GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-ⅡFOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION

Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.

Optimization of dynamic aperture by using non-dominated sorting genetic algorithm-Ⅱ in a diffraction-limited storage ring with solenoids for generating round beam

Purpose Round beam,i.e.,with equal horizontal and vertical emittance,is preferable than a horizontally flat one for some beamline applications in Diffraction-limited storage rings(DLSRs),for the purposes of reducing the number of photons getting discarded and better phase space match between photon and electron beam.Conventional methods of obtaining round beam inescapably results in a reduction of dynamic aperture(DA).In order to recover the DA as much as possible for improving the injection efficiency,the DA optimization by using Non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ)to generate round beam,particularly to one of the designed lattice of the High Energy Photon Source(HEPS)storage ring,are presented.Method According to the general unconstrained model of NSGA-Ⅱ,we modified the standard model by using parallel computing to optimize round beam lattices with errors,especially for a strong coupling,such as solenoid scheme.Results and conclusion The results of numerical tracking verify the correction of the theory framework of solenoids with fringe fields and demonstrates the feasibility on the HEPS storage ring with errors to operate in round beam mode after optimizing DA.

Suspended sediment load prediction using non-dominated sorting genetic algorithm Ⅱ

Awareness of suspended sediment load (SSL) and its continuous monitoring plays an important role in soil erosion studies and watershed management.Despite the common use of the conventional model of the sediment rating curve (SRC) and the methods proposed to correct it,the results of this model are still not sufficiently accurate.In this study,in order to increase the efficiency of SRC model,a multi-objective optimization approach is proposed using the Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) algorithm.The instantaneous flow discharge and SSL data from the Ramian hydrometric station on the Ghorichay River,Iran are used as a case study.In the first part of the study,using self-organizing map (SOM),an unsupervised artificial neural network,the data were clustered and classified as two homogeneous groups as 70% and 30% for use in calibration and evaluation of SRC models,respectively.In the second part of the study,two different groups of SRC model comprised of conventional SRC models and optimized models (single and multi-objective optimization algorithms) were extracted from calibration data set and their performance was evaluated.The comparative analysis of the results revealed that the optimal SRC model achieved through NSGA-Ⅱ algorithm was superior to the SRC models in the daily SSL estimation for the data used in this study.Given that the use of the SRC model is common,the proposed model in this study can increase the efficiency of this regression model.

Models for Location Inventory Routing Problem of Cold Chain Logistics with NSGA-Ⅱ Algorithm

In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location,inventory and transportation.Due to the complex of LIR problem( LIRP), a multi-objective genetic algorithm(GA), non-dominated sorting in genetic algorithm Ⅱ( NSGA-Ⅱ) has been introduced. Its performance is tested over a real case for the proposed problems. Results indicate that NSGA-Ⅱ provides a competitive performance than GA,which demonstrates that the proposed model and multi-objective GA are considerably efficient to solve the problem.

Multi-objective Function Optimization for Environmental Control of a Greenhouse Based on a RBF and NSGA-Ⅱ

To better meet the needs of crop growth and achieve energy savings and efficiency enhancements,constructing a reliable environmental model to optimize greenhouse decision parameters is an important problem to be solved.In this work,a radial-basis function(RBF)neural network was used to mine the potential changes of a greenhouse environment,a temperature error model was established,a multi-objective optimization function of energy consumption was constructed and the corresponding decision parameters were optimized by using a non-dominated sorting genetic algorithm with an elite strategy(NSGA-Ⅱ).The simulation results showed that RBF could clarify the nonlinear relationship among the greenhouse environment variables and decision parameters and the greenhouse temperature.The NSGA-Ⅱ could well search for the Pareto solution for the objective functions.The experimental results showed that after 40 min of combined control of sunshades and sprays,the temperature was reduced from 31℃to 25℃,and the power consumption was 0.5 MJ.Compared with tire three days of July 24,July 25 and July 26,2017,the energy consumption of the controlled production greenhouse was reduced by 37.5%,9.1%and 28.5%,respectively.

考虑交货期的双资源柔性作业车间节能调度

为解决含有机器和工人双资源约束的柔性作业车间节能调度问题,在考虑交货期的基础上,建立了以总提前和拖期惩罚值及总能耗最小为目标的双资源柔性作业车间节能调度模型。提出了一种改进的非支配排序遗传算法(improved non-dominated sorting genetic algorithmⅡ,INSGA-Ⅱ)进行求解。针对所优化的目标,设计了一种三阶段解码方法以获得高质量的可行解;利用动态自适应交叉和变异算子以获得更多优良个体;改进拥挤距离以获得收敛性和分布性更优的种群。将INSGA-Ⅱ与多种多目标优化算法进行对比分析,实验结果表明所提算法可行且有效。

基于混合遗传蚁群算法的多目标FJSP问题研究

针对多目标柔性作业车间调度问题求解过程中未综合考虑解集多样性与求解效率的问题,提出了一种混合遗传蚁群算法来求解。首先,通过改进的NSGA-Ⅱ(non-dominated sorting genetic algorithmⅡ)获取问题的较优解,以此来确定蚁群算法的初始信息素分布;其次,根据提出的自适应伪随机比例规则和改进的信息素更新规则来优化蚂蚁的遍历过程;最后,通过邻域搜索,扩大蚂蚁的搜索空间,从而提高解集的多样性。通过Kacem和BRdata算例进行实验验证,证明混合遗传蚁群算法具有更高的求解效率和更好解集多样性。

Multi-objective optimization of the cathode catalyst layer micro-composition of polymer electrolyte membrane fuel cells using a multi-scale,two-phase fuel cell model and data-driven surrogates

Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectiveness of using platinum(Pt)in them.The cathode catalyst layer(CL)is considered a core component in PEMFCs,and its composition often considerably affects the cell performance(V_(cell))also PEMFC fabrication and production(C_(stack))costs.In this study,a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcelland Cstack.Four essential cathode CL parameters,i.e.,platinum loading(L_(Pt)),weight ratio of ionomer to carbon(wt_(I/C)),weight ratio of Pt to carbon(wt_(Pt/c)),and porosity of cathode CL(ε_(cCL)),are considered as the design variables.The simulation results of a three-dimensional,multi-scale,two-phase comprehensive PEMFC model are used to train and test two famous surrogates:multi-layer perceptron(MLP)and response surface analysis(RSA).Their accuracies are verified using root mean square error and adjusted R^(2).MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithmⅡ.Compared to a typical PEMFC stack,the results of the optimal study show that the single-cell voltage,Vcellis improved by 28 m V for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by$5.86/k W for the same stack performance.

Evolutionary genetic optimization of the injector beam dynamics for the ERL test facility at IHEP

The energy recovery linac test facility （ERL-TF）, a compact ERL-FEL （free electron laser） two-purpose machine, has been proposed at the Institute of High Energy Physics, Beijing. As one important component of the ERL-TF, the photo-injector was designed and preliminarily optimized. In this paper an evolutionary genetic method, non-dominated sorting genetic algorithm II, is applied to optimize the injector beam dynamics, especially in the high-charge operation mode. Study shows that using an incident laser with rms transverse size of 1-1.2 ram, the normalized emittance of the electron beam can be kept below 1 mm.mrad at the end of the injector. This work, together with the previous optimization of the low-charge operation mode by using the iterative scan method, provides guidance and confidence for future construction and commissioning of the ERL-TF injector.

Orbit Design for Responsive Space Using Multiple-objective Evolutionary Computation

Responsive orbits have exhibited advantages in emergencies for their excellent responsiveness and coverage to targets.Generally,there are several conflicting metrics to trade in the orbit design for responsive space.A special multiple-objective genetic algorithm,namely the Nondominated Sorting Genetic AlgorithmⅡ(NSGAⅡ),is used to design responsive orbits.This algorithm has considered the conflicting metrics of orbits to achieve the optimal solution,including the orbital elements and launch programs of responsive vehicles.Low-Earth fast access orbits and low-Earth repeat coverage orbits,two subtypes of responsive orbits,can be designed using NSGAI under given metric tradeoffs,number of vehicles,and launch mode.By selecting the optimal solution from the obtained Pareto fronts,a designer can process the metric tradeoffs conveniently in orbit design.Recurring to the flexibility of the algorithm,the NSGAI promotes the responsive orbit design further.

Multi-objective simultaneous optimal planning of electric vehiclefast charging stations and DGs in distribution system

The large-scale construction of fast charging stations(FCSs)for electric vehicles(EVs)is helpful inpromoting the EV.It creates a significant challenge for the distribution system operator to determine the optimal planning,especially the siting and sizing of FCSs in the electrical distribution system.Inappropriate planning of fast EV charging stations(EVCSs)cause a negative impact on the distribution system.This paper presented a multiobjective optimization problem to obtain the simultaneous placement and sizing of FCSs and distributed generations(DGs)with the constraints such as the number of EVs in all zones and possible number of FCSs based on the road and electrical network in the proposed system.The problem is formulated as a mixed integer non-linear problem(MINLP)to optimize the loss of EV user,network power loss(NPL),FCS development cost and improve the voltage profile of the electrical distribution system.Non-dominated sorting genetic algorithmⅡ(NSGA-Ⅱ)is used for solving the MINLP.The performance of the proposed technique is evaluated by the 118-bus electrical distribution system.

Multi-objective Dimensional Optimization of a 3-DOF Translational PKM Considering Transmission Properties

Multi-objective dimensional optimization of parallel kinematic manipulators(PKMs) remains a challenging and worthwhile research endeavor. This paper presents a straightforward and systematic methodology for implementing the structure optimization analysis of a 3-prismatic-universal-universal(PUU) PKM when simultaneously considering motion transmission, velocity transmission and acceleration transmission. Firstly, inspired by a planar four-bar linkage mechanism, the motion transmission index of the spatial parallel manipulator is based on transmission angle which is defined as the pressure angle amongst limbs. Then, the velocity transmission index and acceleration transmission index are derived through the corresponding kinematics model. The multi-objective dimensional optimization under specific constraints is carried out by the improved non-dominated sorting genetic algorithm(NSGA Ⅱ), resulting in a set of Pareto optimal solutions. The final chosen solution shows that the manipulator with the optimized structure parameters can provide excellent motion, velocity and acceleration transmission properties.

Multi-Objective Optimization of Rail Pre-Grinding Profile in Straight Line for High Speed Railway

In order to modify the rail pre-grinding profile smoothly,non-uniform rational B-spline(NURBS)curve with weight factors is used to establish a parameterized model of the profile.A wheel-rail contact stochastic finite element model(FEM) is constructed by the Latin hypercube sampling method and 3 D elasto-plastic FEM,in which the wheelset's lateral displacement quantity is regarded as a random variable.The maximum values of nodal accumulated contact stress(NACS) and nodal mean contact stress(NMCS) in different pre-grinding profiles with differential weight factors are calculated and taken as the training samples to establish two Kriging models.A multi-objective optimization model of pre-grinding profile is established,in which the objective functions are the NACS and NMCS Kriging models.The optimum weight factors are sought using a non-dominated sorting genetic algorithm II(NSGA-II),and the corresponding optimum pre-grinding profile is obtained.The contact stress calculation before and after optimization indicates that the maximum values of NACS and NMCS decline significantly.