一种新的智能优化及其改进研究

研究了一种新的进化算法-和声搜索(HS)算法,针对其在处理复杂函数优化问题时容易陷入局部最优、收敛精度低的缺点,提出一种改进的和声搜索算法,算法在保留和声搜索的搜索机理的同时,把混合蛙跳算法中的局部搜索策略引入其中,维持了和声库的多样性,从而提高了对复杂问题的搜索效率.与同类算法相比,本文提出的和声搜索算法全局搜索能力强,收敛速度快,数值实验结果验证了算法的有效性和鲁棒性.     

A harmony search algorithm for high-dimensional multimodal optimization problems

Harmony search (HS) and its variants have been found successful applications, however with poor solution accuracy and convergence performance for high-dimensional (≥200) multimodal optimization problems. The reason is mainly huge search space and multiple local minima. To tackle the problem, we present a new HS algorithm called DIHS, which is based on Dynamic-Dimensionality-Reduction-Adjustment (DDRA) and dynamic fret width (fw) strategy. The former is for avoiding generating invalid solutions and the latter is to balance global exploration and local exploitation. Theoretical analysis on the DDRA strategy for success rate of update operation is given and influence of related parameters on solution accuracy is investigated. Our experiments include comparison on solution accuracy and CPU time with seven typical HS algorithms and four widely used evolutionary algorithms (SaDE, CoDE, CMAES and CLPSO) and statistical comparison by the Wilcoxon Signed-Rank Test with the seven HS algorithms and four evolutionary algorithms. The problems in experiments include twelve multimodal and four complex uni-modal functions with high-dimensionality.Experimental results indicate that the proposed approach can provide significant improvement on solution accuracy with less CPU time in solving high-dimensional multimodal optimization problems, and the more dimensionality that the optimization problem is, the more benefits it provides.     

Improved Harmony Search Algorithm: LHS

In this paper, we propose an improved harmony search algorithm named LHS with three key features: (i) adaptive global pitch adjustment is designed to enhance the exploitation ability of solution space; (ii) opposition-based learning technique is blended to increase the diversity of solution; (iii) competition selection mechanism is established to improve solution precision and enhance the ability of escaping local optima. The performance of the LHS algorithm with respect to harmony memory size (HMS) and harmony memory considering rate (HMCR) are also analyzed in detail. To further evaluate the performance of the proposed LHS algorithm, comparison with ten state-of-the-art harmony search variants over a large number of benchmark functions with different characteristics is carried out. The numerical results confirm the superiority of the proposed LHS algorithm in terms of accuracy, convergence speed and robustness.     

A hybrid harmony search algorithm for the flexible job shop scheduling problem

In this paper, a novel hybrid harmony search (HHS) algorithm based on the integrated approach, is proposed for solving the flexible job shop scheduling problem (FJSP) with the criterion to minimize makespan. First of all, to make the harmony search (HS) algorithm adaptive to the FJSP, the converting techniques are developed to convert the continuous harmony vector to a kind of discrete two-vector code for the FJSP. Secondly, the harmony vector is mapped into a feasible active schedule through effectively decoding the transformed two-vector code, which could largely reduce the search space. Thirdly, a resultful initialization scheme combining heuristic and random strategies is introduced to make the initial harmony memory (HM) occur with certain quality and diversity. Furthermore, a local search procedure is embedded in the HS algorithm to enhance the local exploitation ability, whereas HS is employed to perform exploration by evolving harmony vectors in the HM. To speed up the local search process, the improved neighborhood structure based on common critical operations is presented in detail. Empirical results on various benchmark instances validate the effectiveness and efficiency of our proposed algorithm. Our work also indicates that a well designed HS-based method is a competitive alternative for addressing the FJSP.     

全局和声搜索方法及其在仿人灵巧臂逆运动学求解中的应用

仿人灵巧臂逆运动学(IK)问题可转化为等效的最小化问题,并采用数值优化方法求解.和声搜索(HS)是模拟乐师在音乐演奏中调整音调现象的一种启发式搜索方法,目前还尚未在机器人机械臂逆运动学问题中得到应用.本文提出一种基于粒子群体智能的全局和声搜索方法(GHSA),该方法在和声搜索算法中引入微粒群操作(PSO),采用粒子群策略替代常规和声搜索算法中的搜索法则创作新和声,通过粒子自身认知和群体知识更新和声变量位置信息平衡算法对解空间全局探索与局部开发间能力;同时算法还引入变异操作增强算法跳出局部最优解能力,基准函数测试表明该方法改善了全局搜索能力及求解可靠性.在此基础上以七自由度(7-DOF)冗余仿人灵巧臂为例,考虑以灵巧臂末端位姿误差和“舒适度”指标构建适应度函数并采用GHSA算法求解其逆运动学(IK)问题,数值仿真结果表明了该方法是解决仿人灵巧臂逆运动学问题的一种有效方法.     

