Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.

Nonlinear Model-Based Process Operation under UncertaintyUsing Exact Parametric Programming

In the present work, two new, （multi-）parametric programming （mp-P）-inspired algorithms for the solutionof mixed-integer nonlinear programming （MINLP） problems are developed, with their main focus being onprocess synthesis problems. The algorithms are developed for the special case in which the nonlinearitiesarise because of logarithmic terms, with the first one being developed for the deterministic case, and thesecond for the parametric case （p-MINLP）. The key idea is to formulate and solve the square system of thefirst-order Karush-Kuhn-Tucker （KKT） conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution tech-niques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, twoprocess synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicitfunction of the uncertain parameters.

Design of a Computational Heuristic to Solve the Nonlinear Liénard Differential Model

In this study,the design of a computational heuristic based on the nonlinear Liénard model is presented using the efficiency of artificial neural networks(ANNs)along with the hybridization procedures of global and local search approaches.The global search genetic algorithm(GA)and local search sequential quadratic programming scheme(SQPS)are implemented to solve the nonlinear Liénard model.An objective function using the differential model and boundary conditions is designed and optimized by the hybrid computing strength of the GA-SQPS.The motivation of the ANN procedures along with GA-SQPS comes to present reliable,feasible and precise frameworks to tackle stiff and highly nonlinear differentialmodels.The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models.The achieved numerical outcomes on multiple trials using the designed procedures are compared to authenticate the correctness,viability and efficacy.Moreover,statistical performances based on different measures are also provided to check the reliability of the ANN along with GASQPS.

Genetic programming-based chaotic time series modeling

This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.

Bi-Level Programming for the Optimal Nonlinear Distance-Based Transit Fare Structure Incorporating Principal-Agent Game

The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.

A TRUST REGION METHOD WITH A CONIC MODEL FOR NONLINEARLY CONSTRAINED OPTIMIZATION

Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.

基于SMPA的半挂车自动泊车运动规划方法研究

半挂车辆的非稳定运动学特性为其泊车过程中自主运动规划带来严峻挑战。针对半挂车在多障碍物的静态场景中泊车运动规划算法效率低、结果平滑性差等问题,本文提出了序列式运动规划方法(sequential motion planning algorithm,SMPA)。首先,提出了基于二次规划策略和改进双向快速扩展随机树(bidirectional rapidly-exploring random tree algorithm,Bi-RRT)的初始路径生成方法。然后,结合车辆非完整微分约束下的路径节点可行性判别方法研究,提出基于概率的目标偏向采样策略,提高了采样效率。最后,构建了面向车辆系统控制变量连续性的非线性最优化控制模型,解决泊车换向点的对接问题,提高了泊车轨迹平滑性。仿真结果表明,该方法在多障碍物场景中,规划时间相比Hybrid A*和Bi-RRT分别降低了86.71%和21.44%,轨迹质量也更具优越性。

基于非线性规划的多波束测线优化设计

为获取不同地形情况下的测线布设优化方案,文章对多波束探测技术展开了研究,首先应用几何关系得到了多波束测深的覆盖宽度模型和重叠率模型;其次通过建立海底坡面参数方程与多波束探测面所在平面参数方程,得到了不定测线方向覆盖宽度模型;最后综合已有模型及边角关系,针对矩形海域建立了测线总长度的优化模型。

Optimal Antibody Puri cation Strategies Using Data-Driven Models

This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational ow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, ow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody puri cation process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models.

Research of Enterprise Storage Ecosystem Based on Storage Theory and Nonlinear Discrete Optimization

Warehousing and transferring strategies are an important part of business operations. The issue of optimal warehousing and transferring strategy is studied in this paper. Wal-Mart in Wuhan serves as an example to establish a (s, S) random storage strategy model, a Markov chain model, and a nonlinear discrete programming model, aiming at maximizing the profit per cycle of every branch and further maximizing the company’s total profit per cycle. Among them, the random storage strategy model establishes a security zone of inventory for every branch, that is, it can meet consumers’ demand without spending too much storage costs. The Markov chain model is used to get the probability of losing sales opportunities in every branch. The nonlinear discrete programming model takes into account the horizontal transferring among branches, which further maximizes the company’s overall profit expectations. The three models above can be used to formulate inventory strategies, assess risks, and provide advice for every branch in order to form a complete storage ecosystem and provide constructive suggestions for the company’s operations.

