多车场一体化集货送货车辆路径问题的混合遗传算法

为满足电子商务客户多样化和个性化的需求,建立多车场一体化装卸混合车辆调度模型。针对模型的特点,采用混合遗传算法求解。即利用模拟退火算法的Boltzmann机制,控制遗传算法的交叉、变异操作,加强染色体的局部搜索能力,提高了算法的收敛速度和搜索效率。仿真结果表明在解决大规模实际问题时,混合遗传算法在求解质量和计算效率上好于标准遗传算法。     

顺序相依拆卸线平衡多目标优化模型及算法研究

拆卸是产品回收过程最关键环节之一,拆卸效率直接影响再制造成本。本文在分析现有模型不足基础上,考虑最小化总拆卸时间,建立多目标顺序相依拆卸线平衡问题优化模型,并提出了一种自适应进化变邻域搜索算法。所提算法引入种群进化机制,并采用一种组合策略构建初始种群,通过锦标赛法选择个体进化;在局部搜索时,设计了邻域结构自适应选择策略,并采用基于交叉的全局学习机制加速跳出局部最优,以提高算法寻优能力。对比实验结果,证实了所提模型的合理性以及算法的高效性。     

多目标0-1规划问题的元胞狼群优化算法研究

针对多目标0-1规划问题,首先基于元胞自动机原理和人工狼群智能算法,提出一种元胞狼群优化算法,该算法将元胞机的演化规则与嚎叫信息素更新规则、人工狼群更新规则进行组合,采用元胞及其邻居来增强搜索过程的多样性和分布性,使人工头狼在元胞空间搜索的过程中,增强了人工狼群算法的全局搜索能力,并获得更多的全局非劣解;其次结合多目标0-1规划模型对元胞狼群算法进行了详细的数学描述,定义了人工狼群搜索空间、移动算子、元胞演化规则和非劣解集更新规则,并给出了元胞狼群算法的具体实现步骤;最后通过MATLAB软件对3个典型的多目标0-1规划问题算例进行解算,并将解算结果与其它人工智能算法的结果进行比较,结果表明:元胞狼群算法在多目标0-1规划问题求解方面可获得更多的非劣解集和更优的非劣解,并具有较快的收敛速度和较好的全局寻优能力。     

面向多目标优化的一种混合进化算法

针对多目标优化问题,设计一种基于量子计算和非支配排序遗传算法相结合的智能算法进行求解,综合量子算法和非支配排序遗传算法的优点,在局部搜索和全局搜索之间进行权衡。混合算法采用量子比特对问题的解进行编码,基于量子旋转门算子、分散交叉算子以及高斯变异算子对种群进行更新。进行局部深入搜索时,用一个解在目标空间中跟理想点的距离来评价该解的优劣;进行全局搜索时,基于非支配排序遗传算法中的有效前沿的划分和解之间的拥挤距离来评价某个解。最后,在经典的测试函数ZDT5上对所提混合算法进行了测试。通过对比分析若干项针对有效解集的评价指标,该混合算法在跟最优有效前沿的逼近程度以及有效解集分布的均匀程度上均优于目前得到广泛应用的非支配排序遗传算法。     

现金押运路线问题——基于多类型的风险

以人民币现金押运为研究背景,考虑了一种基于多类型风险的现金押运路线问题,以在途风险成本、库存现金风险成本以及运输成本为优化目标,建立了混合整数线性规划模型,并提出了一种基于多样化策略和改进邻域搜索的混合遗传算法,其中遗传算法对押运路线进行选择,贪心算法用来求解各类风险指标。数值实验分别对问题特性和算法性能进行了分析。实验结果表明:1)混合遗传算法能求解更大规模的问题,得到较好的解,并很好地平衡了运行时间和求解质量;2)多类型风险影响了行驶路线;3)客户的期望需求影响了库存现金风险。     

