｏｓ２１４（：３３．ｕｃｎ．ｍｐｔｒＥｎｉｅｒｎｎｐｉｔｎ。０１，７９）３－６ｉｃｉ
Ａｂｔａｔｓｒｃ：ＡｂｉＰｒｉｌＳｒＨｙｒｄａｔｅｗａｍＯｐｉｚｔｎ（ＳｃｔｍｉａｉＨＰＯ）ａｇｒｈ，ｉｈｃｍｂｎｓｈａｖｎａｅｏｈｍｅｈｄＨｏｋ－ｏｌｏｔｍｗｈｃｏｉｅｔｅｄａｔｇｓｆｔｅｉｔｏｏｅＪｅｅ（）ａｄＰｒｉｌｗａｍＯｐｉｚｔｎ（ＳｅｖｓＨＪｎａｔｅｃＳｒｔａｉＰＯ），ｓｕｆｒｒｔｓｌｅｙｔｍｓｆｎｎｉｅｒｕｃｉｎ，ｎｔａｂｍｉｏｉｐｔｏｗａｄｏｏｖｓｓｅｏｏｌａｆｎｔｓａｄｉｎｏｃｎｅ
ＯＡＮＧＡｉＬＵｉｉＹｕｎｘｅＬｎｉＵＹｉａ，ＩＬｂｎ，ＵＥＧａｇｕ，ＩＫｅｌｉ１兴学院数理与信息工程学院，江嘉兴３４０．嘉浙１０１
２池州学院数学与计算机科学系，．安徽池州２７０４００３南大学计算机与通信学院，．湖长沙４０８１０２

混合粒子群算法及在可靠性优化中的应用

ｌ前言
粒子群优化（ＰｒｃｗｒｐｉｉｔｎＰＯ是ａｔｌＳａｍＯｔｚｉ，Ｓ）ｉｅｍａｏ
一
本文利用混沌（ｈｏ）ｃａｓ￣动具有的随机性、遍历性和规律性及具有较强的全局寻优能力，不易陷入局部极小点特点，结合和声搜索算法（ｒｎｅｒＨＳＨａｍｏｙＳａｃｈ，）的启发式全局搜索和强开发能力，提出一种基于混沌和声搜索的混合粒子样优化算法。该算法采用Ｔｎ映ｅｔ射，利用混沌产生大量初始粒子并选择较优的粒子作
有较强的开发能力。
；＝Ｘｒ，ｉ＋ｏ，／，，ｇ：
（７）
式中：７为扰动幅数：Ｏ为方差向量；ｉ７值参、
；分别为整体和个体步长：Ａ、Ｂ为比例系数。
３３自适应参数策略．
由于参数Ｏ、和是影响ＰＯ收敛效果的关ＪＳ
键因素，在ＰＯ算法中，和都是被设置为绝对随Ｓ机数，其实这样并不能保证在优化时对状态空间进行完全遍历。为了提高算法的全局收敛性，本文采用公式（）对参数和进行混沌优化：８
为初始粒子群，同时采用和声策略对解空问进行开发，
种高效的优化搜索算法，源于对鸟群和鱼群群体运
动行为的研究。ＰＯ的基本思想是通过群体中个体间Ｓ
的协作和信息共亨来寻找最优解。ＰＯ算法简单、容Ｓ
易实现、搜索速度快、搜索范围大，ＰＯ算法在很多Ｓ问题中已成功应用。与其他智能算法类似，ＰＯ也存Ｓ
本文利用混沌变量的遍历特性在解空间内进行有效探索，同时采用和声算法中的和声策略对解空间进

遗传粒子群优化算法混合

遗传粒子群优化算法混合遗传算法（Genetic Algorithm，GA）和粒子群优化算法（Particle Swarm Optimization，PSO）是两种常见的进化优化算法，它们各自有着优点和不足。

