多种群伪正态分布估计算法

为了提高基于正态分布模型的分布估计算法子代候选解的质量,防止早熟收敛,文中提出多种群伪正态分布估计算法.首先,采用佳点集方法进行种群初始化,将种群分为3个子群.然后,采用样本重心取代样本均值的方式,获得伪正态分布模型.最后,融合种群与子群伪正态分布模型,得到子群进化的概率模型.23个基准函数的对比测试表明,文中算法在求解质量和收敛速度上较优.针对多约束条件下的并行装配优化问题,提出工序池、员工池、罚函数等措施,将具有工序约束和人员约束的离散组合优化问题转化为无约束的多种群伪正态分布估计优化问题.工程应用结果表明,只需要将候选解的无限集合修正为有限集合,文中算法可方便地用于离散组合优化问题的快速求解.     

基于分布估计算法的连续函数全局优化问题研究

分布估计算法从宏观的角度建立一个概率模型,用来描述解空间的分布,从而通过进化计算获得优势个体。目前,离散型分布估计算法研究已经比较成熟,而连续型分布估计算法研究进展缓慢。采用均匀分布缩小采样领域的思想,设计新的分布估计算法求解连续型优化问题。实验数据表明,该分布估计算法对于求解连续型问题是有效的。     

改进的分布估计算法求解软硬件划分问题

软硬件划分是软硬件协同设计中的关键步骤,为NP难问题。分布估计算法可以解难优化问题,具有很好的全局搜索能力,但存在局部搜索能力差、种群多样性易失问题。针对此问题,对分布估计算法进行改进,对精英解进行克隆选择以加强局部搜索能力,对概率模型进行修正以改善种群多样性损失问题。同时,针对划分问题提出一种不可行解的修复方法。将改进后的分布估计算法应用于软硬件划分问题,并与现有算法做比较,结果表明所提算法在不同的约束条件下均可获得更好的优化结果。     

置换流水车间调度问题的两阶段分布估计算法

针对置换流水车间调度问题,以最小化总流水时间为目标,提出了一种新颖的两阶段分布估计算法。第一阶段先利用NEH（Nawaz-Enscore-Ham,NEH）启发式构造一个较优的初始个体,然后随机生成初始种群,为保留种群的多样性,提出一种择优机制来选择个体并建立概率模型,同时在当代种群中利用精英机制保留当代种群中的最优解,最后利用概率模型采样并生成下一代种群。第二阶段采用插入、互换操作算子对第一阶段得到的最优解进行邻域搜索,来提高分布估计算法的全局搜索能力,阻止其陷入局部最优解。通过对算例进行实验、对比和分析,证明该算法的可行性和有效性。     

基于多维EDA算法的低碳分布式装配流水车间调度

针对低碳分布式装配置换流水车间调度问题(LC＿DAPFSP),建立以同时最小化总能耗和总完工时间为优化目标的数学模型,进而提出一种多维分布估计算法(MEDA)以进行求解.首先,采用随机方法和启发式算法共同生成初始化种群;其次,建立基于矩阵立方体的概率模型,用于合理学习并积累优质解的块结构信息和序关系信息,同时设计有效采样机制对概率模型采样以生成新种群,从而合理引导算法搜索方向并发现可行解空间中的优质解区域;然后,为平衡算法的全局探索与局部开发能力,提出基于问题特性的变邻域局部搜索方法,可对全局搜索发现的优质解区域进行细致搜索;最后,通过仿真实验与算法对比验证MEDA是求解LC＿DAPFSP的有效算法.     

基于贝叶斯统计推断的离散分布估计算法

将贝叶斯统计推断理论引入分布估计算法概率模型中,提出一种基于贝叶斯统计推断的离散分布估计算法。根据离散优化问题中解的分布规律建立先验概率模型,将优势群体的概率模型和二元边缘分布算法中森林结构的概率模型相结合,得出条件概率模型,利用贝叶斯统计推断,并结合上述2种概率模型建立后验概率模型,以指导新群体的产生。仿真结果表明,该算法求解gr21旅行商问题的收敛速度大于EDAs1算法,在种群规模、最大运行代数等参数固定的情况下,分别分析结合速率和学习速率对算法性能的影响,得出当其值取0.2时,算法性能最稳定。     

求解连续空间优化问题的改进蜂群算法

为了有效地解决人工蜂群算法容易陷入局部最优的缺陷,提出了一种改进蜂群算法。首先,利用反向学习方法构建初始种群,以提高初始化解的质量。同时,利用分布估计算法构造优秀个体解空间的概率模型以进行邻域搜索,以改善算法的搜索性能并防止陷入局部最优。对连续空间优化问题进行了仿真实验,结果表明改进算法具有较快的收敛速度,全局寻优能力显著提高。     

利用条件概率和Gibbs抽样技术为分布估计算法构造通用概率模型

本文针对传统分布估计算法在建立概率模型时面临的各种困难,提出一种基于条件概率和Gibbs抽样的概率模型,能有效改进分布估计算法的通用性.使用该模型的分布估计算法利用进化过程中有前途的优秀个体构造出多个监督学习样本集,并对每个样本集估计出对应分量的条件概率,再使用这一组条件概率进行Gibbs抽样产生新的个体替代种群中的劣等个体.通过仿真实验表明,改进后的算法能够求解出可加性降解函数的全局最优解,表现出较强的全局优化能力.     

