基于DE 和SA 的Memetic 高维全局优化算法

针对高维复杂多模态优化问题,传统的进化算法存在收敛速度慢,求解精度低等缺点,提出一种面向高维优化问题的Memetic全局优化算法。算法通过全局搜索和局部搜索结合的混合搜索策略,采用多模式并行差分进化算法进行全局搜索,基于高斯分布估计的模拟退火算法进行局部搜索。改进后的Memetic算法不仅继承了差分进化算法能发现全局最优解的优点,而且能大幅度提高搜索效率。最后,通过对4个高维多峰值Benchmark函数进行仿真实验,实验结果表明本文算法有效提高了算法的收敛速度和求解精度。     

基于抽象凸估计选择策略的差分进化算法

针对传统差分进化算法计算代价、可靠性及收敛速度的问题,提出一种基于抽象凸估计选择策略的差分进化算法(DEUS).首先,通过提取新个体的邻近个体建立局部抽象凸下界松弛模型;然后,利用下界松弛模型估计目标函数值来指导种群更新,同时利用下界估计区域极值点快速枚举算法系统排除部分无效区域;最后,借助线性拟凸包络的广义下降方向有效地实现局部增强.12个标准测试函数的实验结果表明,所提算法计算代价、可靠性及收敛速度均优于DE及DERL,DELB,Sa DE等改进算法.     

基于状态估计反馈的策略自适应差分进化算法

借鉴闭环控制思想, 提出基于状态估计反馈的策略自适应差分进化(Differential evolution, DE)算法, 通过设计状态评价因子自适应判定种群个体所处于的阶段, 实现变异策略的反馈调节, 达到平衡算法全局探测和局部搜索的目的.首先, 基于抽象凸理论对种群个体建立进化状态估计模型, 提取下界估计信息并结合进化知识设计状态评价因子, 以判定当前种群的进化状态; 其次, 利用状态评价因子的反馈信息, 实现不同进化状态下策略的自适应调整以指导种群进化, 达到提高算法搜索效率的目的.另外, 20个典型测试函数与CEC2013测试集的实验结果表明, 所提算法在计算代价、收敛速度和解的质量方面优于主流改进差分进化算法和非差分进化算法.     

基于抽象凸下界估计的群体全局优化算法

针对确定性全局优化算法极高的计算复杂度以及随机性全局优化算法可靠性较低的问题,在群体进化算法框架下,结合抽象凸理论,提出一种基于抽象凸下界估计的群体全局优化算法。首先,对整个初始群体构建抽象凸下界估计松弛模型;然后,利用不断收紧的下界估计信息安全排除部分无效区域,并指导种群更新,同时借助支撑面的下降方向作局部增强;最后,根据进化信息更新支撑面。数值实验结果表明了所提出算法的有效性。     

局部抽象凸区域剖分差分进化算法

在差分进化算法框架下, 结合抽象凸理论, 提出一种局部抽象凸区域剖分差分进化算法(Local partition based differential evolution, LPDE). 首先, 通过对新个体的邻近个体构建分段线性下界支撑面, 实现搜索区域的动态剖分; 然后, 利用区域剖分特性逐步缩小搜索空间, 同时根据下界估计信息指导种群更新, 并筛选出较差个体; 其次, 借助下界支撑面的广义下降方向作局部增强, 并根据进化信息对搜索区域进行二次剖分; 最后, 根据个体的局部邻域下降方向对部分较差个体作增强处理. 数值实验结果表明了所提算法的有效性.     

基于局部抽象凸支撑面的多模态优化算法

在基本进化算法框架下,结合抽象凸理论,提出一种基于局部抽象凸支撑面的多模态优化算法.首先,采用模型变换方法将原优化问题转变为单位单纯形约束条件下的严格递增射线凸松弛问题;其次,针对新生成个体的邻域信息构建局部抽象凸支撑面,并利用局部下界知识动态识别种群模态,从而减少替换误差,避免出现早熟现象;最后,借助支撑面下降方向进一步实现模态内部的局部增强过程.数值研究表明,针对给定的绝大部分测试问题,提出的算法在精度和可靠性指标方面均优于文中给出的其他算法.     