Maximum likelihood estimation of nonlinear mixed-effects models with crossed random effects by combining first-order conditional linearization and sequential quadratic programming

Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.

基于溶蚀速率的灰岩边坡服役寿命研究

边坡服役寿命的预测能够定量、精确地评价灰岩边坡的长期安全性,但其预测模型尚未成熟。因此,为解决计算灰岩边坡服役寿命这一难题,提出基于溶蚀速率的灰岩边坡服役寿命优化计算方法。将灰岩边坡服役寿命作为目标函数,根据溶蚀速率和抗剪参数衰减速率计算灰岩边坡服役若干年后结构面贯通段和非贯通段的有效长度以及结构面的抗剪参数;结合滑体的平衡方程以及结构面贯通段和非贯通段的屈服条件,建立灰岩边坡长期服役的稳定性非线性数学规划模型,使用“序列二次规划法”求解数学规划模型,获得边坡的服役寿命。经验证,本文算法得出的边坡安全系数与有限元法数值模拟计算结果的平均相对误差为2.47%,表明本文算法能较为精确地预测灰岩边坡的服役寿命。

考虑轮换的易逝性应急物资储备策略研究

针对易逝性应急物资价值随时间递减和过期浪费等问题,考虑过期之前用新物资替换旧物资的轮换策略,并研究不确定需求下易逝性应急物资最优储备问题。以应急物资储备量和轮换时间为决策变量,以单位时间内期望总成本和总损失之和最小为目标建立随机非线性规划模型,并对模型结构进行分析。通过模拟算例,分析不同类型应急物资的价值函数与最优储备量和最佳轮换时间的关系,进一步对比分析采取轮换策略的必要性。结果表明:对于易逝性应急物资采取定期轮换策略能有效降低物资储备成本和期望损失,减少应急物资的过期浪费。本文可为制定不同类型应急物资的最优储备与轮换策略提供参考。

兼顾公平与效率的无人机应急中继通信选址优化问题

为提高应急救援中无人机应急中继通信资源配置的公平与效率,在考虑无人机中继通信覆盖范围限制、各受灾用户集群点分布情况、受灾群众公平性感知的基础上,构建以最大化系统吞吐量为效率目标、最小化受灾群众公平损失值为公平目标的无人机应急中继通信选址多目标0-1非线性整数规划模型,采用基于k-means的模拟退火算法对其进行求解,并以实际案例为背景构造算例,验证本文提出模型和算法的可行性与有效性,并进行多目标分析及参数敏感性分析。研究结果表明:本文提出的模型和算法能在较短时间得到无人机应急中继通信选址方案,保证所有受灾用户集群点获得通信中继;同时,确定最佳无人机设备数量,验证公平目标与效率目标存在悖反关系。

计及管储模型的电-气IES低碳协同运行策略

为解决综合能源系统风能利用率低、燃煤机组碳排放高的情况,考虑建立碳捕集-电转气协同运行模型,充分挖掘其对可再生能源消纳和碳减排的潜力。首先,建立系统内重要能源耦合设备的运行表达式以及各能源网络的约束平衡条件,通过气管道节点压强、流量的关系推导出管储模型方程,关注其对系统运行经济性的影响;其次,利用分段线性化和二阶锥松弛技术将约束条件非线性部分作线性化处理,采用拉丁超立方抽样结合K氏距离法来描述风电功率的不确定性;接着,建立9节点电力和6节点天然气网络耦合的系统进行仿真计算,分析3种方案下系统运行的经济性、环境性,重点讨论限制电转气运行的关键因素;最后,通过风能利用、碳捕集运行、管储能力阐述多目标优化问题中的矛盾关系,结果表明所提模型对减少系统碳排放和提升风能利用率具有积极作用。

基于改进非线性自回归网络的洪水预测算法

针对流域的洪水预测具有高度非线性和随机性的问题,提出了一种混合预测模型用于流域的洪水预测.该模型是一个集成了数据预处理模块的具有外部输入的非线性自回归神经网络,采用小波变换进行时间序列分解,利用多基因遗传编程进行细节缩放,以提高时域和频域特性的提取能力,进一步捕获时间序列的非平稳性,与NARX结合可以大幅提高洪水预测的准确性,利用栾川水文站15年中所测水文数据对所提模型进行验证和测试.实验结果表明,相比较于传统算法和其他预测算法,所提出的算法具有更高的预测准确度和性能,可广泛应用在洪水预测等领域.