面向多目标流水车间调度的多种群多目标遗传算法

针对制造型企业普遍存在的流水车间调度问题,建立了以最小化最迟完成时间和总延迟时间为目标的多目标调度模型,并提出一种基于分解方法的多种群多目标遗传算法进行求解.该算法将多目标流水车间调度问题分解为多个单目标子问题,并分阶段地将这些子问题引入到算法迭代过程进行求解.算法在每次迭代时,依据种群的分布情况选择各子问题的最好解及与其相似的个体分别为当前求解的子问题构造子种群,通过多种群的进化完成对多个子问题最优解的并行搜索.通过对标准测试算例进行仿真实验,结果表明所提出的算法在求解该问题上能够获得较好的非支配解集.     

求解TSP问题的一种改进的+进制MIMIC算法

十进制MIMIC算法是基于MIMIC二进制编码算法思想的可用来求解TSP的离散分布估计算法。着重考虑该算法在较大规模TSP问题上的算法缺陷,对其编码方式和概率模型进行了改进,提出了新的个体生成策略,在初始化种群阶段使用了贪心算法,在进化过程中引入了杂交算子、变异算子、映射算子、优化算子等演化算子,采用了动态调整方法来确定优势群体的规模。以上改进使得算法在小种群解大规模TSP问题的情况下仍可保持种群的多样性。实验结果表明,改进算法在求解规模、求解质量和寻优速度上都有明显提高。     

基于转移概率的分布估算算法在p-median问题上的应用

分布估算算法(EDA)是近几年出现的一种启发式进化算法,在组合优化问题中得到了广泛、有效的应用.概率模型直接决定着该算法的性能,如何构建一个高性能的概率模型成为分布估算算法的研究核心.把转移概率模型引入分布估算算法,并对p-median问题进行求解,结果表明,基于转移概率模型的分布估算算法能够有效地求解p-median问题,并极大地提高了算法的效率与精确性.     

求解混合流水车间调度问题的分布估计算法

针对混合流水车间调度问题(Hybrid flow-shop scheduling problem, HFSP)的特点, 设计了基于排列的编码和解码方法, 建立了描述问题解空间的概率模型, 进而提出了一种有效的分布估计算法(Estimation of distribution algorithm, EDA). 该算法基于概率模型通过采样产生新个体, 并基于优势种群更新概率模型的参数. 同时, 通过实验设计方法对算法参数设置进行了分析并确定了有效的参数组合. 最后, 通过基于实例的数值仿真以及与已有算法的比较验证了所提算法的有效性和鲁棒性.     

DE/EDA: A new evolutionary algorithm for global optimization

Differential evolution (DE) was very successful in solving the global continuous optimization problem. It mainly uses the distance and direction information from the current population to guide its further search. Estimation of distribution algorithm (EDA) samples new solutions from a probability model which characterizes the distribution of promising solutions. This paper proposes a combination of DE and EDA (DE/EDA) for the global continuous optimization problem. DE/EDA combines global information extracted by EDA with differential information obtained by DE to create promising solutions. DE/EDA has been compared with the best version of the DE algorithm and an EDA on several commonly utilized test problems. Experimental results demonstrate that DE/EDA outperforms the DE algorithm and the EDA. The effect of the parameters of DE/EDA to its performance is investigated experimentally.     

Combining tabu Hopfield network and estimation of distribution for unconstrained binary quadratic programming problem

Unconstrained binary quadratic programming problem (UBQP) consists in maximizing a quadratic 0–1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. This paper combines a tabu Hopfield neural network (HNN) (THNN) with estimation of distribution algorithm (EDA), and thus a THNN–EDA is proposed for the UBQP. In the THNN, the tabu rule, instead of the original updating rule of the HNN, is used to govern the state transition or updating of neurons to search for the global minimum of the energy function. A probability vector in EDA model is built to characterize the distribution of promising solutions in the search space, and then the THNN is guided by the global search information in EDA model to search better solution in the promising region. Thus, the short term memory of the tabu mechanism in the THNN cooperates with the long term memory mechanism in the EDA to help the network escape from local minima. The THNN–EDA is tested on 21 UBQP benchmark problems with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. Simulation results show that the THNN–EDA is better than the other HNN based algorithms, and is better than or competitive with metaheuristic algorithms and state-of-the-art algorithms.     