基于混合差分进化算法的无等待流水车间总流水时间优化*

以调度的总流水时间为优化目标, 提出一种混合差分进化算法。 首先, 建立无等待流水车间调度的问题模型,并用快速方法评估总流水时间指标。 其次,采用LPV规则,实现离散问题的连续编码; 用差分进化算法对总流水时间指标执行优化;引入插入邻域和基于pairwise的局部搜索算法, 分别对差分进化算法产生的新个体和差分进化算法的最优解执行邻域搜索, 达到优化目标全局和局部的最优。 最后,通过计算标准算例, 并与其他算法比较, 验证该混合差分进化算法的有效性。     

一种新的蛋白质结构预测多模态优化算法

针对现阶段药物设计中对于蛋白质结构多模态的需求,提出了一种基于排挤差分进化策略的多模态优化算法.为了降低蛋白质构象空间求解的复杂度,算法采用能量极小化过程,有效缩小了可行域的搜索空间;同时,为了有效地平衡多模态优化问题的局部收敛性和模态多样性,在排挤差分进化算法的框架下,在保证算法收敛速度的前提下,算法采用空间局部性原理,同时随机选取不同交叉策略的集结思想又有效改善了种群的多样性.以脑啡肽为例,算法不仅得到了其全局最稳定结构,还获得了一系列局部最优结构.     

基于参数动态调整的多目标差分进化算法

针对多目标差分进化算法最优解难以获取的问题,提出一种基于参数动态调整的多目标差分进化(AMODE)算法.AMODE算法通过设计变异率和交叉率的自适应调整策略,实现进化过程中变异率和交叉率的动态调整,均衡多目标差分进化算法的局部搜索能力和全局探索能力,获得收敛性、多样性和均匀性较好的最优解.实验结果表明,基于参数动态调整的AMODE算法能够有效改善多目标差分进化算法的逼近能力(IGD)和均匀性(SP),具有较好的优化效果.     

基于副本交换的局部增强差分进化蛋白质结构从头预测方法

针对蛋白质高维构象空间搜索问题,提出一种基于副本交换的局部增强差分进化蛋白质结构从头预测方法(RLDE)。首先,采用基于知识的Rosetta粗粒度能量模型显著降低构象空间优化变量维数;其次,引入基于片段库知识的片段组装技术进一步减小构象搜索空间,有效避免搜索过程中的熵效应;此外,在每个副本层设置构象种群,采用差分进化算法对种群进行更新,然后利用Monte Carlo算法对种群做局部增强,以此得到全局和部分局部最优构象。综上,RLDE利用差分进化算法较强的全局搜索能力可以对构象空间进行有效的全局搜索;借助Monte Carlo算法局部搜索性能对构象空间局部极小区域进行更为充分的采样;副本交换策略保证了副本层中种群的多样性,同时能够增强算法跳出局部极小的能力,从而使得算法对构象空间的搜索能力进一步增强。15个目标蛋白测试结果表明,所提方法能够有效地对构象空间采样,得到高精度的近天然态蛋白质构象。     

A novel differential evolution algorithm using local abstract convex underestimate strategy for global optimization

Two main challenges in differential evolution (DE) are reducing the number of function evaluations required to obtain optimal solutions and balancing the exploration and exploitation. In this paper, a local abstract convex underestimate strategy based on abstract convexity theory is proposed to address these two problems. First, the supporting hyperplanes are constructed for the neighboring individuals of the trial individual. Consequently, the underestimate value of the trial individual can be obtained by the supporting hyperplanes of its neighboring individuals. Through the guidance of the underestimate value in the select operation, the number of function evaluations can be reduced obviously. Second, some invalid regions of the domain where the global optimum cannot be found are safely excluded according to the underestimate information to improve reliability and exploration efficiency. Finally, the descent directions of supporting hyperplanes are employed for local enhancement to enhance exploitation capability. Accordingly, a novel DE algorithm using local abstract convex underestimate strategy (DELU) is proposed. Numerical experiments on 23 bound-constrained benchmark functions show that the proposed DELU is significantly better than, or at least comparable to several state-of-the art DE variants, non-DE algorithms, and surrogate-assisted evolutionary algorithms.     

基于RSS的无线传感器网络半定规划定位算法研究

在无线传感器网络定位中,基于RSS测量的定位方法是最常用的方法之一。由于传统的最大似然估计(MLE)算法的目标函数具有非线性和非凸性,在应用于无线传感器网络定位时,会产生多个局部最优值。针对该问题提出一种基于半定规划(SDP)的凸优化定位方法。首先采用泰勒级数近似对目标函数进行线性化处理,然后通过引入冗余变量将原无约束优化问题转化为约束优化问题,最后应用半定松弛(SDR)技术将约束优化问题转化为半定规划(SDP)凸优化问题进行求解。通过仿真实验的比较,说明本文提出的优化算法在定位精度、鲁棒性方面优于已有算法。     

Optimal Kullback–Leibler approximation of Markov chains via nuclear norm regularisation

This paper is concerned with model reduction for Markov chain models. The goal is to obtain a low-rank approximation to the original Markov chain. The Kullback–Leibler divergence rate is used to measure the similarity between two Markov chains; the nuclear norm is used to approximate the rank function. A nuclear-norm regularised optimisation problem is formulated to approximately find the optimal low-rank approximation. The proposed regularised problem is analysed and performance bounds are obtained through the convex analysis. An iterative fixed point algorithm is developed based on the proximal splitting technique to compute the optimal solutions. The effectiveness of this approach is illustrated via numerical examples.     

