Development of hybrid optimization algorithm for structures furnished with seismic damper devices using the particle swarm optimization method and gravitational search algorithm

Previous studies about optimizing earthquake structural energy dissipation systems indicated that most existing techniques employ merely one or a few parameters as design variables in the optimization process,and thereby are only applicable only to simple,single,or multiple degree-of-freedom structures.The current approaches to optimization procedures take a specific damper with its properties and observe the effect of applying time history data to the building;however,there are many different dampers and isolators that can be used.Furthermore,there is a lack of studies regarding the optimum location for various viscous and wall dampers.The main aim of this study is hybridization of the particle swarm optimization(PSO) and gravitational search algorithm(GSA) to optimize the performance of earthquake energy dissipation systems(i.e.,damper devices) simultaneously with optimizing the characteristics of the structure.Four types of structural dampers device are considered in this study:(ⅰ) variable stiffness bracing(VSB) system,(ⅱ) rubber wall damper(RWD),(ⅲ) nonlinear conical spring bracing(NCSB) device,(iv) and multi-action stiffener(MAS) device.Since many parameters may affect the design of seismic resistant structures,this study proposes a hybrid of PSO and GSA to develop a hybrid,multi-objective optimization method to resolve the aforementioned problems.The characteristics of the above-mentioned damper devices as well as the section size for structural beams and columns are considered as variables for development of the PSO-GSA optimization algorithm to minimize structural seismic response in terms of nodal displacement(in three directions) as well as plastic hinge formation in structural members simultaneously with the weight of the structure.After that,the optimization algorithm is implemented to identify the best position of the damper device in the structural frame to have the maximum effect and minimize the seismic structure response.To examine the performance of the proposed PSO-GSA optimization method,it has been applied to a three-story reinforced structure equipped with a seismic damper device.The results revealed that the method successfully optimized the earthquake energy dissipation systems and reduced the effects of earthquakes on structures,which significantly increase the building’s stability and safety during seismic excitation.The analysis results showed a reduction in the seismic response of the structure regarding the formation of plastic hinges in structural members as well as the displacement of each story to approximately 99.63%,60.5%,79.13% and 57.42% for the VSB device,RWD,NCSB device,and MAS device,respectively.This shows that using the PSO-GSA optimization algorithm and optimized damper devices in the structure resulted in no structural damage due to earthquake vibration.

Optimal Energy Consumption Optimization in a Smart House by Considering Electric Vehicles and Demand Response via a Hybrid Gravitational Search and Particle Swarm Optimization Algorithm

Buildings are the main energy consumers across the world,especially in urban communities.Building smartization,or the smartification of housing,therefore,is a major step towards energy grid smartization too.By controlling the energy consumption of lighting,heating,and cooling systems,energy consumption can be optimized.All or some part of the energy consumed in future smart buildings must be supplied by renewable energy sources(RES),which mitigates environmental impacts and reduces peak demand for electrical energy.In this paper,a new optimization algorithm is applied to solve the optimal energy consumption problem by considering the electric vehicles and demand response in smart homes.In this way,large power stations that work with fossil fuels will no longer be developed.The current study modeled and evaluated the performance of a smart house in the presence of electric vehicles(EVs)with bidirectional power exchangeability with the power grid,an energy storage system(ESS),and solar panels.Additionally,the solar RES and ESS for predicting solar-generated power prediction uncertainty have been considered in this work.Different case studies,including the sales of electrical energy resulting from PV panels’generated power to the power grid,time-variable loads such as washing machines,and different demand response(DR)strategies based on energy price variations were taken into account to assess the economic and technical effects of EVs,BESS,and solar panels.The proposed model was simulated in MATLAB.A hybrid particle swarm optimization(PSO)and gravitational search(GS)algorithm were utilized for optimization.Scenario generation and reduction were performed via LHS and backward methods,respectively.Obtained results demonstrate that the proposed model minimizes the energy supply cost by considering the stochastic time of use(STOU)loads,EV,ESS,and PV system.Based on the results,the proposed model markedly reduced the electricity costs of the smart house.

