An application of interactive multi-criteria optimization to air pollution control

In this paper a problem of air pollution control is studied, posing it as a multi-objective control problem of partial differential equations. The original problem, dealing with the optimal management of a set of industrial plants inside a populated area, is formulated by means of the diffusion transport equation, including a linear reaction term and source terms modelled by Dirac deltas. Introducing adjoint state techniques, the problem transforms into a problem of multi-objective optimization in Banach spaces, where the large number of objective functions discourages the complete search of its Pareto front. Therefore, in order to solve the problem, two interactive methods of multi-objective programming are proposed: the VIA and the STEM algorithms. Finally, the paper illustrates how to combine both algorithms to solve in a more effective way a realistic problem posed in the Metropolitan Area of Guadalajara (Mexico).     

包含约束下C^1，1多目标问题的二阶最优性条件

本文讨论当目标函数与支撑函数F是C1,2时,包含约束下多目标规划问题的二阶最优性条件,并根据向量函数的二阶次微分建立了有效解的二阶充分必要条件.     

一种新广义凸多目标分式规划的最优性充分条件

提出了（F,α,ρ,θ）-b-凸函数的概念,它是一类新的广义凸函数,并给出了这类广义凸函数的性质.在此基础上,讨论了目标函数和约束函数均为（F,α,ρ,θ）-b-凸函数的多目标分式规划,利用广义K-T条件,得到了这类多目标规划有效解和弱有效解的几个充分条件,推广了已有文献的相关结果.     

考虑序列设置时间的混合流水车间多目标调度研究

基于混合流水车间多品种的特性,序列设置时间和工序跳跃是很多车间在调度时需要考虑的两个重要问题,论文充分考虑这两种生产约束,建立了以最大完工时间和负荷均衡指标为双目标的混合流水车间多目标调度数学模型,并运用改进的NSGA-II算法对基于实际企业生产数据假设的算例进行仿真求解,结果表明求解的调度方案符合实际需求,能够为企业的实际调度提供有效的方案。     

双目标DEA模型及其在商业银行评价中的应用

为了解决传统DEA模型所存在的判别能力弱和不现实权重两个缺陷,本文提出了一种双目标DEA模型。该模型在相同的约束条件下,同时以最大化各自效率和最小化所有效率值差异为目标。最后,通过某商业银行分支机构效率评价实例对所提出的方法进行了演示,说明了所提出方法的优点,着重说明了该方法可以很好地解决传统DEA方法所存在的两个缺陷。     

具有偏好锥的面向输出的超效率DEA模型分析

鉴于传统DEA模型无法区分有效决策单元,超效率DEA模型未考虑决策者的偏好,现提出面向输出的权重受限的综合超效率DEA模型及其投影概念,并讨论该模型与其他超效率DEA模型之间的关系.接着,分析模型的最优目标函数值与决策单元有效性之间的关系,并讨论面向输出的权重受限的综合超效投影与多目标规划问题的非支配解之间的关系.最后,通过对中国西部12个地区工业企业科技创新效率综合评价,并与原有方法进行比较研究,得出本文方法更具优势和合理性.     

Target setting in the general combined-oriented CCR model using an interactive MOLP method

The traditional data envelopment analysis (DEA) model does not include a decision maker’s (DM) preference structure while measuring relative efficiency, with no or minimal input from the DM. To incorporate DM’s preference information in DEA, various techniques have been proposed. An interesting method to incorporate preference information, without necessary prior judgment, is the use of an interactive decision making technique that encompasses both DEA and multi-objective linear programming (MOLP). In this paper, we will use Zionts-Wallenius (Z-W) method to reflecting the DM’s preferences in the process of assessing efficiency in the general combined-oriented CCR model. A case study will conducted to illustrate how combined-oriented efficiency analysis can be conducted using the MOLP method.     

顺序相依拆卸线平衡多目标优化模型及算法研究

拆卸是产品回收过程最关键环节之一,拆卸效率直接影响再制造成本。本文在分析现有模型不足基础上,考虑最小化总拆卸时间,建立多目标顺序相依拆卸线平衡问题优化模型,并提出了一种自适应进化变邻域搜索算法。所提算法引入种群进化机制,并采用一种组合策略构建初始种群,通过锦标赛法选择个体进化;在局部搜索时,设计了邻域结构自适应选择策略,并采用基于交叉的全局学习机制加速跳出局部最优,以提高算法寻优能力。对比实验结果,证实了所提模型的合理性以及算法的高效性。     

基于产品可持续制造过程的多目标决策

研究产品制造过程对经济、环境和社会的影响,使其具有可持续性。以资源约束为主线,考虑产品制造过程中可回收利用材料的使用比例,结合制造过程中安排操作工人的人数,综合优化产品制造过程的生产成本、排放物及单位工人的工作量。建立多目标优化模型,设计专门的非支配遗传算法(NSGA-Ⅱ),获得全局的Pareto最优解集。通过敏感性分析,获得模型中权重系数的合理取值,以及操作工人、可回收利用材料、原始材料的单位成本对模型结果的影响,可以使决策者在制定产品的可持续制造决策时有所依据。文中通过定量分析的方法,对可持续制造的决策理论进行了深入研究。     

Hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear systems with fuzzy parameters

This paper proposes a decomposition method for hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear programming (MONLP) problems with fuzzy parameters in the objective functions and in the constraints (FMONLP). These fuzzy parameters are characterized by fuzzy numbers. For such problems, the concept of α-Pareto optimality introduced by extending the ordinary Pareto optimality based on the α-level sets of fuzzy numbers. The decomposition method is based on the principle of decompose the original problem into interdependent sub-problems. In this method, the global multi-objective non-linear problem is decomposed into smaller multi-objective sub-problems. The smaller sub-problems, which obtained solved separately by using the weighting method and through an operative procedure. All these solution are coordinates in such a way that an optimal solution for the global problem achieved. In addition, an interactive fuzzy decision-making algorithm for hierarchical generation of α-Pareto optimal solution through the decomposition method is developed. Finally, two numerical examples given to illustrate the results developed in this paper.