为了充分发挥它们的优势并弥补其不足之处，研究者们对这两种算法进行了混合。

本文将详细介绍遗传粒子群优化算法混合的相关内容。

首先，我们来了解一下遗传算法和粒子群优化算法的原理和特点。

遗传算法是一种模拟生物进化过程的优化算法，其基本思想是通过生物进化中的遗传、变异和选择等算子来最优解。

遗传算法通常由编码、适应度评价、选择、交叉和变异等步骤组成。

编码将待优化问题的解表示为染色体，适应度评价函数用于度量染色体的优劣，选择算子根据适应度选择个体进行繁殖，交叉算子和变异算子模拟生物的遗传和变异操作。

粒子群优化算法是一种模拟鸟群觅食行为的优化算法，其基本思想是通过多个粒子在解空间中的和迭代来找到最优解。

每个粒子都有自己的位置和速度，通过更新速度和位置来不断调整方向和距离。

粒子群优化算法主要包括初始化粒子群、更新速度和位置、更新最优个体和全局最优个体等步骤。

遗传粒子群优化算法混合的基本思想是将粒子群优化算法的能力和遗传算法的全局优化能力结合起来，形成一种新的混合优化算法。

具体来说，在遗传算法的基础上引入粒子群优化算法的思想和操作，使得算法能够更好地在空间中寻找到全局最优解。

将遗传算法和粒子群优化算法进行混合有以下几种常见的方式：1.遗传算法与粒子群优化算法交替使用：先使用遗传算法进行初始化种群和进行交叉变异操作，然后再使用粒子群优化算法进行和更新操作。

通过交替使用这两种算法，可以综合利用它们的优点，提高算法的效率和精度。

2.遗传算子和粒子群优化算法算子的融合：将遗传算法和粒子群优化算法的算子进行融合，形成一种新的算子。

例如，可以将遗传算法的交叉操作与粒子群优化算法的速度更新操作相结合，形成一种新的交叉操作方式；或者将遗传算法的变异操作与粒子群优化算法的位置更新操作相结合，形成一种新的变异操作方式。

混合粒子群优化算法

ＨｅｉｌｇｆｏａｉｎａｄＴｃｎｌｇ，ｂ，ｎｎ４８３，ｉａｂｌｅｏＶｃｔｎｅｈｏｏｙＨｅｉＨｅａ５００ＣｈｎＣｏｅｏ
ＺＨＵｉｇＱＩｉｇｕ．ｂｉａｔｌｒｏｔｚｔｎａｇｒｔｍ．ｍｐｔｒｎｉｅｒｇａｄＡｐｉｔｎ，０２４（）Ｂｎ．ｎｊｎＨｙｒｄｐｒｃｓｍｐｍｉｉｌｏｉＭｉｅｗａｉａｏｈＣｏｕｅｇｎｅｎｎｐｌａｏｓ２１，８９：Ｅｉｃｉ
ｃｅｓｒａｇｒｔｍｉｈｈｓｏｌｎｔｅｓａｕ，ｔａａｔｒｃｎｅｇｎｅｒｔ．ｓｅｉｌｅｈｂｉａｔｌｗａｍｐｉｚｔｎｌｗａｍｌｏｈｗｈｃａｎｙｏｅｆｎｓｌｅｉｈｓｆｓｅｏｖｒｅｃａｅＥｐｃａｌｔｙｒｄｐｒｃｅｓｒｏｔｉｉｖｙｈｉｍｉａｉｏ
ＣｍｕｒｎｉｅｉｄｐｌａｏｓｏｐｔｇｎｒｇｎＡｐｉｔｎ计算机工程与应用ｅＥｅｎａｃｉ
混合粒子群优化算法
朱冰，齐名军
ＺＨＵｎ，ｎｊｎＢｉｇＱｉＭｉｇｕ
鹤壁职业技术学院，河南鹤壁４８３５００
ＫｅｒｓＰｒｉｌｗａｔｚｔｎｍｕｔ—ｔａｅｃａｉｍ；ｒｍａｕｉｃａｉｍｙｗｏｄ：ａｔｅＳｒＯｐｉａｉ；ｌｓｔｇｍｅｈｎｓｐｅｔｒｔｍａｈｎｓｃｍｍｉｏｉｒｙｙ

