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为了研究树木的生长是否也存在突变的问题,将突变论的尖角模型理论应用于我国北方——内蒙古赤峰市旺业甸林场10个常见树种单木材积的测定和计算。选取10个北方常见树种,对其树高(H)、胸径(D)、材积(V)、地径(D0)等参数进行测定,并以此作为真值,利用改进差分进化算法对建立的“材积–树高–胸径”模型进行内符合精度检验,利用边缘树种对模型进行外符合精度检验,比较模型计算值与仪器测量值之间的差异。在经过一定的迭代之后,结果表明:模型的总体相对误差RS在[0.001,0.05]范围,平均相对误差E在[-0.11,0.02]范围,总体预估精度P大于80%,说明模型拟合较好,即突变论中的尖角模型理论适用于我国北方10个树种单木材积模型的建立,同时说明随着树木的不断生长,当树高达到一定高度时,材积将遵循突变论的尖角模型理论。这是突变论的尖角模型理论首次应用到单木材积的测定,并得到较好的拟合结果。同时,在不连续的测量状态下建立的突变低维模型为树木材积的研究和各树种间的空间竞争研究提供了一定的理论和实践依据。

In order to solve the problem that some test data cannot be measured or the measurement is difficult, a combined aerodynamic parameters identification method for missing test data is proposed. In this method, the aerodynamic parameter identification problem is modified into an optimization problem. The initial value of the flight state and the aerodynamic parameter interpolation table are used as design variables, and the motion equation of the aircraft including all aerodynamic parameters is used as a model to construct an objective function containing multiple pieces of test data information. In the optimization, the aerodynamic parameter database and the identification results of the existing methods are used as the prior knowledge. The initial value of the unmeasured data is fitted as the reference value. Then, the feasible sample selection method is designed. Finally, the differential evolution algorithm is used to solve the problem. The proposed method is used to process 264 pieces of test data, and the results show that compared with the existing aerodynamic parameter identification methods, the proposed identification method can obtain all aerodynamic parameters with higher accuracy and can inversely calculate and obtain unmeasured flight test data practical engineering significance. 为解决试验中部分数据缺失或难以测量的问题, 提出了一种适用于部分试验数据缺失的气动参数联合辨识方法。该方法将气动参数辨识问题转为优化问题, 以飞行状态初值和气动参数插值表为设计变量, 使用包含全部气动参数的弹道模型, 构建包含多条数据的目标函数。优化中以气动参数数据库和现有方法辨识结果为先验知识, 拟合出未测量数据的初值作为基准值, 设计了可行样本选取方法, 利用差分进化算法进行求解。应用所提方法处理264条试验数据, 结果表明相比于现有气动参数辨识方法, 所提方法能辨识全部气动参数, 准确度更高, 且能反算出未测量的飞行试验数据, 具有实际工程意义。

This paper proposes the generation scheduling approach for a microgrid comprised of conventional generators, wind energy generators, solar photovoltaic (PV) systems, battery storage, and electric vehicles. The electrical vehicles (EVs) play two different roles: as load demands during charging, and as storage units to supply energy to remaining load demands in the MG when they are plugged into the microgrid (MG). Wind and solar PV powers are intermittent in nature; hence by including the battery storage and EVs, the MG becomes more stable. Here, the total cost objective is minimized considering the cost of conventional generators, wind generators, solar PV systems and EVs. The proposed optimal scheduling problem is solved using the hybrid differential evolution and harmony search (hybrid DE-HS) algorithm including the wind energy generators and solar PV system along with the battery storage and EVs. Moreover, it requires the least investment.

The hybrid power source needs to achieve the excellent power distribution control to enhance the vehicle performance, the optimization algorithm can automatically seek the optimal target according to vehicle requirements to achieve the best power distribution of hybrid power source. Power consumption is one of the core indicators for evaluating power distribution control of hybrid power source, as well as the current fluctuation of battery is an important factor that affects its power consumption and cycle life. Taking the fully-active hybrid power source configuration as the application object, a differential evolution algorithm with fast convergence speed and strong global search ability to achieve real-time power distribution control with multiple optimization goals is introduced by fully considering two important parameters of power consumption and battery current fluctuation, the power consumption model for the hybrid power source is established, the functional relationship between the power consumption of hybrid power source, current change of battery and its output current is given. In this algorithm, the minimum power consumption of the hybrid power source and the minimum change rate of the battery output current are selected as the optimization goals, the weight coefficients of the two optimization goals are assigned to seek the influence relationship between the two optimization goals. The empirical results from a simulation verify effectiveness and reliability of the designed scheme. The research results provide a reference for controlling the power distribution and optimizing the hybrid power source of electric vehicle. 混合电源需实现卓越的功率分配控制以提升车辆性能, 而优化算法可根据车辆需求自动地寻求既定目标的最优解, 以实现混合电源的最佳功率分配。功耗是评价功率分配控制的核心指标, 蓄电池的电流变化率是影响其功耗和寿命的重要因素。以全主动配置的混合电源拓扑结构为应用对象, 引入一种新颖的具有收敛速度快且全局搜索能力强的差分进化算法以实现多优化目标的实时功率分配控制；充分考虑功耗和蓄电池的电流变化率2个重要参数, 建立了混合电源的功耗模型, 给出了混合电源的功耗、蓄电池输出电流与蓄电池电流变化率之间的函数关系；以混合电源的功耗最小以及蓄电池输出电流变化率最小为优化目标, 赋予2个优化目标权重系数, 以寻求2个优化目标之间的影响关系。仿真实例结果验证了所设计方案的有效性和可靠性。研究结果为电动汽车混合电源功率分配控制及优化提供参考。