Optimization of Thermal Aware VLSI Non-Slicing Floorplanning Using Hybrid Particle Swarm Optimization Algorithm-Harmony Search Algorithm

Floorplanning is a prominent area in the Very Large-Scale Integrated (VLSI) circuit design automation, because it influences the performance, size, yield and reliability of the VLSI chips. It is the process of estimating the positions and shapes of the modules. A high packing density, small feature size and high clock frequency make the Integrated Circuit (IC) to dissipate large amount of heat. So, in this paper, a methodology is presented to distribute the temperature of the module on the layout while simultaneously optimizing the total area and wirelength by using a hybrid Particle Swarm Optimization-Harmony Search (HPSOHS) algorithm. This hybrid algorithm employs diversification technique (PSO) to obtain global optima and intensification strategy (HS) to achieve the best solution at the local level and Modified Corner List algorithm (MCL) for floorplan representation. A thermal modelling tool called hotspot tool is integrated with the proposed algorithm to obtain the temperature at the block level. The proposed algorithm is illustrated using Microelectronics Centre of North Carolina (MCNC) benchmark circuits. The results obtained are compared with the solutions derived from other stochastic algorithms and the proposed algorithm provides better solution.

A composite particle swarm algorithm for global optimization of multimodal functions

During the last decade, many variants of the original particle swarm optimization （PSO） algorithm have been proposed for global numerical optimization, hut they usually face many challenges such as low solution quality and slow convergence speed on multimodal function optimization. A composite particle swarm optimization （CPSO） for solving these difficulties is presented, in which a novel learning strategy plus an assisted search mechanism framework is used. Instead of simple learning strategy of the original PSO, the proposed CPSO combines one particle＇s historical best information and the global best information into one learning exemplar to guide the particle movement. The proposed learning strategy can reserve the original search information and lead to faster convergence speed. The proposed assisted search mechanism is designed to look for the global optimum. Search direction of particles can be greatly changed by this mechanism so that the algorithm has a large chance to escape from local optima. In order to make the assisted search mechanism more efficient and the algorithm more reliable, the executive probability of the assisted search mechanism is adjusted by the feedback of the improvement degree of optimal value after each iteration. According to the result of numerical experiments on multimodal benchmark functions such as Schwefel, Rastrigin, Ackley and Griewank both with and without coordinate rotation, the proposed CPSO offers faster convergence speed, higher quality solution and stronger robustness than other variants of PSO.

A Hybrid Optimizer Based On Firefly Algorithm And Particle Swarm Optimization Algorithm

As two widely used evolutionary algorithms,particle swarm optimization(PSO)and firefly algorithm(FA)have been successfully applied to diverse difficult applications.And extensive experiments verify their own merits and characteristics.To efficiently utilize different advantages of PSO and FA,three novel operators are proposed in a hybrid optimizer based on the two algorithms,named as FAPSO in this paper.Firstly,the population of FAPSO is divided into two sub-populations selecting FA and PSO as their basic algorithm to carry out the optimization process,respectively.To exchange the information of the two sub-populations and then efficiently utilize the merits of PSO and FA,the sub-populations share their own optimal solutions while they have stagnated more than a predefined threshold.Secondly,each dimension of the search space is divided into many small-sized sub-regions,based on which much historical knowledge is recorded to help the current best solution to carry out a detecting operator.The purposeful detecting operator enables the population to find a more promising sub-region,and then jumps out of a possible local optimum.Lastly,a classical local search strategy,i.e.,BFGS QuasiNewton method,is introduced to improve the exploitative capability of FAPSO.Extensive simulations upon different functions demonstrate that FAPSO is not only outperforms the two basic algorithm,i.e.,FA and PSO,but also surpasses some state-of-the-art variants of FA and PSO,as well as two hybrid algorithms.

An Improved Lung Cancer Segmentation Based on Nature-Inspired Optimization Approaches

