A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: An NSGA-II with tuned parameters

In this research, a bi-objective vendor managed inventory model in a supply chain with one vendor (producer) and several retailers is developed, in which determination of the optimal numbers of different machines that work in series to produce a single item is considered. While the demand rates of the retailers are deterministic and known, the constraints are the total budget, required storage space, vendor's total replenishment frequencies, and average inventory. In addition to production and holding costs of the vendor along with the ordering and holding costs of the retailers, the transportation cost of delivering the item to the retailers is also considered in the total chain cost. The aim is to find the order size, the replenishment frequency of the retailers, the optimal traveling tour from the vendor to retailers, and the number of machines so as the total chain cost is minimized while the system reliability of producing the item is maximized. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimization algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. The parameters of both algorithms are first calibrated using the Taguchi approach. Then, the performances of the two algorithms are compared in terms of some multi-objective performance measures. Moreover, a local searcher, named simulated annealing (SA), is used to improve NSGA-II. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.     

基于改进NSGA-II的车间排产优化算法研究

针对NSGA-II算法在处理车间排产优化问题中出现的子代种群多样性差、收敛能力差等问题,提出了一种改进NSGA-II的车间排产优化算法。改进NSGA-II算法主要对传统NSGA-II算法的交叉和变异环节,提出新的改进自适应交叉和变异算子,通过对个体拥挤度与种群平均拥挤度进行对比,并结合种群迭代进化过程,将遗传概率与种群个体及种群进化迭代次数关联,避免盲目导向性,提高种群的收敛速度;提出新的均匀进化精英保留策略,通过自适应分层次选取种群个体,解决子代种群多样性差的问题。针对车间排产问题,选择“最大化最小交货提前期”和“最小化最大理想加工时间偏差”作为目标函数,运用改进NSGA-II算法进行实际工程的仿真分析,对比改进前后算法优化的结果,验证了算法的有效性,同时证明了其应用于实际生产排产调度问题的价值参考性。     

电动汽车参与经济调度的多目标模型

电动汽车通过V2G技术可以作为电网负荷侧的备用容量,由此提出了一个多目标优化模型,将电动汽车车主成本和经济调度成本作为其目标函数,并让电动汽车通过有序充放电来作为经济调度时的备用容量.在满足各种约束条件下,采用多目标遗传算法(NSGA-Ⅱ)对模型进行求解.电动汽车的负荷特性、负荷波动、真实风能输出和机组停运状态均采用蒙特卡洛算法得到,并以一小时为时间间隔来进行仿真.由模型的求解结果可知,通过选择合适的pareto解集中的值,可以节省车主成本和经济调度的成本,并且可以实现对负荷削峰填谷的功能.     

Design and implementation of a general software library for using NSGA-II with SWAT for multi-objective model calibration

Calibrating watershed-scale hydrologic models remains a critical but challenging step in the modeling process. The Soil and Water Assessment Tool (SWAT) is one example of a widely used watershed-scale hydrologic model that requires calibration. The calibration algorithms currently available to SWAT modelers through freely available and open source software, however, are limited and do not include many multi-objective genetic algorithms (MOGAs). The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) has been shown to be an effective and efficient MOGA calibration algorithm for a wide variety of applications including for SWAT model calibration. Therefore, the objective of this study was to create an open source software library for multi-objective calibration of SWAT models using NSGA-II. The design and implementation of the library are presented, followed by a demonstration of the library through a test case for the Upper Neuse Watershed in North Carolina, USA using six objective functions in the model calibration.     

Nonlinear optimized adaptive trajectory control of helicopter

This paper attempts to develop an optimized adaptive trajectory control system for helicopters based on the dynamic inversion method. This control algorithm is implemented by three time-scale separation architectures. Pseudo control hedging (PCH) is used to protect the adaptive element from actuator saturation nonlinearities and also from the inner-outer-loop interaction. In addition, to augment the attitude control system, two online adaptive architectures that employ a neural network are used. By tuning the neural network based on the system model, a better and faster learning will be achieved, but this is a frustrating and time consuming process. Due to complexity in accurate tuning of neural network, this paper introduces a non-dominated sorting genetic algorithm II (NSGA-II) for off-line optimization of the neural network. Thus, in the proposed method, the neural network can compensate model inversion error caused by the deficiency of full knowledge of helicopter dynamics more accurately. The effectiveness of proposed method is demonstrated by numerical simulations.     

