动态种群规模协同进化算法求解多目标投资组合优化问题

为了解决仅含预算约束的投资组合优化模型,提出一种基于种群密度的多目标协同进化算法.算法采用种群竞争的策略自适应的产生不定规模的种群,避免了固定种群规模的缺点.在进化过程中每个种群都会参考自身的最优个体以及竞争种群对自身的影响,超级个体集合存储进化过程中产生的最优解,通过最优个体的引导使算法快速收敛至Pareto前沿.实验结果表明,与NSGA-2算法相比,提出的算法在稳定性和收敛性都有很好的表现,是一种有效的多目标进化算法.     

求解双层规划的多目标布谷鸟算法

双层规划是一类具有主从递阶结构的优化问题,属于NP-hard范畴。本文利用KKT条件将双层规划问题转化为等价的单层约束规划问题,通过约束处理技术进一步转化为带偏好双目标无约束优化问题,提出多目标布谷鸟算法求解策略。该算法采用Pareto支配和ε-个体比较准则,充分利用种群中优秀不可行解的信息指导搜索过程;设置外部档案集存储迭代过程中的优秀个体并通过高斯扰动改善外部档案集的质量,周期性替换群体中的劣势个体,引导种群不断向可行域或最优解逼近。数值实验及其参数分析验证了算法的有效性。     

基于模糊系统的改进型NSGA-III算法

在利用多目标进化算法解决高维多目标优化问题时，随着目标函数个数的增加，非支配解的个数呈指数增长，使得在环境选择阶段缺少足够的选择压力，进而影响算法性能。基于分解的NSGA-III算法是一种能够有效解决上述问题的多目标进化算法，但在该算法中采用固定的交叉概率和变异概率生成新的解，使得算法在处理一些复杂的高维多目标问题时表现较差。因此，本文提出一种基于模糊系统的改进型NSGA-III算法，该算法利用模糊系统动态调整子代生成过程中算子的交叉概率与变异概率。对于模糊系统的设计，采用与算法密切相关的Spread值和迭代次数作为输入，利用模糊逻辑推理后输出交叉概率与变异概率。将所提算法与其他基于分解技术的算法在20个高维多目标优化问题上进行实验对比，结果表明本文算法可以有效提高收敛速度，且能很好地保持种群的多样性和收敛性。     

改进种群多样性的双变异差分进化算法

差分进化算法(DE)是一种基于种群的启发式随机搜索技术,对于解决连续性优化问题具有较强的鲁棒性.然而传统差分进化算法存在种群多样性和收敛速度之间的矛盾,一种改进种群多样性的双变异差分进化算法(DADE),通过引入BFS-best机制(基于排序的可行解选取递减策略)改进变异算子"DE/current-to-best",将其与DE/rand/1构成双变异策略来改善DE算法中种群多样性减少的问题.同时,每个个体的控制参数基于排序自适应更新.最后,利用多个CEC2013标准测试函数对改进算法进行测试,实验结果表明,改进后的算法能有效改善种群多样性,较好地提高了算法的全局收敛能力和收敛速度.     

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。     

采用复合规则约束的多种群自适应进化算法

针对种群固定的进化算法容易使个体集中分布在局部区域,不利于处理大尺度空间和多峰类型的优化问题,提出了一种多种群分布并且动态变化的种群自适应进化算法.采用Logistic模型模拟多个种群在有限资源下的竞争关系,设计了稳定性规则、熵规则和精英规则以确定不同种群的Logistic模型参数,从而控制种群数量的变化.同时,算法引入了算术内插和外插两种交叉算子,使得各个种群依据自身类型来缩小或扩展搜索空间.此外,算法还通过周期性的调整规则重新构建种群和分配资源.通过5组大尺度和多峰优化问题的测试结果表明,所提的种群自适应方法能够有效改善算法的寻优性能,在达到同等优化水平时所提算法消耗的函数调用次数为对比算法的61.08%～91.55%.     

考虑帕累托最优解的多目标优化进化算法

大多数现有的进化算法在处理多目标优化问题(multi-objective optimization problem,MOP)时会遇到Pareto最优解稀疏的困难,特别是当决策变量的数目很大时,如旨在从大量候选特征中找出小部分特征的特征选择.为此,提出了一种求解大规模稀疏MOP的进化算法.算法考虑Pareto最优解的稀疏性,提出了一种新的种群初始化策略和遗传算子,以保证解的稀疏性.此外,还设计了一个测试套件来评估该算法在大规模稀疏MOP中的性能,实验结果和应用实例证明了该算法在处理大规模稀疏MOP问题上的优越性.     