基于差分进化混合粒子群算法的电力系统无功优化

一
（ｏＯＢｓ０）０Ｇｃｓｏｉｏ＝＋ｎ．
Ｑ— Ｖ
（ｉ０－ｏＯ）ＯＧｓＢｃｓ￣＝ｎ
（）２
置为＝ｘ … … ，；ｉ粒子飞行历史中的（ＸＸ）第个
最优位置为Ｐ＝ｐ …… ，，ｉ（Ｐｐ）设为所有Ｐ中的Ｉ最优值；ｉ粒子的速度为向量＝Ｖ，第个（ …… ，
ＲｅｃｉｅＰｏｒＯｐｉｚｔｏｆＰｗｅｙｔｍｓｄｏｆｅｅｔａａｔｖｗｅｔｍｉａｉｎｏｏｒＳｓｅＢａｅｎＤｉｒｎｉｌ
ＥＶｌｔ０ — ａｔｃｅＳｒｔｉａｉｎ０ｕｉｎｐｒｉｌｗａｍＯｐｉｚｔｏｍ
Ｖ（１＝ｏ（＋１ｒｎ（ ×尸（）（１／ｔ）ｃＤ＋ × ｆｃｘａｄ）【 — ＋） — ）
（）不等式约束３配电网无功优化问题中的变量可分为控制变
量和状态变量。
ｃｘａｄ）【ｔ－］２ｒｎ（ ×ｐ）ｘ（）（
ｓｌｔｎｏｅａｏｆｉｅｎｉｖｌｔｎ（Ｅｏｃｅｔｎｗｇｏｐ，ｎｅｏｓｌａｓａｈｎｙｐｒｃｅｓａｍｏｔｉｔｎｅｃｉｐｒｔｒｆｒｔｌｏｕｉＤ）ｔｒａｅｒｕｓａｄｔｎｄｅｃｌｅｒｉｇｂａｔｌｗｒｐｉｚｉｅｏｏｄｆｅａｅｏｅｈｏｃｉｍａｏ
和ＤＥ的全局优化性能好的优势，有效克服各自的并

求解非线性方程组的混合粒子群算法_欧阳艾嘉

1 引言
非线性方程组的求解是一个基本而又重要的问题，这是因为在工程技术、经济学、信息安全和动力学等方面有大量的实际问题最终转化为非线性方程组的求解问题。长期以来，对非线性方程组在理论和数值计算方面都做了大量的研究，但是对其求解还是一个难题[1]，由于传统数值求解常用的牛顿-拉普辛迭代法需要给定初始迭代值，而且具有对初始迭代值的敏感性，同时牛顿-拉普辛方法还会遇到计算函数的导数和矩阵求逆问题，对于某些导数不存在或是导数难求的方程，牛顿-拉普辛方法具有一定局限性[2-4]。Hooke-Jeeves 具有算法简单，不需要求解目标函数的导数，收敛快速的求解特点，存在的缺点是对初始值敏感。粒子群优化算法是群智能算法中的一种，该方法具有群体智能、迭代过程相对简单和收敛速度较快等优点，但是它的局部搜索能力比较差，不能有效求解高维、复杂的非线性方程组问题。
Abstract：A Hybrid Particle Swarm Optimization（HPSO） algorithm，which combines the advantages of the method HookeJeeves（HJ） and Particle Swarm Optimization（PSO），is put forward to solve systems of nonlinear functions，and it can be used to overcome the difficulty in selecting good initial guess for HJ and inaccuracy of PSO due to being easily trapped into local optimal.The algorithm has sufficiently displayed the performance of PSO’s global search and HJ’s accurate local search.Numerical computations show that the approach has great robustness，high convergence rate and precision，and it can give satisfactory solutions. Key words：systems of nonlinear functions；Hooke-Jeeves；particle swarm optimization

采用混合粒子群算法实现匹配追踪算法

中图分类号：Ｔ２７Ｐ７文献标识码：Ａ
在信号处理理论研究和工程应用中，号的分解信
和表达是一个根本性的问题，有非常重要的意义。具通用的信号分解方法是把信号分解在一组完备正交基上，如傅里叶变换、小波变换等。为了改善一些复杂信
从公式（）（）以看出，于Ｍ的信号分解１，２可基Ｐ
中，每一步都要完成信号或信号残差在过完备库中的每一个原子上的投影计算，后取极大值。按照公式然
（）求，２要每一步分解实质上要进行的计算都是一个在高维空间进行多次的内积计算，这是造成使用ＭＰ进行
（）２
在实际应用中，ＭＰ每次求解匹配的最佳原子参数
为．ｔ第ｋ次分解后的残差信号，为参数组厂）（，
时，般采用牛顿法或者遗传算法等方法进行计一算ｌ。但是采用牛顿法需要进行大量的内积运算，＿３ ¨ 所以当选择使用较大的时频原子库时，算量太大将计
得到矢量的线性组合的信号分解方法，里表示信号这分解的基函数被称为原子，可以自适应的根据信号它本身的特点灵活选取，解结果简洁。目前Ｍ分Ｐ在信号
压缩、噪、码、别、去编识时频分布和微弱信号的提取中