The distinction and precise identification of tumor nodules are crucial for timely lung cancer diagnosis andplanning intervention. This research work addresses the major issues pertaining to the field of medical imageprocessing while focusing on lung cancer Computed Tomography (CT) images. In this context, the paper proposesan improved lung cancer segmentation technique based on the strengths of nature-inspired approaches. Thebetter resolution of CT is exploited to distinguish healthy subjects from those who have lung cancer. In thisprocess, the visual challenges of the K-means are addressed with the integration of four nature-inspired swarmintelligent techniques. The techniques experimented in this paper are K-means with Artificial Bee Colony (ABC),K-means with Cuckoo Search Algorithm (CSA), K-means with Particle Swarm Optimization (PSO), and Kmeanswith Firefly Algorithm (FFA). The testing and evaluation are performed on Early Lung Cancer ActionProgram (ELCAP) database. The simulation analysis is performed using lung cancer images set against metrics:precision, sensitivity, specificity, f-measure, accuracy,Matthews Correlation Coefficient (MCC), Jaccard, and Dice.The detailed evaluation shows that the K-means with Cuckoo Search Algorithm (CSA) significantly improved thequality of lung cancer segmentation in comparison to the other optimization approaches utilized for lung cancerimages. The results exhibit that the proposed approach (K-means with CSA) achieves precision, sensitivity, and Fmeasureof 0.942, 0.964, and 0.953, respectively, and an average accuracy of 93%. The experimental results prove thatK-meanswithABC,K-meanswith PSO,K-meanswith FFA, andK-meanswithCSAhave achieved an improvementof 10.8%, 13.38%, 13.93%, and 15.7%, respectively, for accuracy measure in comparison to K-means segmentationfor lung cancer images. Further, it is highlighted that the proposed K-means with CSA have achieved a significantimprovement in accuracy, hence can be utilized by researchers for improved segmentation processes of medicalimage datasets for identifying the targeted region of interest.

Binary Gravitational Search based Algorithm for Optimum Siting and Sizing of DG and Shunt Capacitors in Radial Distribution Systems

This paper presents a binary gravitational search algorithm (BGSA) is applied to solve the problem of optimal allotment of DG sets and Shunt capacitors in radial distribution systems. The problem is formulated as a nonlinear constrained single-objective optimization problem where the total line loss (TLL) and the total voltage deviations (TVD) are to be minimized separately by incorporating optimal placement of DG units and shunt capacitors with constraints which include limits on voltage, sizes of installed capacitors and DG. This BGSA is applied on the balanced IEEE 10 Bus distribution network and the results are compared with conventional binary particle swarm optimization.

Hypersonic reentry trajectory planning by using hybrid fractional-order particle swarm optimization and gravitational search algorithm

This paper proposes a novel hybrid algorithm called Fractional-order Particle Swarm optimization Gravitational Search Algorithm(FPSOGSA)and applies it to the trajectory planning of the hypersonic lifting reentry flight vehicles.The proposed method is used to calculate the control profiles to achieve the two objectives,namely a smoother trajectory and enforcement of the path constraints with terminal accuracy.The smoothness of the trajectory is achieved by scheduling the bank angle with the aid of a modified scheme known as a Quasi-Equilibrium Glide(QEG)scheme.The aerodynamic load factor and the dynamic pressure path constraints are enforced by further planning of the bank angle with the help of a constraint enforcement scheme.The maximum heating rate path constraint is enforced through the angle of attack parameterization.The Common Aero Vehicle(CAV)flight vehicle is used for the simulation purpose to test and compare the proposed method with that of the standard Particle Swarm Optimization(PSO)method and the standard Gravitational Search Algorithm(GSA).The simulation results confirm the efficiency of the proposed FPSOGSA method over the standard PSO and the GSA methods by showing its better convergence and computation efficiency.

A hybrid constriction coefficientbased particle swarm optimization and gravitational search algorithm for training multi-layer perceptron

Purpose-In this paper,a newly proposed hybridization algorithm namely constriction coefficient-based particle swarm optimization and gravitational search algorithm(CPSOGSA)has been employed for training MLP to overcome sensitivity to initialization,premature convergence,and stagnation in local optima problems of MLP.Design/methodology/approach-In this study,the exploration of the search space is carried out by gravitational search algorithm(GSA)and optimization of candidate solutions,i.e.exploitation is performed by particle swarm optimization(PSO).For training the multi-layer perceptron(MLP),CPSOGSA uses sigmoid fitness function for finding the proper combination of connection weights and neural biases to minimize the error.Secondly,a matrix encoding strategy is utilized for providing one to one correspondence between weights and biases of MLP and agents of CPSOGSA.Findings-The experimental findings convey that CPSOGSA is a better MLP trainer as compared to other stochastic algorithms because it provides superior results in terms of resolving stagnation in local optima and convergence speed problems.Besides,it gives the best results for breast cancer,heart,sine function and sigmoid function datasets as compared to other participating algorithms.Moreover,CPSOGSA also provides very competitive results for other datasets.Originality/value-The CPSOGSA performed effectively in overcoming stagnation in local optima problem and increasing the overall convergence speed of MLP.Basically,CPSOGSA is a hybrid optimization algorithm which has powerful characteristics of global exploration capability and high local exploitation power.In the research literature,a little work is available where CPSO and GSA have been utilized for training MLP.The only related research paper was given by Mirjalili et al.,in 2012.They have used standard PSO and GSA for training simple FNNs.However,the work employed only three datasets and used the MSE performance metric for evaluating the efficiency of the algorithms.In this paper,eight different standard datasets and five performance metrics have been utilized for investigating the efficiency of CPSOGSA in training MLPs.In addition,a non-parametric pair-wise statistical test namely the Wilcoxon rank-sum test has been carried out at a 5%significance level to statistically validate the simulation results.Besides,eight state-of-the-art metaheuristic algorithms were employed for comparative analysis of the experimental results to further raise the authenticity of the experimental setup.