自适应多种群回溯群居蜘蛛算法求解TSP问题

在群居蜘蛛优化算法中引入自适应决策半径,将蜘蛛种群动态地分成多个种群,种群内适应度不同的个体采取不同的更新方式.在筛选全局极值的基础上,根据进化程度执行回溯迭代更新,提出一种自适应多种群回溯群居蜘蛛优化算法,旨在提高种群样本多样性和算法全局寻优能力.函数寻优结果表明改进算法具有较快的收敛速度和较高的收敛精度.最后将其应用于TSP问题的求解.     

基于混沌集群智能优化算法的多目标粗糙集属性约减

针对管理实践及大数据处理过程中具有多决策属性的粗糙集属性约减问题,将条件属性依赖度与知识分辨度进行结合构建属性权重,分别建立针对不同决策属性的约减目标函数,引入帕累托最优思想,将基于多决策属性的粗糙集属性约减问题转化为离散多目标优化问题。针对该问题的结构设计了具有集群智能优化思想的元胞自动机求解算法,在算法中引入基于个体的非支配解集平衡局部最优与全局最优的关系,引入混沌遗传算子增加种群多样性。以某铁路局设备安全风险处理数据为案例构建多决策属性粗糙集决策表进行优化计算并进行管理决策分析。研究发现:(1)相对于传统的NSGA-II与MO-cell算法,本文提出的算法具有更强的多目标属性挖掘性能;(2)帕累托最优思想可以较好地解释多决策属性粗糙集在管理实践中的意义。     

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。     

Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems

The structure-control design approach of mechatronic systems requires a different design formulation where the mechanical structure and control system are simultaneously designed. Optimization problems are commonly stated to confront the structure-control design formulation. Nevertheless, these problems are often very complex with a highly nonlinear dependence between the design variables and performance functions. This fact has made the use of evolutionary algorithms, a feasible alternative to solve the highly nonlinear optimization problem; the method to find the best solution is an open issue in the structure-control design approach. Hence, this paper presents a mechanism to exhaustively exploit the solutions in the differential evolution (DE) algorithm in order to find more non-dominated solutions with uniformly distributed Pareto front and better trade-offs in the structure-control design framework. The proposed approach adopts an external population to retain the non-dominated solutions found during the evolutionary process and includes a mechanism to mutate the individuals in their corresponding external population region. As a study case, the structure-control design of a serial-parallel manipulator with its control system is stated as a dynamic optimization problem and is solved by using the proposed approach. A comparative analysis shows that the multi-objective exhaustive exploitation differential evolution obtained a superior performance in the structure-control design framework than a DE algorithm which did not consider the proposal. Hence, the resulting designs provide better trade-offs between the structure-control performance functions.     

A dynamic clustering based differential evolution algorithm for global optimization

A dynamic clustering based differential evolution algorithm (CDE) for global optimization is proposed to improve the performance of the differential evolution (DE) algorithm. With population evolution, CDE algorithm gradually changes from exploring promising areas at the early stages to exploiting solution with high precision at the later stages. Experiments on 28 benchmark problems, including 13 high dimensional functions, show that the new method is able to find near optimal solutions efficiently. Compared with other existing algorithms, CDE improves solution accuracy with less computational effort.     

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。     

A global best artificial bee colony algorithm for global optimization

The artificial bee colony (ABC) algorithm is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in the ABC algorithm regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by differential evolution (DE), we propose a modified ABC algorithm (denoted as ABC/best), which is based on that each bee searches only around the best solution of the previous iteration in order to improve the exploitation. In addition, to enhance the global convergence, when producing the initial population and scout bees, both chaotic systems and opposition-based learning method are employed. Experiments are conducted on a set of 26 benchmark functions. The results demonstrate good performance of ABC/best in solving complex numerical optimization problems when compared with two ABC based algorithms.     