混合粒子群算法的软件测试数据自动生成

混合粒子群算法的软件测试数据自动生成AbstractSoftware testing is a crucial part of software development, and the accuracy of testing largely depends onthe quality of test data. In recent years, the application of artificial intelligence in software testing has been widely studied. Among them, Particle Swarm Optimization (PSO) andits variant, Hybrid Particle Swarm Algorithm (HPSO), havebeen successfully applied to software testing data generation. In this paper, we introduce the HPSO algorithm and its application in software testing data generation. We conduct experiments to demonstrate the effectiveness and efficiencyof the HPSO algorithm in generating test data.Keywords: software testing, test data generation, HPSO algorithm, particle swarm optimization, hybridization.1. IntroductionSoftware testing is an important aspect of software development process. The purpose of software testing is to ensure the software system meets its functional requirements and that it performs as expected before it is released to the end-users. Test data generation is a crucial part of software testing. The quality of testing is largely dependent on the quality of test data. As such, designing high-quality testdata is a key element of software testing. Good test data should be able to cover all possible conditions and scenarios to achieve the maximum possible testing coverage.Conventionally, software testing is done manuallythrough test case design by human testers. However, manualtesting can be time-consuming, labor-intensive, and not comprehensive enough to achieve maximum coverage. Moreover, manual testing can be error-prone, leading to inaccurate test results. As such, software testing has seen the integration of artificial intelligence in an attempt to automate the test data generation process.Artificial intelligence has been employed to develop algorithms that aim to generate high-quality test data. Among these algorithms, Particle Swarm Optimization (PSO) has been widely researched for its capability of generating high-quality test data. Hybrid Particle Swarm Optimization (HPSO), a variant of the PSO algorithm, has also been developed to improve test data generation. In this paper, we explore HPSO and its application in software testing data generation.2. Particle Swarm OptimizationParticle Swarm Optimization (PSO) is a swarmintelligence algorithm that was inspired by the social behavior of bird flocking and fish schooling. It was first introduced by Kennedy, and Eberhart in the year 1995. PSO is categorized as a population-based optimization algorithm, and it is one of the most commonly used metaheuristic algorithms in the literature due to its simplicity and efficiency.PSO is an iterative optimization algorithm that starts with the initialization of a population of random particles, each particle is associated with a location in the search space and a velocity vector. Each particle within the population represents a potential solution to theoptimization problem. In each iteration, the particles adjust their position and velocity towards their own best solution and the best solution of the swarm. The position of aparticle is updated using Equation 1, where xi, vi, pbesti,and gbest represent the current position of the ith particle, the velocity of the ith particle, the best solution found by the ith particle, and the best solution found by the swarm, respectively. The parameters w, c1, and c2 are the inertia weight, the cognitive weight, and the social weight, respectively, and rand1, and rand2 are random numbers in the range [0,1].xi(t + 1) = xi(t) + vi(t + 1) (1)vi(t + 1) = wvi(t) + c1rand1(pbesti – xi(t)) + c2rand2(gbest – xi(t)) (2)The update rule in Equation 1 determines the newposition of the ith particle by adding its current velocity vector to its current position vector. The velocity vector of a particle is updated using Equation 2, which considers the previous velocity of the particle, the distance to its own best position, and the best position of the swarm.In PSO algorithm, the parameters w, c1, and c2 control the strength of the inertia term, cognitive component and social component, respectively. The inertial weight controls the amount of momentum of the particle velocity while the cognitive component and social component regulate the contribution of the personal and social experiences of the particle, respectively. The parameters w, c1, and c2 are typically fine-tuned for each optimization problem in practice.3. Hybrid Particle Swarm AlgorithmIn real-world problems such as software testing, PSO suffers from several limitations. One of the most significant drawbacks of the PSO algorithm is its premature convergence problem. This occurs when some particles in the swarm converge towards a suboptimal solution instead of the globaloptimum. This problem arises due to the exploration-exploitation trade-off issue, where exploration is requiredto avoid getting stuck in local optima while exploitation is necessary to converge to a global optimum.Hybrid Particle Swarm Optimization Algorithm (HPSO) is developed by combining the PSO with a local search operatorto remedy the premature convergence problem of the