Damage detection in steel plates using feed-forward neural network coupled with hybrid particle swarm optimization and gravitational search algorithm

Over recent decades,the artificial neural networks(ANNs)have been applied as an effective approach for detecting damage in construction materials.However,to achieve a superior result of defect identification,they have to overcome some shortcomings,for instance slow convergence or stagnancy in local minima.Therefore,optimization algorithms with a global search ability are used to enhance ANNs,i.e.to increase the rate of convergence and to reach a global minimum.This paper introduces a two-stage approach for failure identification in a steel beam.In the first step,the presence of defects and their positions are identified by modal indices.In the second step,a feedforward neural network,improved by a hybrid particle swarm optimization and gravitational search algorithm,namely FNN-PSOGSA,is used to quantify the severity of damage.Finite element(FE)models of the beam for two damage scenarios are used to certify the accuracy and reliability of the proposed method.For comparison,a traditional ANN is also used to estimate the severity of the damage.The obtained results prove that the proposed approach can be used effectively for damage detection and quantification.

Hybrid Optimization Based PID Controller Design for Unstable System

PID controllers play an important function in determining tuning para-meters in any process sector to deliver optimal and resilient performance for non-linear,stable and unstable processes.The effectiveness of the presented hybrid metaheuristic algorithms for a class of time-delayed unstable systems is described in this study when applicable to the problems of PID controller and Smith PID controller.The Direct Multi Search(DMS)algorithm is utilised in this research to combine the local search ability of global heuristic algorithms to tune a PID controller for a time-delayed unstable process model.A Metaheuristics Algorithm such as,SA(Simulated Annealing),MBBO(Modified Biogeography Based Opti-mization),BBO(Biogeography Based Optimization),PBIL(Population Based Incremental Learning),ES(Evolution Strategy),StudGA(Stud Genetic Algo-rithms),PSO(Particle Swarm Optimization),StudGA(Stud Genetic Algorithms),ES(Evolution Strategy),PSO(Particle Swarm Optimization)and ACO(Ant Col-ony Optimization)are used to tune the PID controller and Smith predictor design.The effectiveness of the suggested algorithms DMS-SA,DMS-BBO,DMS-MBBO,DMS-PBIL,DMS-StudGA,DMS-ES,DMS-ACO,and DMS-PSO for a class of dead-time structures employing PID controller and Smith predictor design controllers is illustrated using unit step set point response.When compared to other optimizations,the suggested hybrid metaheuristics approach improves the time response analysis when extended to the problem of smith predictor and PID controller designed tuning.

基于CPSOGSA算法的威布尔参数估计及其在民机设备可靠性评估中的应用

为了解决小样本条件下民机装备可靠性模型参数的估计问题,本文提出一种基于收缩系数的粒子群万有引力搜索算法(Contraction factor Particle Swarm Optimization-Gravitational Search Algorithm,CPSOGSA)的参数估计算法。该方法提升了粒子群算法寻优性能,有效提升威布尔模型的参数估计精度。通过算例证明:该方法可以很好地用于民机设备的小样本可靠性参数估计,估计结果具有较高的精度,且耗时更短,表明了该方法的有效性和可行性。