随机混流U型拆卸线平衡排序问题多目标进化算法优化

针对混流U型拆卸线平衡排序问题,考虑拆卸时间不确定,建立了该问题最小拆卸线平均闲置率、尽早拆卸危害和高需求零部件、最小化平均方向改变次数的多目标优化模型,并提出一种基于分解和动态邻域搜索的混合多目标进化算法(Hybrid Multi-objective Evolutionary Algorithm Based on Decomposition, HMOEA/D)。该算法通过采用弹性任务分配策略、动态邻域结构和动态调整权重以保证解的可行性并搜索得到分布较好的非劣解集。最后,仿真求解实验设计技术(DOE)生成的测试算例,结果表明HMOEA/D较其它算法能得到更接近Pareto最优、分布更好的近似解集。     

基于精英区域学习的多种群自适应的差分进化算法

为了进一步提高差分进化算法的收敛速度、算法精度和稳定性,采用多种群技术来增加算法收敛速度和降低复杂度;利用精英区域学习策略来对算法的全局搜索能力和算法精度进一步提升,引进自适应免疫搜索策略,以实现自适应修正差分算法的变异因子和交叉因子。通过五个测试函数,把本文算法与最新文献中的算法进行对比,表明算法在收敛速度、精度和高维问题寻优能力方面的优越性。     

一种多种群综合学习粒子群优化算法

针对综合学习算法(Comprehensive learning particle swarm optimization,CLPSO)在解决全局优化问题时精度不高且收敛速度慢的问题,提出一种多种群综合学习算法(MS_CLPSO).该算法将传统粒子群算法的社会部分引入CLPSO算法,有效提高了算法的收敛速度和局部开采能力;同时,为扩大粒子的空间搜索范围,算法引入多种群策略,提高了算法全局勘探能力;并针对可能陷入局部极值的粒子,采用全局学习策略更新学习样本,增加了种群中粒子多样性.实验结果表明,在处理单峰和多峰标准测试函数中,MSCLPSO算法有效提高了CLPSO算法的精度和收敛速度.     

基于差分变异与扰动变异的多目标克隆选择算法

为了更加有效解决多目标优化问题,提出了一种基于差分变异和扰动变异相结合的多目标克隆选择算法(MCSA-MDD).该算法对非支配抗体进行克隆操作,从而有利于向着理想Pareto前端搜索;采用差分变异与扰动变异相结合的方式来进行免疫基因操作,有利于解的多样性.数值实验分为两组,一组选取4个常用测试函数并与其它五个多目标算法进行比较,数值实验结果表明了MCSA-MDD算法的有效性.另一组仅用差分变异和扰动变异的多目标免疫克隆算法进行比较,数值实验结果验证了采用差分变异与扰动变异相结合的免疫操作提高了算法的性能.     

改进的布谷鸟算法求解考虑运输时间的分布式柔性流水车间调度问题

针对分布式制造环境下多车间调度问题特点,结合企业实际生产情况,考虑相邻工序间的运输时间,建立以最小化最大完工时间为优化目标的分布式柔性流水车间调度模型,提出一种改进布谷鸟算法用于求解该模型。算法改进包括设计了一种基于工序、车间和机器的三层编码方案;根据问题特点设计了混合种群初始化策略以提高种群质量;改进了布谷鸟搜索操作使其适用于求解该模型;设计了一种种群进化策略以提高算法收敛速度及解的质量。最后通过仿真实验,与多种算法对比,验证所提算法的有效性和优越性。     

带学习效应的两台平行机时间表长问题

研究机器带学习效应, 目标函数为时间表长的两台平行机排序问题, 问题是NP-难的. 首先建立了求解该问题最优解的整数规划模型. 其次, 基于模拟退火算法给出了该问题的近似算法SA, 并证明了该算法依概率1 全局收敛到最优解. 最后, 通过数值模拟对所提出的算法进行了性能分析. 数值模拟结果表明, 近似算法SA可以达到最优值的99%, 准确度高, 算法较有效.     

Optimal control of bioprocess systems using hybrid numerical optimization algorithms

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. However, in spite of the improved Broyden–Fletcher–Goldfarb–Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches.     