PSO algorithm. In HPSO, the search space is divided into several regions. Each particle moves within its corresponding search space region. The local search operator is applied to all particles in their respective regions to refine the positions of each particle. Moreover, the elite particles that perform the best during the search are kept in the swarm and their knowledge is used to update the positions of all particles.The HPSO algorithm can be summarized as follows:Step 1. Initialize the particle swarm.Step 2. Evaluate the fitness of each particle in the swarm.Step 3. Update the local best positions of each particle.Step 4. Update the global best position.Step 5. Apply local search to all particles in their local search regions.Step 6. Update the velocity and position of each particle.Step 7. Repeat from Step 2 until the stopping criteria are met.The HPSO algorithm enhances the PSO algorithm by including a local search operator. The local search operator provides an additional exploration strategy to overcome the premature convergence problem of the PSO. The local search operator randomly modifies the solution in the neighbor ofthe current solution to prevent the algorithm from getting stuck in a local optima. Local search operators can take many forms; in software testing, common forms include mutation and crossover operators.4. Application of HPSO in Software TestingThe ultimate goal of software testing is to ensure that the software system performs as expected. To achieve this goal, testers need to generate test data that can effectively reveal defects in the code under test. HPSO algorithm has been applied in software testing to generate high-qualitytest data. The HPSO algorithm can be used to optimize the input values of the software system under test to maximize the coverage of the test suite.In software testing, the HPSO algorithm can be used to optimize the input values of the software system under testto maximize the coverage of the test suite. The HPSO algorithm determines the optimal input values that will help to reveal the most edge case scenarios. The edge-case scenario testing will expose faults and verify the robustness of the software system under test.In the HPSO application for software testing, the search space for optimizing the input values is defined based on the input domains. The input domain is the set of all possible values that can be used to execute the software system. The HPSO algorithm is used to explore the search space to generate test data that can effectively validate the software system. The fitness function in HPSO algorithm calculates the quality of the generated test data. The quality of the generated test data is evaluated based on the coverage achieved in executing the software system under test. The objective is to maximize the coverage of the software systemunder test using the generated test data.5. Experimental ResultsTo evaluate the effectiveness of HPSO in softwaretesting data generation, we conducted experiments on two software systems, S1 and S2. In the experiments, we compared HPSO with two other algorithms, Genetic Algorithm (GA) and PSO.In the first experiment, we tested the HPSO algorithm, and we varied the size of the swarm from 10 to 50 particles. The results show that the size of the swarm has a significant effect on the quality of the generated test data. The larger the swarm size, the higher the coverage achieved by the generated test data.In the second experiment, we tested the HPSO algorithm, and we varied the number of iterations from 100 to 500 iterations. The results show that the number of iterations has a significant effect on the quality of the generated test data. The higher the number of iterations, the higher the coverage achieved by the generated test data.In the third experiment, we tested the HPSO algorithm, and we compared it with GA and PSO. The results show that HPSO outperforms GA and PSO in terms of generating high-quality test data.6. ConclusionIn this paper, we introduced the Hybrid Particle Swarm Optimization algorithm and its application in softwaretesting data generation. We demonstrated that HPSO algorithm outperforms GA and PSO in terms of generating high-quality test data. The HPSO algorithm provides a simple and efficient way to optimize input values of a software system under test. The quality of the generated test data is evaluated based onthe coverage achieved in executing the software system under test. The experimental results show that the size of the swarm and the number of iterations have a significant effect on the quality of the generated test data.Future work can be done to evaluate HPSO algorithm performance in conjunction with other software testing techniques such as model-based and mutation testing. A comprehensive evaluation on different testing techniques is required to establish an accurate benchmark for HPSO algorithm performance. Further studies can also focus on improving hybrid algorithms that are optimized for software testing. In summary, HPSO algorithm provides significant improvements in software testing data generation and has the potential to enhance the quality of software testing.。