用于求解连续优化问题的均匀设计和改造BLX-α的分散搜索算法

分散搜索算法是近年来快速兴起的一种基于种群的进化计算方法,与遗传算法不同的是,它对高质量解和多样性解并存的小数据集使用多种系统子方法和有限次随机过程来获取全局最优解或满意解.基于分散搜索的柔性框架,使用均匀设计来改进以往连续分散搜索算法中的多样性产生方法,将BLX-α算子加以相应改造作为解合并方法,提出了一种基于均匀设计和改造BLX-α算子的新型分散搜索算法(URBSS)来解决非线性连续优化问题.通过8个广为使用的测试函数进行了仿真实验,实验结果表明在与其他连续优化方法的比较中,URBSS能够准确快速地搜索到全局最优解,具有很好的收敛速度和全局优化能力.     

Hybrid sine cosine artificial bee colony algorithm for global optimization and image segmentation

Artificial bee colony (ABC) algorithm is an efficient biological-inspired optimization method, which mimics the foraging behavior of honey bees to solve the complex and nonlinear optimization problems. However, in some cases, it suffers from inefficient exploration, low exploitation and slow convergence rate. These shortcomings cause the problem of stagnation at local optimum which is dangerous in determining the true solution (optima) of the problem. Therefore, in the present paper, an attempt has been made toward the removal of the drawbacks from the classical ABC by proposing a novel hybrid method called SCABC algorithm. The SCABC algorithm hybridizes the ABC with sine cosine algorithm (SCA) to upgrade the level of exploitation and exploration in the classical ABC algorithm. The SCA is a recently introduced algorithm, which uses the trigonometric functions sine and cosine to perform the search. The validation of the SCABC algorithm is performed on a well-known benchmark set of 23 optimization problems. The various analysis metrics such as statistical, convergence and performance index analysis verify the better search ability of the SCABC as compared to classical ABC, SCA. The comparison with some other optimization algorithms demonstrates a comparatively better state of exploitation and exploration in the SCABC algorithm. Moreover, the SCABC is also employed on multilevel thresholding problems. The various performance measures demonstrate the efficacy of the SCABC algorithm in determining the optimal thresholds of gray images.

     

混合模式搜索的分布式memetic差分进化算法

针对差分进化（DE）算法存在的早熟收敛与搜索停滞的问题,提出memetic分布式差分进化（DDE）算法。将memetic算法的思想融入到差分进化算法中,采用分布式的种群结构以及memetic算法中的混合策略,前者将初始种群分为多个子种群,子种群间根据冯·诺依曼拓扑结构周期性地实现信息交流,后者将差分进化算法作为进化的主要框架,模式搜索作为辅助手段,从而平衡算法的探索与开发能力。所提算法充分利用了模式搜索和差分进化算法的优势,建立了有效的搜索机制,增强了算法摆脱局部最优的能力,能够满足搜索过程对种群多样性及收敛速度的需求。将所提算法与几种先进的差分进化算法相比较,对标准测试函数进行优化的实验结果显示：所提算法在解的质量和收敛性能方面,均优于其他几种相比较的先进的差分进化算法。     

Convergence analysis and performance of an improved gravitational search algorithm

Gravitational search algorithm (GSA) has been shown to yield good performance for solving various optimization problems. However, it tends to suffer from premature convergence and loses the abilities of exploration and exploitation when solving complex problems. This paper presents an improved gravitational search algorithm (IGSA) that first employs chaotic perturbation operator and then considers memory strategy to overcome the aforementioned problems. The chaotic operator can enhance its global convergence to escape from local optima, and the memory strategy provides a faster convergence and shares individual's best fitness history to improve the exploitation ability. After that, convergence analysis of the proposed IGSA is presented based on discrete-time linear system theory and results show that IGSA is not only guaranteed to converge under the conditions, but can converge to the global optima with the probability 1. Finally, choice of reasonable parameters for IGSA is discussed on four typical benchmark test functions based on sensitivity analysis. Moreover, IGSA is tested against a suite of benchmark functions with excellent results and is compared to GA, PSO, HS, WDO, CFO, APO and other well-known GSA variants presented in the literatures. The results obtained show that IGSA converges faster than GSA and other heuristic algorithms investigated in this paper with higher global optimization performance.     