According to the actual requirements, profile and rolling energy consumption are selected as objective functions of rolling schedule optimization for tandem cold rolling. Because of mechanical wear, roll diameter has some uncertainty during the rolling process, ignoring which will cause poor robustness of rolling schedule. In order to solve this problem, a robust multi-objective optimization model of rolling schedule for tandem cold rolling was established. A differential evolution algorithm based on the evolutionary direction was proposed. The algorithm calculated the horizontal angle of the vector, which was used to choose mutation vector. The chosen vector contained converging direction and it changed the random mutation operation in differential evolution algorithm. Efficiency of the proposed algorithm was verified by two benchmarks. Meanwhile, in order to ensure that delivery thicknesses have descending order like actual rolling schedule during evolution, a modified Latin Hypercube Sampling process was proposed. Finally, the proposed algorithm was applied to the model above. Results showed that profile was improved and rolling energy consumption was reduced compared with the actual rolling schedule. Meanwhile, robustness of solutions was ensured.

Differential Evolution （DE） has been well accepted ever, it usually involves a large number of fitness evaluations to as an effective evolutionary optimization technique. Howobtain a satisfactory solution. This disadvantage severely restricts its application to computationally expensive problems, for which a single fitness evaluation can be highly timeconsuming. In the past decade, a lot of investigations have been conducted to incorporate a surrogate model into an evolutionary algorithm （EA） to alleviate its computational burden in this scenario. However, only limited work was devoted to DE. More importantly, although various types of surrogate models, such as regression, ranking, and classification models, have been investigated separately, none of them consistently outperforms others. In this paper, we propose to construct a surrogate model by combining both regression and classification techniques. It is shown that due to the specific selection strategy of DE, a synergy can be established between these two types of models, and leads to a surrogate model that is more appropriate for DE. A novel surrogate model-assisted DE, named Classification- and Regression-Assisted DE （CRADE） is proposed on this basis. Experimental studies are carried out on a set of 16 benchmark functions, and CRADE has shown significant superiority over DE-assisted with only regression or classification models. Further comparison to three state-of-the-art DE variants, i.e., DE with global and local neighborhoods （DECL）, JADE, and composite DE （CODE）, also demonstrates the superiority of CRADE.

In differential evolution (DE), the salient feature lies in its mutationmechanismthat distinguishes it from other evolutionary algorithms. Generally, for most of the DE algorithms, the parents for mutation are randomly chosen from the current population. Hence, all vectors of population have the equal chance to be selected as parents without selective pressure at all. In this way, the information of population cannot be fully exploited to guide the search. To alleviate this drawback and improve the performance of DE, we present a new selection method of parents that attempts to choose individuals for mutation by utilizing the population information effectively. The proposed method is referred as fitnessand- position based selection (FPS), which combines the fitness and position information of population simultaneously for selecting parents in mutation of DE. In order to evaluate the effectiveness of FPS, FPS is applied to the original DE algorithms, as well as several DE variants, for numerical optimization. Experimental results on a suite of benchmark functions indicate that FPS is able to enhance the performance of most DE algorithms studied. Compared with other selection methods, FPS is also shown to be more effective to utilize information of population for guiding the search of DE.

Compact algorithms are Estimation of Distribution Algorithms which mimic the behavior of population-based algorithms by means of a probabilistic representation of the population of candidate solutions. These algorithms have a similar behaviour with respect to population-based algorithms but require a much smaller memory. This feature is crucially important in some engineering applications, especially in robotics. A high performance compact algorithm is the compact Differential Evolution （cDE） algorithm. This paper proposes a novel implementation of cDE, namely compact Differential Evolution light （cDElight）, to address not only the memory saving necessities but also real-time requirements, cDElight employs two novel algorithmic modifications for employing a smaller computational overhead without a performance loss, with respect to cDE. Numerical results, carried out on a broad set of test problems, show that cDElight, despite its minimal hardware requirements, does not deteriorate the performance of cDE and thus is competitive with other memory saving and population-based algorithms. An application in the field of mobile robotics highlights the usability and advantages of the proposed approach.

Close formation flight is one of the most complicated problems on multi-uninhabited aerial vehicles （UAVs） coordinated control. Based on the nonlinear model of multi-UAVs close formation, a novel type of control strategy of using hybrid receding horizon control （RHC） and differential evolution algorithm is proposed. The issue of multi-UAVs close formation is transformed into several on-line optimization problems at a series of receding horizons, while the differential evolution algorithm is adopted to optimize control sequences at each receding horizon. Then, based on the Markov chain model, the convergence of differential evolution is proved. The working process of RHC controller is presented in detail, and the stability of close formation controller is also analyzed. Finally, three simulation experiments are performed, and the simulation results show the feasibility and validity of our proposed control algorithm.

Load distribution is a key technology in hot strip rolling process, which directly influences strip product quality. A multi-objective load distribution model, which takes into account the rolling force margin balance, roll wear ratio and strip shape control, is presented. To avoid the selection of weight coefficients encountered in single objective optimization, a multi-objective differential evolutionary algorithm, called MaximinDE, is proposed to solve this model. The experimental results based on practical production data indicate that MaximinDE can obtain a good pareto-optimal solution set, which consists of a series of alternative solutions to load distribution. Decision-makers can select a trade-off solution from the pareto-optimal solution set based on their experience or the importance of ob- iectives. In comparison with the empirical load distribution solution, the trade-off solution can achieve a better per- formance, which demonstrates the effectiveness of the multi-objective load distribution optimization. Moreover, the conflicting relationship among different objectives can be also found, which is another advantage of multi-objective load distribution optimization.