On an open problem in spherical facility location

In this paper we partially resolve an open problem in spherical facility location. The spherical facility location problem is a generalization of the planar Euclidean facility location problem. This problem was first studied by Katz and Cooper and by Drezner and Wesolowsky where a Weszfeld-like algorithm was proposed. This algorithm is very simple and does not require a line search. However, its convergence has been an open problem for more than ten years. In this paper, we prove that the sequence generated by the algorithm converges to the unique optimal solution under the condition that the oscillation of the sequence converges to zero. We conjecture that the algorithm is a descent algorithm and prove that the sequence generated by the algorithm converges to the optimal solution under this conjecture.     

Strong Convergence of an Inexact Proximal Point Algorithm for Equilibrium Problems in Banach Spaces

We develop an inexact proximal point algorithm for solving equilibrium problems in Banach spaces which consists of two principal steps and admits an interesting geometric interpretation. At a certain iterate, first we solve an inexact regularized equilibrium problem with a flexible error criterion to obtain an axillary point. Using this axillary point and the inexact solution of the previous iterate, we construct two appropriate hyperplanes which separate the current iterate from the solution set of the given problem. Then the next iterate is defined as the Bregman projection of the initial point onto the intersection of two halfspaces obtained from the two constructed hyperplanes containing the solution set of the original problem. Assuming standard hypotheses, we present a convergence analysis for our algorithm, establishing that the generated sequence strongly and globally converges to a solution of the problem which is the closest one to the starting point of the algorithm.     

带1-范数约束的分裂可行问题的投影算法

本文主要研究带1-范数约束的分裂可行问题的求解算法.用一种交替投影算法,求得了问题的解,提出松弛交替投影算法,改进了直接往闭凸集上投影这一不足,并证明了该算法的收敛性.     

Minimization of equilibrium problems,variational inequality problems and fixed point problems

In this paper, we devote to find the solution of the following quadratic minimization problem

$\min_{x\in \Omega}\|x\|^2,$

where Ω is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping and the solution set of some variational inequality. In order to solve the above minimization problem, we first construct an implicit algorithm by using the projection method. Further, we suggest an explicit algorithm by discretizing this implicit algorithm. Finally, we prove that the proposed implicit and explicit algorithms converge strongly to a solution of the above minimization problem.

     

Geometrically convergent projection method in matrix games

We propose a method which evaluates the solution of a matrix game. We reduce the problem of the search for the solution to a convex feasibility problem for which we present a method of projection onto an acute cone. The algorithm converges geometrically. At each iteration, we apply a combinatorial algorithm in order to evaluate the projection onto the standard simplex.     

The reconstruction of a special kind of periodic Jacobi matrices

In this paper, we investigate the properties of a special kind of periodic Jacobi matrices. We show that the solution of the inverse problem for periodic Jacobi matrices is unique if and only if the matrix is of that special kind. Moreover, we present an algorithm to construct the solution of that inverse problem and give some illustrative examples. Finally, we perform a stability analysis of the algorithm.     

Proximal algorithm for solving monotone variational inclusion

In this paper, we introduce a contraction algorithm for solving monotone variational inclusion problem. To reach this goal, our main iterative algorithm combine Dong’s projection and contraction algorithm with resolvent operator. Under suitable assumptions, we prove that the sequence generated by our main iterative algorithm converges weakly to the solution of the considered problem. Finally, we give two numerical examples to verify the feasibility of our main algorithm.     

A Lagrangian search method for the <Emphasis Type="Italic">P</Emphasis>-median problem

In this paper, we propose a novel algorithm for solving the classical P-median problem. The essential aim is to identify the optimal extended Lagrangian multipliers corresponding to the optimal solution of the underlying problem. For this, we first explore the structure of the data matrix in P-median problem to recast it as another equivalent global optimization problem over the space of the extended Lagrangian multipliers. Then we present a stochastic search algorithm to find the extended Lagrangian multipliers corresponding to the optimal solution of the original P-median problem. Numerical experiments illustrate that the proposed algorithm can effectively find a global optimal or very good suboptimal solution to the underlying P-median problem, especially for the computationally challenging subclass of P-median problems with a large gap between the optimal solution of the original problem and that of its Lagrangian relaxation.