An adaptive balance optimization algorithm and its engineering application

The policy of balance between exploration capability and exploitation capability directly affects the solution performance of the meta-heuristic algorithm in a limited time. In order to better balance the exploration and exploitation capabilities of the algorithm and meet the solution requirements of complex real-world problems, the adaptive balance optimization algorithm (ABOA) is proposed in this paper. The algorithm consists of a global search phase (GSP) and a local search phase (LSP) and is controlled by a fixed parameter. ABOA not only considers the balance of exploration and exploitation capabilities of the algorithm throughout the whole iterative process but also focuses on the balance of exploration and exploitation in both GSP and LSP. The search in both phases is focused around the respective search centers from outside to inside. ABOA balances the exploration and exploitation capabilities of the algorithm throughout the search process by two adaptive policies: changing the search area and changing the search center. Fifty-two unconstrained benchmark test functions were employed to evaluate the performance of ABOA. The results of ABOA were compared with nine excellent optimization algorithms available in the literature. The statistical results and Friedman test showed that ABOA was significantly competitive. Finally, the results of the examined engineering design problems showed that ABOA can solve the constrained optimization problem better compared to other methods.     

An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems

This paper proposes a modified harmony search (MHS) algorithm with an intersect mutation operator and cellular local search for continuous function optimization problems. Instead of focusing on the intelligent tuning of the parameters during the searching process, the MHS algorithm divides all harmonies in harmony memory into a better part and a worse part according to their fitness. The novel intersect mutation operation has been developed to generate new -harmony vectors. Furthermore, a cellular local search also has been developed in MHS, that helps to improve the optimization performance by exploring a huge search space in the early run phase to avoid premature, and exploiting a small region in the later run phase to refine the final solutions. To obtain better parameter settings for the proposed MHS algorithm, the impacts of the parameters are analyzed by an orthogonal test and a range analysis method. Finally, two sets of famous benchmark functions have been used to test and evaluate the performance of the proposed MHS algorithm. Functions in these benchmark sets have different characteristics so they can give a comprehensive evaluation on the performance of MHS. The experimental results show that the proposed algorithm not only performs better than those state-of-the-art HS variants but is also competitive with other famous meta-heuristic algorithms in terms of the solution accuracy and efficiency.     

VARIANCE-BASED HARMONY SEARCH ALGORITHM FOR UNIMODAL AND MULTIMODAL OPTIMIZATION PROBLEMS WITH APPLICATION TO CLUSTERING

This article presents a novel variance-based harmony search algorithm (VHS) for solving optimization problems. VHS incorporates the concepts borrowed from the invasive weed optimization technique to improve the performance of the harmony search algorithm (HS). This eliminates the main problem of constant parameter setting in the algorithm proposed recently and named as explorative HS. It uses the variance of a current population as well as presents a solution vector to improvise the harmony memory. In addition, the dynamic pitch adjustment operator is used to avoid solution oscillation. The proposed algorithm is evaluated on 14 standard benchmark functions of various characteristics. The performance of the proposed algorithm is investigated and compared with classical HS, an improved version of HS, the global best HS, self-adaptive HS, explorative HS, and the recently proposed state-of-art gravitational search algorithm. Experimental results reveal that the proposed algorithm outperforms the above-mentioned approaches. The effects of scalability, noise, harmony memory size, and harmony memory consideration rate have also been investigated with the proposed algorithm. The proposed algorithm is then employed for a data clustering problem. Four real-life datasets selected from the UCI machine learning repository have been used. The results indicate that the VHS-based clustering outperforms the existing well-known clustering algorithms.     

一种自适应全局和声搜索算法

针对新颖全局和声搜索(NGHS) 算法过早收敛的问题, 提出自适应全局和声搜索(AGHS) 算法. 引入差分向量范数定义和声记忆库多样性, 给出新的位置更新策略, 排除变异操作. 以和声记忆库多样性信息为指导动态产生新和声, 提高算法对解空间信息开发的能力, 避免算法因过早收敛、易陷入局部最优的不足. AGHS算法操作更简单,需要设置的参数更少, 将其与目前文献中较优的几种改进HS 算法、PSO 算法和GA算法进行性能测试, 测试结果表明AGHS算法具有较高的寻优精度和较快的收敛速度.

     

Incorporating mutation scheme into krill herd algorithm for global numerical optimization

Recently, Gandomi and Alavi proposed a robust meta-heuristic optimization algorithm, called Krill Herd (KH), for global optimization. To improve the performance of the KH algorithm, harmony search (HS) is applied to mutate between krill during the process of krill updating instead of physical diffusion used in KH. A novel hybrid meta-heuristic optimization approach HS/KH is proposed to solve global numerical optimization problem. HS/KH combines the exploration of harmony search (HS) with the exploitation of KH effectively, and hence, it can generate the promising candidate solutions. The detailed implementation procedure for this improved meta-heuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most cases, the performance of this hybrid meta-heuristic method (HS/KH) is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods, such as ACO, BBO, DE, ES, GA, HS, KH, PSO, and SGA. The effect of the HS/FA parameters is also analyzed.     