基于简化模型的电动汽车充电站布局非线性规划

为寻求充电站建设布局最优规划问题,以交通流量、充电距离、充电时间、渗透率等为约束条件,引入充电站建设的固定成本、变动成本、充电站的运营成本以及消费者的时间成本等数据,构建成本之和最小为目标函数。以某一规划区域充电站数量为变量,假设小区域为正方形,推导出充电需求距离与充电站数量的简化模型,得到充电站成本与充电站数量之间的非线性多项式数学方程。再次,根据南昌高新区地理环境实际情况,采用专家访谈法,以车辆密度、人口密度和经济活跃度三维度确定分区权重,可规划出四种不同的充电站建设方案,通过计算机模拟充电车辆随机分布在规划区域内,利用构建的模型,可测算出不同固定成本投入时的充电站建设社会成本最小方案,即当充电站建设为6个时为最优方案。研究的结果有利于改善交通环境,提升城市交通运营效率。

Energy Management of Networked Smart Railway Stations Considering Regenerative Braking, Energy Storage System, and Photovoltaic Units

The networking of microgrids has received significant attention in the form of a smart grid.In this paper,a set of smart railway stations,which is assumed as microgrids,is connected together.It has been tried to manage the energy exchanged between the networked microgrids to reduce received energy from the utility grid.Also,the operational costs of stations under various conditions decrease by applying the proposed method.The smart railway stations are studied in the presence of photovoltaic(PV)units,energy storage systems(ESSs),and regenerative braking strategies.Studying regenerative braking is one of the essential contributions.Moreover,the stochastic behaviors of the ESS’s initial state of energy and the uncertainty of PV power generation are taken into account through a scenario-based method.The networked microgrid scheme of railway stations(based on coordinated operation and scheduling)and independent operation of railway stations are studied.The proposed method is applied to realistic case studies,including three stations of Line 3 of Tehran Urban and Suburban Railway Operation Company(TUSROC).The rolling stock is simulated in the MATLAB environment.Thus,the coordinated operation of networked microgrids and independent operation of railway stations are optimized in the GAMS environment utilizing mixed-integer linear programming(MILP).

倾转旋翼机过渡段动态最优控制技术研究

针对倾转旋翼机的最优过渡问题,采用动态最优控制来减小过渡时间、姿态角变化以及缓解驾驶员工作负荷。在飞行动力学模型的基础上引入操纵方程,通过引入操纵量方程来缓解操纵量的跳变;随后将飞行器的最优动态倾转过渡过程转变成非线性动态最优控制问题,引入合理的性能指标,基于序列二次规划算法进行求解;最终以XV-15为例,分析系统各个通道抗风扰能力以及进行全航线飞行仿真。实验结果表明,所设计的过渡段最优控制在倾转旋翼机的各个通道抗风扰性能突出,系统鲁棒性较好,具有较好的实际应用价值。

利用ARIMA-SSA-LSTM组合模型的碳排放交易价格预测

单一的预测方法在不同方面各有优劣,为了提高碳排放交易价格预测的精确度,从智能算法出发提出ARIMA-SSA-LSTM组合碳排放交易价格预测模型。该模型通过结合非线性规划局部搜索的优势和遗传算法全局搜索的优势使用非线性规划遗传算法分配差分整合移动平均自回归(ARIMA)模型和麻雀搜索算法优化后的长短时记忆(LSTM)模型(SSA-LSTM)的权重,通过加权得到最终的碳排放交易价格预测结果。运用ARIMA-SSA-LSTM组合模型,ARIMA模型,LSTM模型和SSA-LSTM模型分别对湖北省与广东省碳排放交易价格进行短期和长期预测。实证结果表明,相比单一的ARIMA模型、LSTM模型、SSA-LSTM模型,ARIMA-SSA-LSTM组合模型三个预测精度评价指标均为最小,碳排放交易价格预测精度最优。相比于传统ARIMA模型,机器学习LSTM模型具有更精确的预测结果,并且趋势预测更优。引入智能算法后,权重分配结果更加准确,LSTM模型的预测性能得到提升,印证了智能算法在碳排放交易价格预测领域的有效性。