求解背包问题的混合粒子群优化算法

ｅＥｎｉｅｒｇａｄＡｐｉｔｎ，０２４（）４ —６ｒｇｎｅｉｎｐｌａｉｓ２１，８１：４４．ｎｃｏ
ＡｂｔａｔＡｅｇｎｔｄａｔａｆｓｒｇ’ ｅｅｉｅｉｅｙｉａｅｔＳｒｔｅａｒｄｃｄｂｉｌｒｓｓｐｏｏｅ． — ｓｒｃ：ｎｗｅｅｉｉｅｔｆｐｎＳｎｓｄｃｄｄｂｓｐｒｎ ’ ，ａｈｒｔｎｐｏｕｅｙａｓｍｐｅｃｏｓｉｒｐｓｄＡｃｃｈｏｉｇｔｈｃｒｉｇｔｈｓｉｅ，ｗｏｍｅｈｄｆｒｄｃｎｆｓｒｇｗｉｅｅｉｒｂｂｌｙａｅｐｏｕｅｎｅｅｃｍｂｎｄｗｉｅｐｒｉｌｏｄｎｔｉａｔｔｏｓｏｏｕｉｇｏｐｉｔｇｎｔｐｏａｉｔｒｒｄｃｄａｄｔｙａｏｏｄｐｎｈｃｉｈｒｉｅｔｔａｔｅｈｈｃｓｒｎｏｔｚｔｎｒｓｅｔｅｙＴｅｔｏｈｂｉａｉｌｗａｍｐｉｚｔｎｒｐｌｄｔｏｖｎｎｐａｋｐｏｌｍ，ｎｅｒｐｒｗａｌｐｉａｉｅｐｃｉｌ．ｈｙｒｄｐｒｃｅｓｒｏｔｍｉｏｖｗｔｍｉａｉｓａｅａｐｉｓｌｉｇｋａｓｃｒｂｅａｄｔｉｅ－ｏｅｏｈ
Ｋｅｒｓｐｒｃｅｓｒｏｔｚｔｎｋａｓｃｒｂｅ；ｅｅｉｒｂｂｌｙｙｗｏｄ：ａｔｌｗａｍｐｉａｉ；ｉｍｉｏｎｐａｋｐｏｌｍｇｎｔｐｏａｉｔｃｉ

差分进化混合粒子群算法求解项目调度问题

信息判断而陷入局部最优点。采用标准测试函数和具体算例进行检验，结果表明ＰＯＥ算法可以较好地解决ＳＤ
ＲＣＰ问题。Ｓ
关键词：差分进化混合粒子群算法；粒子群算法；差分进化算法；目调度项
中图分类号：Ｔ３１Ｐ９文献标志码：Ａ文章编号：１０ —６５２１）４１８ —４０１３９（０１０ —２６０
Ａｓａｔｏｒｓｕｃ —ｏｓａｎｄｐｏｃｓｈｄｌｇｐｏｌＲＰＰ，ｐｏｏｅｈｙｒａｉｅｓａｍｏｔｉｔｎｂｔｃ：Ｆｒｅｏｒｅｃｎｔｉｅｒｅｔｅｅｕｉｒｂｅｒｒｊｎｍ（ＣＳ）ｒｓｄｔｈｂｉｐｒｃｗｒｐｍｚｉｐｅｄｔｌｉａｏ（ＳＰＯＤＥ）ａｅｎｄｆｒｎｉｌｅｏｕｉｎ（Ｅ）ｈｅｌｏｉｍｅｔｂｉｈｄａｎｏｍａｉｎｅｃａｇｃａｉｍｂｔｅｎｂｓｄｏｉｅｅｔｖｌｔｆａｏＤ．Ｔｅｎｗａｇｒｈｓａｌｅｎｉｆｒｔｘｈｎｅｍｅｈｎｓｅｗｅｔｓｏ
ａｄｓｅｉｉｘｍｐｌｓＴｉｅｒｓｔｈＷｈｔＰＳｎｐｃｆｃｅａｅ．ｌｅｕｌｓｓｏｔａＯＤＥａｇｒｔｌｏｉｈｍａｌｏｖｃｎｗｅｌｓｌｅＲＣＰＳＰ．
ＫｅｒｓｙｒａｔｌｓａｍｐｉｚｔｎａｇｒｈａｅｎｄｆｒｎｉｌｖｌｔｎａｔｃｅｓａｆｐｉｚｔｎＰＯ）ｙｗｏｄ：ｈｂｉｐｒｃｅｗｒｏｔａｉｌｏｉｍｂｓｄｏｉｅｅｔｏｕｉ；ｐｒｌｗｒ３ｏｔａｉ（Ｓ；ｄｉｍｉｏｔｆａｅｏｉｉｍｉｏｄｆｒｎａｅｏｔｎｐｏｃｓｈｄｌｇｉｅｅｔｌｖｌｉ：ｒｅｔｃｅｕｎｉｉｕｏｊｉ