求解作业车间调度问题的禁忌分布估计算法

为优化作业车间调度问题的解,提出一个禁忌和分布估计的混合算法。分布估计算法是一种新的进化模式,通过概率优化模型在连续空间进行求解;通过对已获得的群体进行选择操作生成优势群体,提出的分布估计算法使用单变量边缘分布算法构建概率模型,估计离散空间中的联合概率分布,从概率向量采样生成新群体;采用基于工件编号的编码和解码机制保证解的可行性。为提高局部搜索能力,算法基于禁忌搜索算法设计新的双重移动组合、块禁忌和选择策略,在搜索陷入局部最优时利用遗传算法的变异算子生成新解;算法通过混合分布估计算法和禁忌搜索算法的优点,兼具全局搜索与局部搜索能力,提高了搜索的效率和性能。通过与现有算法在典型实例上的实验结果比较,表明该算法在求解作业车间调度问题上具有可行性和有效性。     

Drift and scaling in estimation of distribution algorithms

This paper considers a phenomenon in Estimation of Distribution Algorithms (EDA) analogous to drift in population genetic dynamics. Finite population sampling in selection results in fluctuations which get reinforced when the probability model is updated. As a consequence, any probability model which can generate only a single set of values with probability 1 can be an attractive fixed point of the algorithm. To avoid this, parameters of the algorithm must scale with the system size in strongly problem-dependent ways, or the algorithm must be modified. This phenomenon is shown to hold for general EDAs as a consequence of the lack of ergodicity and irreducibility of the Markov chain on the state of probability models. It is illustrated in the case of UMDA, in which it is shown that the global optimum is only found if the population size is sufficiently large. For the needle-in-a haystack problem, the population size must scale as the square-root of the size of the search space. For the one-max problem, the population size must scale as the square-root of the problem size.     

A hybrid multi-objective PSO–EDA algorithm for reservoir flood control operation

Reservoir flood control operation (RFCO) is a complex multi-objective optimization problem (MOP) with interdependent decision variables. Traditionally, RFCO is modeled as a single optimization problem by using a certain scalar method. Few works have been done for solving multi-objective RFCO (MO-RFCO) problems. In this paper, a hybrid multi-objective optimization approach named MO-PSO–EDA which combines the particle swarm optimization (PSO) algorithm and the estimation of distribution algorithm (EDA) is developed for solving the MO-RFCO problem. MO-PSO–EDA divides the particle population into several sub-populations and builds probability models for each of them. Based on the probability model, each sub-population reproduces new offspring by using PSO based and EDA methods. In the PSO based method, a novel global best position selection method is designed. With the help of the EDA based reproduction, the algorithm can lean linkage between decision variables and hence have a good capability of solving complex multi-objective optimization problems, such as the MO-RFCO problem. Experimental studies on six benchmark problems and two typical multi-objective flood control operation problems of Ankang reservoir have indicated that the proposed MO-PSO–EDA performs as well as or superior to the other three competitive multi-objective optimization algorithms. MO-PSO–EDA is suitable for solving MO-RFCO problems.     

An effective hybrid EDA-based algorithm for solving multidimensional knapsack problem

In this paper, an effective hybrid algorithm based on estimation of distribution algorithm (EDA) is proposed to solve the multidimensional knapsack problem (MKP). With the framework of EDA, the probability model is built with the superior population and the new individuals are generated based on probability model. In addition, an updating mechanism of the probability model is proposed and a mechanism for initializing the probability model based on the specific knowledge of the MKP is also proposed to improve the convergence speed. Meanwhile, an adaptive local search is proposed to enhance the exploitation ability. Furthermore, the influences of parameters are investigated based on Taguchi method of design of experiment and the importance of repair operator is also studied via simulation testing and comparisons. Finally, numerical simulation is carried out based on the benchmark instances, and the comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm.     

面向纸板三维装箱问题的剩余空间最优算法

针对瓦楞纸板在装箱过程中遇到的多种实际约束,提出一种基于剩余空间最优和多种实际约束的快速求解算法。该算法先根据纸板的先进后出和组合装载约束,确定纸板的装箱序列,接着将三维装箱问题转换成带高度约束的二维装箱问题,再基于剩余空间最优策略,选择空间的分割方式和纸板的放置方式,并对剩下的空间进行合并和重新分割,从而求解得到纸板装载放置的结果,实现容器空间利用率最高和使用数目最小的目标。通过计算随机算例和实际算例,以及对结果的三维可视化显示,验证该算法能实现多种约束,空间利用率高,运算效率高并具有有效性和实用性。     

Competitive Hopfield Network Combined With Estimation of Distribution for Maximum Diversity Problems

This paper presents a discrete competitive Hopfield neural network (HNN) (DCHNN) based on the estimation of distribution algorithm (EDA) for the maximum diversity problem. In order to overcome the local minimum problem of DCHNN, the idea of EDA is combined with DCHNN. Once the network is trapped in local minima, the perturbation based on EDA can generate a new starting point for DCHNN for further search. It is expected that the further search is guided to a promising area by the probability model. Thus, the proposed algorithm can escape from local minima and further search better results. The proposed algorithm is tested on 120 benchmark problems with the size ranging from 100 to 5000. Simulation results show that the proposed algorithm is better than the other improved DCHNN such as multistart DCHNN and DCHNN with random flips and is better than or competitive with metaheuristic algorithms such as tabu-search-based algorithms and greedy randomized adaptive search procedure algorithms.