蜂窝网络下基于max-min公平性的D2D功率分配

针对多个终端直通通信（D2D）用户共享多个蜂窝用户资源的公平性问题,在保证蜂窝用户速率的前提下,提出了基于最大最小公平性（max-min fairness）的功率分配算法。该算法首先将非凸优化问题转化为含凸函数的差（DC）规划问题,然后采用凸近似的全局优化算法和对分算法对D2D实现功率优化。仿真结果表明,与只采用凸近似的全局优化算法相比,所提算法收敛性更优,同时最大化了瓶颈用户的速率。     

Multi-objective node deployment in WSNs: In search of an optimal trade-off among coverage,lifetime, energy consumption,and connectivity

The increased demand of Wireless Sensor Networks (WSNs) in different areas of application have intensified studies dedicated to the deployment of sensor nodes in recent past. For deployment of sensor nodes some of the key objectives that need to be satisfied are coverage of the area to be monitored, net energy consumed by the WSN, lifetime of the network, and connectivity and number of deployed sensors. In this article the sensor node deployment task has been formulated as a constrained multi-objective optimization (MO) problem where the aim is to find a deployed sensor node arrangement to maximize the area of coverage, minimize the net energy consumption, maximize the network lifetime, and minimize the number of deployed sensor nodes while maintaining connectivity between each sensor node and the sink node for proper data transmission. We assume a tree structure between the deployed nodes and the sink node for data transmission. Our method employs a recently developed and very competitive multi-objective evolutionary algorithm (MOEA) known as MOEA/D-DE that uses a decomposition approach for converting the problem of approximation of the Pareto fronts (PF) into a number of single-objective optimization problems. This algorithm employs differential evolution (DE), one of the most powerful real parameter optimizers in current use, as its search method. The original MOEA/D has been modified by introducing a new fuzzy dominance based decomposition technique. The algorithm introduces a fuzzy Pareto dominance concept to compare two solutions and uses the scalar decomposition method only when one of the solutions fails to dominate the other in terms of a fuzzy dominance level. We have compared the performance of the resulting algorithm, called MOEA/DFD, with the original MOEA/D-DE and another very popular MOEA called Non-dominated Sorting Genetic Algorithm (NSGA-II). The best trade-off solutions from MOEA/DFD based node deployment scheme have also been compared with a few single-objective node deployment schemes based on the original DE, an adaptive DE-variant (JADE), original particle swarm optimization (PSO), and a state-of-the art variant of PSO (Comprehensive Learning PSO). In all the test instances, MOEA/DFD performs better than all other algorithms. Also the proposed multi-objective formulation of the problem adds more flexibility to the decision maker for choosing the necessary threshold of the objectives to be satisfied.     

Un problema di approssimazione connesso con la sintesi di filtri digitali non ricorsivi

In this paper we present a synthesis algorithm for non-recursive digital filters. By the well-known «frequency sampling method», the approximation problem can be related to a convex optimization problem. Finally, we exhibit a synthesis procedure based on the classical simplex algorithm.     

赋权图匹配问题的一种新的松弛模型

图匹配是一个NP难(NP-hard)问题. 基于置换矩阵是非负正交矩阵这一经典结论, 提出赋权图匹配(Weighted graph matching, WGM)的双向松弛障碍规划, 理论上证明新模型的解与原模型的解是一致的. 该规划是一个二元连续规划, 它是正交矩阵上的线性优化问题, 同时也是非负矩阵上的凸二次优化问题. 故设计求解新模型的交替迭代算法, 并证明算法的局部收敛性. 数值实验表明, 在匹配精度方面, 新方法强于线性规划方法和特征值分解方法.     

Approximate branch-and-bound global optimization using B-spline hypervolumes

This paper presents a B-spline-based branch-and-bound algorithm for unconstrained global optimization. The key components of the branch-and-bound, a well-known algorithm paradigm for global optimization, are a subdivision scheme and a bound calculation scheme. For these schemes, we first introduce a B-spline hypervolume to approximate an objective function defined in a design space, where the approximation is based on Latin-hypercube sampling points. We then describe a proposed algorithm for finding global solutions approximately within a prescribed tolerance. The algorithm includes two procedures that are performed iteratively until all stopping conditions are satisfied. One involves subdivision into mutually disjoint subspaces and computation of their bound information, both of which are accomplished by using B-spline hypervolumes. The other updates a search tree that represents a hierarchical structure of subdivided subspaces during the solution process. Finally, we examine the computational performance of the proposed algorithm on various test problems that cover most of the difficulties encountered in global optimization. The results show that the proposed algorithm is complete without using heuristics and has good potential for application in large-scale NP-hard optimization.