Parameter identification of Rossler’s chaotic system by an evolutionary algorithm

In this paper, a differential evolution (DE) algorithm is applied to parameter identification of Rossler’s chaotic system. The differential evolution has been shown to possess a powerful searching capability for finding the solutions for a given optimization problem, and it allows for parameter solution to appear directly in the form of floating point without further numerical coding or decoding. Three unknown parameters of Rossler’s Chaotic system are optimally estimated by using the DE algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed method.     

Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization

Dynamic optimization and multi-objective optimization have separately gained increasing attention from the research community during the last decade. However, few studies have been reported on dynamic multi-objective optimization (dMO) and scarce effective dMO methods have been proposed. In this paper, we fulfill these gabs by developing new dMO test problems and new effective dMO algorithm. In the newly designed dMO problems, Pareto-optimal decision values (i.e., Pareto-optimal solutions: POS) or both POS and Pareto-optimal objective values (i.e., Pareto-optimal front: POF) change with time. A new multi-strategy ensemble multi-objective evolutionary algorithm (MS-MOEA) is proposed to tackle the challenges of dMO. In MS-MOEA, the convergence speed is accelerated by the new offspring creating mechanism powered by adaptive genetic and differential operators (GDM); a Gaussian mutation operator is employed to cope with premature convergence; a memory like strategy is proposed to achieve better starting population when a change takes place. In order to show the advantages of the proposed algorithm, we experimentally compare MS-MOEA with several algorithms equipped with traditional restart strategy. It is suggested that such a multi-strategy ensemble approach is promising for dealing with dMO problems.     

正则参数求解的微分进化算法

研究了正则化方法中正则参数的求解问题,提出了利用微分进化算法获取正则参数.微分进化算法属于全局最优化算法,具有鲁棒性强、收敛速度快、计算精度高的优点.把正则参数的求解问题转化为非线性优化问题,通过保持在解空间不同区域中各个点的搜索,以最大的概率找到问题的全局最优解,同时还利用数值模拟将此方法与广义交叉原理、L-曲线准则、逆最优准则等进行了对比,数值模拟结果表明该方法具有一定的可行性和有效性.     

Hybridizing local search algorithms for global optimization

In this paper, we combine two types of local search algorithms for global optimization of continuous functions. In the literature, most of the hybrid algorithms are produced by combination of a global optimization algorithm with a local search algorithm and the local search is used to improve the solution quality, not to explore the search space to find independently the global optimum. The focus of this research is on some simple and efficient hybrid algorithms by combining the Nelder–Mead simplex (NM) variants and the bidirectional random optimization (BRO) methods for optimization of continuous functions. The NM explores the whole search space to find some promising areas and then the BRO local search is entered to exploit optimal solution as accurately as possible. Also a new strategy for shrinkage stage borrowed from differential evolution (DE) is incorporated in the NM variants. To examine the efficiency of proposed algorithms, those are evaluated by 25 benchmark functions designed for the special session on real-parameter optimization of CEC2005. A comparison study between the hybrid algorithms and some DE algorithms and non-parametric analysis of obtained results demonstrate that the proposed algorithms outperform most of other algorithms and their difference in most cases is statistically considerable. In a later part of the comparative experiments, a comparison of the proposed algorithms with some other evolutionary algorithms reported in the CEC2005 confirms a better performance of our proposed algorithms.     

Cognitive learning in differential evolution and its application to model order reduction problem for single-input single-output systems

Differential evolution (DE) is a well known and simple population based probabilistic approach for global optimization over continuous spaces. It has reportedly outperformed a few evolutionary algorithms and other search heuristics like the particle swarm optimization when tested over both benchmark and real world problems. DE, like other probabilistic optimization algorithms, has inherent drawback of premature convergence and stagnation. Therefore, in order to find a trade-off between exploration and exploitation capability of DE algorithm, a new parameter namely, cognitive learning factor (CLF) is introduced in the mutation process. Cognitive learning is a powerful mechanism that adjust the current position of individuals by the means of some specified knowledge (previous experience of individuals). The proposed strategy is named as cognitive learning in differential evolution (CLDE). To prove the efficiency of various approaches of CLF in DE,?CLDE is tested over 25 benchmark problems. Further, to establish the wide applicability of CLF,?CLDE is applied to two advanced DE variants. CLDE is also applied to solve a well known electrical engineering problem called model order reduction problem for single input single output systems.