一种基于运动方向变异的混合粒子群算法研究

的优化问题。但该算法全局探索能力较弱，一旦算法发现局部最优点，粒子会聚集到该点并停止移动，导致过早收敛而出现早熟现象，因此前人提出了一些改进后的ＰＳＯ算法＿１］。
１．１运动方向变异的改进粒子群算法原理
节向全局最好粒子和个体最好位置方向飞行的最大步长。合适的ｃ和ｃ。可以加快收敛且不易陷入局部最优；ｒａｎｄ和ｒａｎｄ是两个相互独立的随机数，取值一般为［ｏ，１］］。粒子群算法自提出以来，因为参数调整简单、计算效率高等特点，受到广泛的关注，成功应用于各种复杂
增加线性时变学习因子的方法，提出了一种混合改进粒子群算法。
２一种混合改进粒子群算法的原理
２．１分段变异粒子运动方向的改进
相对于粒子运动方向变异的改进中，方向变异贯穿整个迭代过程，虽然增加了迭代初期的粒子运动范围，但也使得迭代后期粒子难以收敛，收敛时间变长。本研究对迭代时间进行分段，即在前一段迭代过程中，
的影响较小，主要是在当前解的附近搜索，局部搜索能力较强，有利于算法收敛。在实际应用中发现，惯性权重与种群规模也有很大的关系，种群规模越小，需要的惯性权重越大，因为此时种群需要更好的探索能力来

一种新型的混合粒子群算法

Ａｂｓｒｃｔａｔ：Ａｉｎｔｔｅｄｓｄａａｅｆｓｏｃｎｅｇｎｅｒｔｎｄｅｓｒｍａｕｒｔｆｐａｔｃｅｓｒｍｉｇａｈｉａｖｎｔｇｓｏｌｗｏｖｒｅｃａｅａａｙｐｅｔｉｙｏｒｉｌｗａｍ
Ａｎｗｈｂｉａｔｌｗｒｏｔｚｔｎｅｙｒｄｐｒｉｅｓａｍｐｉａｉｃｍｉｏ
ＮＵＹｎ－ｅＩｏｇｊｉ
（ｏｕｉｇＣｎｅ，ａ ’ｎＵｉｅｓｙ，Ｙｎａ１００ｈｎ）Ｃｍｐｔｅｔｒｒｎａｎｖｒｆｎｌａ ’ｎ７６０，Ｃｉａ
； ’ 荔信息垫，，勃； —
，
—
２１牟１００第０期
中图分类号：Ｐ０．Ｔ３１６
文献标识码：Ａ
文章编号：０９— ５２２１）０— ０４— ４１０２５（００１０９０
一
种新型的混合粒子群算法
牛永洁
（延安大学计算中心，延安７６０）１００
０引言
粒子群优化算法（ａｉｅｓａｐｉｚｔｎｐｒｃｗｒｏｔａｏ，ｔｌｍｍｉｉ
ｏｔｏ）９５年由美国的Ｋｎｅｙ和Ｅｅｈｒ提出¨ 。１９ｅｎｄｂｒａｔ粒子群优化算法因为具有深刻的智能背景，遗传与
摘
要：针对粒子群算法存在的收敛速度慢，容易早熟的缺点，为了获得更好的算法性能，采
用两种基本的改进策略，在ＭＡＬＢ２０ＴＡ０９中对几个典型测试函数的优化问题进行了实验，即采