基于模糊需求的多产品供应商选择的多目标规划模型

由决策于环境的不确定性,供应商选择问题存在大量的模糊信息,传统的确定性规划模型已经不能够很好地处理此类问题。本文基于模糊需求量信息,对于多产品供应商问题建立了模糊多目标规划模型。同时考虑到各目标及约束的重要性程度不同的影响,通过引进适当的权重对多目标规划模型进行求解。文中结合实际算例验证模型的可行性和有效性。     

基于NSGA-II的应急生产任务多目标优化模型及算法研究

重大突发事件发生后,若灾区的应急物资需求不能通过调用储备得到满足,则应急生产将成为灾区应急物资供应的重要保障手段。本文研究重大突发事件发生后应急物资生产任务的优化问题,重点关注原材料生产能力变化对完成应急生产任务的影响,以应急生产任务完成时间最短、完成成本最低为决策目标,研究了包含多个供应商、多个制造商以及单个受灾点的应急物资生产任务多目标规划模型。运用在求解多目标规划问题时具有众多优势的非支配排序多目标遗传算法(NSGA-II)对模型进行求解。通过算例分析,NSGA-II可以得到较好的Pareto前沿,并且可以根据不同情况给出最优的应急物资生产和原材料保障方案。本文的研究还表明,要想更快完成应急生产任务,需要做好原材料、资金、电力、交通等各种要素的配套保障工作。     

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。     

基于多目标优化的改航策略研究

随着我国航空运输的快速发展,由恶劣天气等原因导致的航班延误日益增多.传统的改航策略选取总延误损失最小为单一目标,不仅难以满足流量管理不同对象、不同阶段的需求,而且易造成空域利用率偏低.首先将改航策略与地面等待和空中等待相结合,然后综合考虑航空公司的利益,建立多目标优化模型,并采用稳定性和健壮性较强的多目标进化算法求解.最后选取全国典型繁忙日的实际飞行计划,进行了仿真验证.仿真结果表明,策略不仅可为航班动态地选择航路以避开容量限制区域,还可供流量管理部门参考不同目标来确定改航方案.     

基于神经网络的多目标演化优化方法

本文考虑在决策者偏好不明确的条件下，使系统获得最优的思想，提出了多目标决策系统最优解的概念。把前馈神经网络与演化算法相结合，用于多目标决策系统最优解的选取。给出了有关定理的证明和示例。     

考虑时间和油耗的拖轮多目标优化调度研究

进出港口的大型船舶需向港口申请拖轮协助以进行靠离泊作业。拖轮调度是港口重要的计划事项之一。针对拖轮调度过程中需要平衡完工时间和油耗量以提高港口服务水平和降低拖轮公司经营成本的问题，本文以最小化拖轮最大完工时间和最小化拖轮总油耗量为目标，构建了混合整数规划拖轮多目标优化调度模型。模型还考虑了潮汐港口大量船舶在潮水期间集中进出港的特点，并根据拖轮在调度过程中的不同状态分类计量其产生的油耗量，以使模型更接近实际状况。为求解模型，运用了带有精英策略的非支配排序遗传算法(NSGA-II),算法采用一维实数编码，以事件建模思想设置适应度函数，并结合拖轮调度特点设计了遗传算子，求得的Pareto前沿解和算法对比验证了该算法的有效性。最后，以广州港港口拖轮调度实际运作数据作为算例，验证了模型的可行性与有效性，为港口拖轮调度计划提供了决策依据。     

基于UTA方法的多目标优化模型

针对多目标线性优化问题进行研究,提出了一种基于效用加性方法(UTA)的多目标线性优化方法.利用不同目标值的组合给出训练方案,决策者针对训练方案给出一些偏好信息,据此推断决策者的效用函数,并进一步求解多目标线性优化模型.进一步给出了算例来说明方法的实施过程及验证可行性.方法较多的考虑了决策者对于决策的偏好,注重决策者的意见,为多目标决策问题提供了一种新的思路.     