基于改进引力搜索算法的水轮机调节系统仿真

针对现阶段水电机组存在多种复杂工况、工程计算受限于算法本身的复杂性等问题,提出一种改进的引力搜索算法(改进PSOGSA),以此提高水轮机控制参数的优化性能,弥补传统控制策略难以满足动态需求的不足.首先,结合PSO算法,在GSA的速度更新公式中引入学习因子进行改进.其次,应用一种权重系数优化其位置更新公式,提高算法的自适应性.最后,结合相关仿真建模试验,使用所提改进PSOGSA对水轮机调节系统PID参数进行优化调节.仿真结果表明,在5%空载频率扰动下,改进PSOGSA的PID控制器明显优于上述传统算法,所调节的模型系统能在更短时间内趋于稳定,此时的超调量远低于传统算法,表明此改进PSOGSA在后续迭代中具备更高的迭代效率,并且改善了常规算法中易陷入局部最优的问题,从而证明了改进PSOGSA的合理有效性,水轮机调节系统的控制效果在一定程度上得到优化.

考虑碳排放的分布式电源优化配置

对分布式电源接入配电网进行合理的优化配置,能在兼顾运营商和用户利益的同时,改善系统整体电压分布。建立了综合考虑分布式电源投资成本、用户购电成本、网损费用和碳排放费用的多目标优化模型。利用改进层次分析法确定各目标的权重,进而转化为单目标函数规划问题。针对天牛须算法个体单一性在解决高维复杂问题时精度低,优化效果不佳的问题,提出了一种改进天牛须粒子群算法,利用混沌映射对参数进行调整,引入动态惯性权重、莱维飞行机制,提高了收敛速度。以IEEE33节点系统为例,将改进天牛须粒子群算法与粒子群算法及天牛须粒子群算法的效果对比,验证改进算法对分布式电源优化配置问题的可行性,有效降低了碳排放费用、用户购电费用,减少了系统网损,改善了系统整体电压分布。

基于深度神经网络的7065铝合金厚板应力检测模型

针对工业生产中传统超声应力检测法对铝合金厚板在不同拉伸率和不同温度条件下存在的测量误差的问题,以7065铝合金厚板为实验对象,提出一种在不同拉伸率和不同温度条件下的基于树突神经网络的应力预测模型与传统超声检测法融合的应力检测模型,然后使用改进的GSA-GRNN对该应力检测模型进行温度补偿。以南南铝公司生产的7065铝合金厚板为研究对象,使用恒温槽为超声检测提供恒温环境,分别对不同拉伸率、不同温度下的7065铝合金厚板进行超声检测,将声时差、拉伸率作为输入参数,应力作为输出参数,创建一个基于树突神经网络的应力检测模型,然后将应力检测模型的输出作为输入,使用改进的GSA-GRNN建立温度补偿模型对应力检测模型进行温度补偿。研究结果表明:融合了传统超声声时差的检测模型均方根误差为0.84636,相关系数为0.99743,和其他神经网络模型对比,该模型拥有更好的精度;在对该模型进行温度补偿后,模型的应力均方根误差和相关系数分别可以达到0.78848和0.99844,模型的精度得到了进一步的提升。证明基于数据驱动的神经网络融合传统超声检测可以有效降低检测误差,同时省去传统检测方法人工计算应力的时间,提高了检测效率。研究结果可以为基于数据驱动的应力检测模型提供进一步的优化参考。

基于相邻争夺算法的无人机多架次植保作业路径规划

为了提高植保无人机作业效率,减少无人机作业损耗,该研究针对传统粒子群优化(particle swarm optimization,PSO)算法在规划植保作业路径时容易陷入局部最优,能耗最优方案的搜索能力低下等问题,该研究提出一种基于相邻争夺(adjacent competition, AC)算法的植保无人机作业路径规划算法。首先,对所有粒子设置作业距离范围,以防止单次作业距离过长或过短的极端情况;其次,在作业距离范围内随机分配每个粒子的作业距离,作为搜索的初始值;最后,相邻粒子相互争夺作业距离间接改变各架次作业距离,搜索出最优路径。相邻争夺算法保证了植保无人机作业总距离一定,对搜索方向进行先验且保证特殊点不被遗漏,避免算法陷入局部最优解。使用Matlab软件对420 m×200 m的模拟植保场地进行算法仿真验证,传统粒子群算法常陷入局部最优解,在10次规划中相较于遍历出的能耗最优规划方案增加了16.16%~38.14%的能耗,本文提出的相邻争夺算法规划结果的能耗远低于传统粒子群算法,算法具有更强的搜索能力。使用RflySim仿真平台搭建植保无人机模型和420 m×200 m的作业场地,在虚拟环境下比较传统粒子群算法与相邻争夺算法规划结果的模拟跟踪情况,相邻争夺算法规划结果的能耗相较传统粒子群算法减少了25.15%。420 m×200 m作业场地实际飞行试验中,相邻争夺算法规划结果的能耗相较传统粒子群算法减少了34.48%,更适应多架次植保作业。