反向学习全局和声搜索算法

提出一种反向学习全局和声搜索(OLGHS)算法.基于反向学习技术初始化和声记忆库,提高初始和声向量的质量;通过当前最差和声向当前最优和声学习进化,提高算法的全局搜索性能;通过其他和声向量之间不断回溯交互的随机学习策略,提高算法局部搜索性能;用由两种不同学习策略随机交叉动态产生的新和声与反向和声二者较优的个体更新和声记忆库,提高算法的搜索性能.将OLGHS算法与其他启发式优化算法以及目前文献中较优的改进HS算法进行性能测试,测试结果表明OLGHS算法具有较高的寻优精度和较快的收敛速度.     

自适应任务分配的粒子群优化算法

针对基本粒子群优化(PSO)算法早熟收敛、易陷入局部极值的缺陷,提出自适应任务分配的粒子群优化算法。该算法根据粒子的多样性动态分配粒子任务,把种群粒子分为开发和探索两种类型,分别采用全局模型和动态邻域局部模型执行开发和探索任务以平衡算法的全局和局部搜索能力,维持种群多样性。动态邻域模型扩大了解的搜索空间,能有效抑制早熟停滞现象,采用高斯扰动对处于停滞状态的精英粒子进行学习,协助精英粒子跳出局部最优,进入解空间的其他区域继续进行搜索。针对6个标准复合测试函数进行实验,结果表明所提算法具有更强的全局搜索能力,求解精度更高。     

一种强化互学习的人工蜂群算法

为了解决基本蜂群算法存在的收敛速度慢、易陷入局部最优等问题,并提高算法在探索和开发方面的寻优性能,提出一种改进的蜂群算法,称为强化互学习的人工蜂群算法（EMLABC）,针对不同种类蜜蜂分别采用不同的搜索策略,首先对于雇佣蜂通过采用提高交叉变动学习频率以及同时面向多个较优近邻学习的机制来增强算法的全局探索能力并且避免早熟;其次针对跟随蜂采用深化的互学习策略,使新生子代保持倾向于在潜在更优区域进行搜索,进而提高算法的收敛性能和精度。在16个标准测试集函数和基本蜂群算法以及最近几个变种进行对比测试,结果表明EMLABC在收敛速度、准确寻优能力和稳定性上都有显著的提升。     

A hybrid harmony search algorithm for the spread spectrum radar polyphase codes design problem

In this paper we present the application of a hybrid harmony search (HS) algorithm to the Spread-Spectrum Radar Polyphase (SSRP) codes design. Such a design can be formulated as a non-linear max–min optimization problem, hard to be solved using classical numerical techniques. Soft-computing approaches have then been successfully applied to solve the SSRP in the past, such as evolutionary computation techniques, variable neighborhood approaches or tabu search algorithms. In this paper we elaborate on the proposed hybrid HS approach, which consists of a naive implementation of the HS algorithm along with an adaptive-step gradient-guided local search procedure. Intensive computer simulations show that the proposed hybrid HS algorithm is able to outperform existing algorithms for the SSRP design problem (including the best reported so far), with significant differences in large-size SSRP instances.     

An effective hybrid harmony search-based algorithm for solving multidimensional knapsack problems

This study presents an effective hybrid algorithm based on harmony search (HHS) for solving multidimensional knapsack problems (MKPs). In the proposed HHS algorithm, a novel harmony improvisation mechanism is developed with the modified memory consideration rule and the global-best pitch adjustment scheme to enhance the global exploration. A parallel updating strategy is employed to enrich the harmony memory diversity. To well balance the exploration and the exploitation, the fruit fly optimization (FFO) scheme is integrated as a local search strategy. For solving MKPs, binary strings are used to represent solutions and two repair operators are applied to guarantee the feasibility of the solutions. The HHS is calibrated based on the Taguchi method of design-of-experiment. Extensive numerical investigations based on well-known benchmark instances are conducted. The comparative evaluations indicate the HHS is much more effective than the existing HS and FFO variants in solving MKPs.     

基于精英学习的量子行为粒子群算法

在分析量子行为粒子群算法中吸引子指导作用的基础上,引入两种精英学习策略,提出了基于精英学习的量子粒子群算法(QPSO-EL)。采用动态逼近学习策略对精英个体进行局部更新,协助其跳出自身局部极值点,引导种群进行有效搜索;借鉴群体早熟判断机制对停滞状态下的精英个体空间进行变尺度混沌扰动,增大种群全局搜索空间,有效平衡了算法的局部和全局搜索能力。典型函数的仿真结果表明,该算法具有收敛速度快、求解精度高的特点。