基于QFD的产品可持续性多目标优化设计

为实现产品设计在社会、经济和环境三方面的可持续发展,将传统质量屋的顾客需求从顾客、企业和环境三个角度出发扩展为产品利益相关者的可持续需求,运用模糊层次分析法、直觉模糊集方法计算QFD(质量功能展开,Quality function deployment)质量屋权重和关联度,由生命周期评价软件Gabi对产品制造阶段主要零件的环境影响值进行建模计算,构成产品可持续设计的环境影响值约束条件,并结合成本和设计周期约束条件,构建产品可持续性多目标优化设计模型.以德国一款SuperCopy XR-2型号复印机为例,验证可持续需求的获取、质量屋数据的计算、Gabi软件的建模和计算以及多目标优化模型的建立和计算的过程.     

框架结构多目标优化方法

提出了一种框架结构多目标优化方法。基于力法给出了框架结构的等效刚度、最大弯矩随结构材料、几何等设计参数的变化,利用动能等效给出了框架结构的等效质量,进而得到框架结构一阶固有频率随结构材料、几何等参数的变化,用有限元方法验证了所得频率、弯矩公式的正确性。以固有频率、最大弯矩为优化目标函数构造框架结构的多目标优化模型,通过单目标优化得到频率、弯矩最优值,以单目标优化值为基础构造全局目标优化函数,将多目标优化转化为单目标优化。     

Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach

Selection of supply chain partners is an important decision involving multiple criteria and risk factors. This paper proposes a fuzzy multi-objective programming model to decide on supplier selection taking risk factors into consideration. We model a supply chain consisting of three levels and use simulated historical quantitative and qualitative data. We propose a possibility approach to solve the fuzzy multi-objective programming model. Possibility multi-objective programming models are obtained by applying possibility measures of fuzzy events into fuzzy multi-objective programming models. Results indicate when qualitative criteria are considered in supplier selection, the probability of a certain supplier being selected is affected.     

Primal and dual multi-objective linear programming algorithms for linear multiplicative programmes

Multiplicative programming problems (MPPs) are global optimization problems known to be NP-hard. In this paper, we employ algorithms developed to compute the entire set of nondominated points of multi-objective linear programmes (MOLPs) to solve linear MPPs. First, we improve our own objective space cut and bound algorithm for convex MPPs in the special case of linear MPPs by only solving one linear programme in each iteration, instead of two as the previous version indicates. We call this algorithm, which is based on Benson’s outer approximation algorithm for MOLPs, the primal objective space algorithm. Then, based on the dual variant of Benson’s algorithm, we propose a dual objective space algorithm for solving linear MPPs. The dual algorithm also requires solving only one linear programme in each iteration. We prove the correctness of the dual algorithm and use computational experiments comparing our algorithms to a recent global optimization algorithm for linear MPPs from the literature as well as two general global optimization solvers to demonstrate the superiority of the new algorithms in terms of computation time. Thus, we demonstrate that the use of multi-objective optimization techniques can be beneficial to solve difficult single objective global optimization problems.     

A constraint shifting homotopy method for convex multi-objective programming

In this paper, a constraint shifting combined homotopy method for solving multi-objective programming problems with both equality and inequality constraints is presented. It does not need the starting point to be an interior point or a feasible point and hence is convenient to use. Under some assumptions, the existence and convergence of a smooth path to an efficient solution are proven. Simple numerical results are given.     

Fuzzy optimality conditions for fractional multi-objective problems

In this article, we are concerned with fractional multi-objective optimization problems. Since those problems are in general nonconvex problems even if the problem data are convex, using techniques from variational analysis especially the approximate extremal principle [B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Series: Fundamental Principles of Mathematical Sciences, Vol. 330, Springer, Berlin, 2006; B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, II: Applications, Grundlehren Series: Fundamental Principles of Mathematical Sciences, Vol. 331, Springer, Berlin, 2006], we develop fuzzy optimality conditions.     