基于低碳物流的危化品仓库堆垛布局优化研究

为保证危化品仓库安全的同时有效减少碳排放并提升经济效益,建立危险指数最小、物料搬运量最小和碳排放成本最小的危化品仓库堆垛布局多目标优化模型,采用改进的粒子群-禁忌搜索混合算法对模型进行求解。该算法在传统粒子群算法的基础上加入多点变异操作,并在粒子群算法得出解的基础上加入禁忌搜索算法,提高算法跳出局部最优解的能力。研究结果表明:利用本文建立的多目标优化模型及改进算法,危险指数、物料搬运量和碳排放成本均有所下降,解集质量较高,从而在保证危化品安全的情况下,有效降低物料搬运量及碳排放成本。研究结果可为危化品企业对仓库内部碳排放量的影响因素和数值计算以及危化品仓库安全性的界定提供参考与借鉴。

基于差分进化粒子群混合算法的多无人机协同区域搜索策略

为提高无人机群在未知环境中的区域搜索效率,提出一种多无人机协同区域搜索策略。首先,根据区域搜索任务需求,建立包含区域覆盖率、区域不确定度、目标存在概率三种属性的区域信息地图;其次,以最大化搜索效率、同时最小化无人机搜索过程中的能耗为目标,建立无人机区域搜索滚动时域优化目标函数,指导无人机在线决策搜索路线;然后针对传统群智能优化算法易陷入局部最优的缺陷,设计差分进化粒子群混合算法在线求解该多目标优化问题,提高算法的寻优性能,从而提高无人机的搜索效率。最后,通过数值仿真实验,对所提算法进行验证,仿真结果表明,文中设计的基于差分进化粒子群混合算法的多无人机协同区域搜索策略与传统的群智能优化算法相比具有更高的区域搜索效率。

天牛须算法在优化磁致伸缩换能器中的应用

磁致伸缩换能器换能效率不高是锚杆无损检测准确度较低的重要原因,确定合适的线圈结构参数对提高换能效率至关重要。基于Comsol多物理场有限元仿真模拟软件建立锚杆无损检测模型,首先,确定不同线圈匝数和不同提离距离对换能效率的影响规律;其次,将天牛须算法和粒子群遗传算法应用于线圈参数的本体优化问题,提出以提高换能器换能效率为优化目标、以线圈匝数和线圈提离距离为自变量的单目标优化设计模型,筛选出最优的线圈结构参数;最后,搭建锚杆无损检测实验平台,将自变量取值范围内的数值分别进行实验验证。研究结果表明:增加线圈的匝数、缩短线圈提离距离可以提高磁致伸缩换能器的换能效率;天牛须算法和粒子群遗传算法优化参数相同且符合仿真得到的影响规律,相比于粒子群遗传算法,天牛须算法原理简单、参数少、运算量少,在处理低维优化问题时具有更大的优越性;实验得到的线圈参数取值与算法优化结果一样,验证了天牛须算法用于锚杆换能器参数优化可靠且快速。

考虑碳交易机制的海港综合能源系统电-热混合储能优化配置

随着港口电气化进程逐渐加速,单一的港口供能方式正在向多种能源深度融合演变.为响应我国“碳达峰、碳中和”战略目标,进一步提升海港综合能源系统的经济与环境双重效益,提出一种考虑碳交易机制的电-热混合式储能优化配置方案.首先,建立海港综合能源系统模型,并给出计及碳交易市场的交易方案;其次,构建双层优化配置框架,上层优化配置混合式储能容量,下层引入碳交易机制,满足港口综合能源系统低碳经济运行需求;最后,结合网格自适应直接搜索法与自适应混沌粒子群算法优势,利用混合式优化算法对双层优化模型进行求解.以天津港的实际运行数据为例,验证该方法的有效性.算例结果表明,所提方法不仅可以降低系统的投入成本,还能显著减少港区碳排放,从而进一步提升港口经济和环境效益.