考虑服务配置的细粒度电力任务云边协同优化调度策略

新型电力系统的建设促使电力业务范围向用户侧深入,业务种类及数量不断增加。边设备资源有限,只能配置有限数量的服务,任务的时延能耗需求与设备资源有限的矛盾日益突出。为实现云边资源协同与任务的优化调度,提出了一种考虑服务配置的细粒度电力任务云边协同优化调度策略。通过建立微服务的时延与能耗模型,并对任务调度中的约束条件进行分析,将时延与能耗的优化决策问题转化为带约束的多目标优化问题,采用NSGA-Ⅱ算法求解。然后通过基于模糊逻辑的多准则决策方法为任务选择调度方案。仿真结果表明,所提策略在时延和能耗方面的性能优于其他策略,能够适应不同的任务场景并做出最优决策,提高了任务的完成率。     

考虑同步机调差系数灵敏度与频率约束的机组组合

为解决高比例新能源并网带来的系统惯量水平降低及频率安全问题,有必要从同步机的角度出发,进一步发挥同步机组的调频能力,提高系统的频率稳定。考虑系统中各同步机组频率支撑能力的不同,基于灵敏度的方法分析不同机组调差系数的改变对最大频率偏差的影响程度。综合考虑同步机与风机参与调频,推导最大频率偏差的解析表达式。在考虑频率安全约束的基础上,提出考虑同步机调差系数灵敏度的多目标机组组合模型,并采用快速非支配多目标优化算法(non-dominated sorting genetic algorithms-II, NSGA-II)进行模型求解。仿真结果表明,所提模型在考虑频率约束的机组组合模型基础上,进一步发挥了同步机组的调频能力,抑制了最低点频率的跌落,改善了系统的频率响应。     

Bi-objective scheduling for reentrant hybrid flow shop using Pareto genetic algorithm

This paper deals with a scheduling problem for reentrant hybrid flowshop with serial stages where each stage consists of identical parallel machines. In a reentrant flowshop, a job may revisit any stage several times. Local-search based Pareto genetic algorithms with Minkowski distance-based crossover operator is proposed to approximate the Pareto optimal solutions for the minimization of makespan and total tardiness in a reentrant hybrid flowshop. The Pareto genetic algorithms are compared with existing multi-objective genetic algorithm, NSGA-II in terms of the convergence to optimal solution, the diversity of solution and the dominance of solution. Experimental results show that the proposed crossover operator and local search are effective and the proposed algorithm outperforms NSGA-II by statistical analysis.     

Three-objective fuzzy chance-constrained programming model for multiproject and multi-item investment combination

This paper presents a new fuzzy chance-constrained programming model to find the solution for multiproject and multi-item investment combination in investment combination problems. The proposed 0-1 integer programming model has three objectives with fuzzy constraints, and NSGA-II is applied to solve the optimization model with a small modification of the constraint-handling rule. A simulation experiment illustrating the application of the proposed model is presented and Pareto-optimal solutions are obtained through a modified NSGA-II algorithm. A comparison among NSGA-II, PSO, and DE shows that modified NSGA-II has some advantages over PSO and DE.     

A cooperative negotiation embedded NSGA-II for solving an integrated product family and supply chain design problem with remanufacturing consideration

Product family design is a popular approach adopted by manufacturers to increase their product varieties in order to satisfy the needs of various markets. In recent years, because of increasing environmental concerns in societies and strict regulations of environmental protection, quite a number of manufacturers adopted remanufacturing strategy in their product development in response to the challenges. Remanufacturing of used products unavoidably involves a closed-loop supply chain system. To achieve the best outcomes, the supply chain design should be considered in product family design process. In this research, a multi-objective optimization model of integrated product family and closed loop supply chain design is formulated based on a cooperative game model for minimizing manufacturer’s total cost and maximize suppliers’ total payoffs. Since the optimization problem could be a large- scale one and involves mixed continuous-discrete variables, a new version of nondominated sorting genetic algorithm-II (NSGA-II), namely cooperative negotiation embedded NSGA-II (NSGA-CO), is proposed to solve the optimization model. Simulation tests are conducted to validate the effectiveness of the proposed NSGA-CO. The test results indicate that the proposed NSGA-CO outperforms NSGA-II in solving various scale of multi-objective optimization problems in terms of convergence. With the formulated optimization model and the proposed NSGA-CO, a case study of integrated product family and supply chain design is conducted to investigate the effects of environmental penalty, quantity of demand and marginal cost of remanufacturing on used product return rate, manufacturers’ and suppliers’ profits and joint payoff.