基于改进NSGA-II算法的云制造服务组合优化研究

云制造任务日趋复杂,与基于云制造的云服务组合优化问题相关的指标日益增多,需要综合考虑各个评价指标,从海量备选云服务中筛选出最优服务组合。本文针对云制造的特点,从线上、线下两方面构建了云制造服务评价指标体系;为了更好地处理高维多目标优化问题并消除实际问题中的量纲影响,本文利用改进的α支配策略代替帕累托支配改进NSGA-II算法,提出了基于nα支配的NSGA-II算法。最后,本文通过一个电机制造案例验证了提出算法的可行性,并通过与标准NSGA-II算法、r-NSGA-II算法和基于模糊支配的NSGA-II算法对比,证明了提出算法得到的解集更优、更小,能够大大减小后续组合优选的计算量。     

A new mechanism to maintain diversity in multi-objective metaheuristics

In this article, a new mechanism to spread the solutions generated by a multi-objective evolutionary algorithm is proposed. This approach is based on the use of stripes that are applied in objective function space and is independent of the search engine adopted. Additionally, it overcomes some of the drawbacks of other previous proposals such as the ?-dominance method. In order to validate the proposed approach, it is coupled to a multi-objective particle swarm optimizer and its performance is assessed with respect to that of state-of-the-art algorithms, using standard test problems and performance measures taken from the specialized literature. The results indicate that the proposed approach is a viable diversity maintenance mechanism that can be incorporated to any multi-objective metaheuristic used for multi-objective optimization.     

An interactive evolutionary multi-objective optimization algorithm with a limited number of decision maker calls

This paper presents a preference-based method to handle optimization problems with multiple objectives. With an increase in the number of objectives the computational cost in solving a multi-objective optimization problem rises exponentially, and it becomes increasingly difficult for evolutionary multi-objective techniques to produce the entire Pareto-optimal front. In this paper, an evolutionary multi-objective procedure is combined with preference information from the decision maker during the intermediate stages of the algorithm leading to the most preferred point. The proposed approach is different from the existing approaches, as it tries to find the most preferred point with a limited budget of decision maker calls. In this paper, we incorporate the idea into a progressively interactive technique based on polyhedral cones. The idea is also tested on another progressively interactive approach based on value functions. Results are provided on two to five-objective unconstrained as well as constrained test problems.     

A hybrid method for solving multi-objective global optimization problems

Real optimization problems often involve not one, but multiple objectives, usually in conflict. In single-objective optimization there exists a global optimum, while in the multi-objective case no optimal solution is clearly defined but rather a set of optimums, which constitute the so called Pareto-optimal front. Thus, the goal of multi-objective strategies is to generate a set of non-dominated solutions as an approximation to this front. However, most problems of this kind cannot be solved exactly because they have very large and highly complex search spaces. The objective of this work is to compare the performance of a new hybrid method here proposed, with several well-known multi-objective evolutionary algorithms (MOEA). The main attraction of these methods is the integration of selection and diversity maintenance. Since it is very difficult to describe exactly what a good approximation is in terms of a number of criteria, the performance is quantified with adequate metrics that evaluate the proximity to the global Pareto-front. In addition, this work is also one of the few empirical studies that solves three-objective optimization problems using the concept of global Pareto-optimality.     

A green train scheduling model and fuzzy multi-objective optimization algorithm

Train scheduling model is traditionally formulated to minimize the energy consumption for reducing the operation cost. As the European Union formulates the first carbon emission trading scheme in the world, it is necessary to extend the operation cost to include the expenses for buying/selling the carbon emission allowances. In this paper, we propose a multi-objective train scheduling model by minimizing the energy and carbon emission cost as well as the total passenger-time, and named it as green train scheduling model. For obtaining a non-dominated timetable which has equal satisfactory degree on both objectives, we apply a fuzzy multi-objective optimization algorithm to solve the model. Finally, we perform two numerical examples to illustrate the efficiency of the proposed model and solution methodology.