Fuzzy multi-objective chance-constrained programming model for hazardous materials transportation

Hazardous materials transportation is an important and hot issue of public safety. Based on the shortest path model, this paper presents a fuzzy multi-objective programming model that minimizes the transportation risk to life, travel time and fuel consumption. First, we present the risk model, travel time model and fuel consumption model. Furthermore, we formulate a chance-constrained programming model within the framework of credibility theory, in which the lengths of arcs in the transportation network are assumed to be fuzzy variables. A hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed for finding a satisfactory solution. Finally, some numerical examples are given to demonstrate the efficiency of the proposed model and algorithm.     

Fuzzy random dependent-chance programming

This paper presents the concepts of uncertain environment, event, chance function and principle of uncertainty for fuzzy random decision systems, thus offering a theoretical framework of fuzzy random dependent-chance programming. A hybrid intelligent algorithm is applied to solving fuzzy random dependent-chance programming models. Some numerical examples are also provided to illustrate the effectiveness of hybrid intelligent algorithm     

Fuzzy random programming with equilibrium chance constraints

To model fuzzy random decision systems, this paper first defines three kinds of equilibrium chances via fuzzy integrals in the sense of Sugeno. Then a new class of fuzzy random programming problems is presented based on equilibrium chances. Also, some convex theorems about fuzzy random linear programming problems are proved, the results provide us methods to convert primal fuzzy random programming problems to their equivalent stochastic convex programming ones so that both the primal problems and their equivalent problems have the same optimal solutions and the techniques developed for stochastic convex programming can apply. After that, a solution approach, which integrates simulations, neural network and genetic algorithm, is suggested to solve general fuzzy random programming problems. At the end of this paper, three numerical examples are provided. Since the equivalent stochastic programming problems of the three examples are very complex and nonconvex, the techniques of stochastic programming cannot apply. In this paper, we solve them by the proposed hybrid intelligent algorithm. The results show that the algorithm is feasible and effectiveness.     

再制造/制造系统集成物流网络模糊机会约束规划模型

在再制造/制造(R/M)系统集成物流网络中,回收产品的数量具有不确定性.根据这一特点,将各消费区域废旧产品的回收数量看成是模糊参数,提出了该集成物流网络的模糊机会约束规划模型.通过把模型中模糊机会约束清晰化,将模型转化为确定性的混合整数规划模型.利用实例数据,针对不同的置信水平对模型进行分析,其结果为该集成物流网络的设计提供了依据.     

模糊铁合金配料机会约束模型

在铁合金配料问题的大量传统研究工作中,多数研究工作均与确定性系统相关。在不确定系统中考虑一类新的带有可信性约束的模糊铁合金配料机会约束模型。由于提出的模糊铁合金配料问题常常包含带有无限支撑的模糊变量参数,因此它是一个很少被直接求解的无穷维优化问题。为了求解这个模糊优化问题,通过逼近方法将模糊铁合金配料机会约束问题转化为一个有限维优化问题。设计一个含有逼近方法、神经网络和遗传算法的混合智能算法求解提出的带有可信性约束的铁合金配料机会约束问题。给出一个数值例子来表明所设计模型和算法的实用性。     

Multi-national capital budgeting using chance-constrained goal programming

A chance-constrained goal programming model is developed for the direct foreign investment decisions of U.S.-based multi-national companies. Goals, objectives and constraints, which are unique to direct foreign investment decisions, are included in the model. The model also considers economic exposure of exchange-rate risk. A solution procedure is suggested. The model is illustrated by a numerical example that includes sensitivity analysis.     

Adaptive sampling immune algorithm solving joint chance-constrained programming

This work investigates one immune optimization algorithm in uncertain environments, solving linear or nonlinear joint chance-constrained programming with a general distribution of the random vector. In this algorithm, an a priori lower bound estimate is developed to deal with one joint chance constraint, while the scheme of adaptive sampling is designed to make empirically better antibodies in the current population acquire larger sample sizes in terms of our sample-allocation rule. Relying upon several simplified immune metaphors in the immune system, we design two immune operators of dynamic proliferation and adaptive mutation. The first picks up those diverse antibodies to achieve proliferation according to a dynamical suppression radius index, which can ensure empirically potential antibodies more clones, and reduce noisy influence to the optimized quality, and the second is a module of genetic diversity, which exploits those valuable regions and finds those diverse and excellent antibodies. Theoretically, the proposed approach is demonstrated to be convergent. Experimentally, the statistical results show that the approach can obtain satisfactory performances including the optimized quality, noisy suppression and efficiency.     

Fuzzy random programming models for location-allocation problem with applications

Three types of fuzzy random programming models based on the mean chance for the capacitated location-allocation problem with fuzzy random demands are proposed according to different criteria, including the expected cost minimization model, the α-cost minimization model, and the chance maximization model. In order to solve the proposed models, some hybrid intelligent algorithms are designed by integrating the network simplex algorithm, fuzzy random simulation, and genetic algorithm. Finally, some numerical examples about a container freight station problem are given to illustrate the effectiveness of the devised algorithms.     

Genetic algorithm-based fuzzy goal programming for class of chance-constrained programming problems

This paper presents a procedure for solving a multiobjective chance-constrained programming problem. Random variables appearing on both sides of the chance constraint are considered as discrete random variables with a known probability distribution. The literature does not contain any deterministic equivalent for solving this type of problem. Therefore, classical multiobjective programming techniques are not directly applicable. In this paper, we use a stochastic simulation technique to handle randomness in chance constraints. A fuzzy goal programming formulation is developed by using a stochastic simulation-based genetic algorithm. The most satisfactory solution is obtained from the highest membership value of each of the membership goals. Two numerical examples demonstrate the feasibility of the proposed approach.     

产品设计方案费效权衡的随机机会约束规划模型

针对产品设计方案费效权衡中由于未考虑生产过程中不确定性因素影响而导致的权衡结果易产生偏差的问题, 提出将不确定优化理论引入产品设计方案费效权衡模型中。在对关键设计参数敏感性分析的基础上,将敏感性变量以及费用估算的偏差描述为随机变量,构建基于以产品设计方案费效权衡的随机机会约束规划模型,并采用嵌入蒙特卡洛模拟的遗传算法求解,得到考虑不确定因素影响的最优产品设计方案。最后以混凝土泵车为实例,验证了模型的有效性。研究表明,采用费效权衡随机机会约束规划模型得到的产品设计方案,更能反映生产实际,可以最大程度保证不确定条件下产品设计决策目标的实现。     

求解随机机会约束规划的混合智能算法

随机机会约束规划是一类有着广泛应用背景的随机规划问题,采用随机仿真产生样本训练BP网络以逼近随机函数,然后在微粒群算法中利用神经网络计算适应值和实现检验解的可行性,从而提出了一种求解随机机会约束规划的混合智能算法。最后通过两个实例的仿真结果说明了算法的正确性和有效性。     

Credibility-based chance-constrained integer programming models for capital budgeting with fuzzy parameters

In this paper, we discuss a problem of capital budgeting in a fuzzy environment. Two types of models are proposed using credibility to measure confidence level. Since the proposed optimization problems are difficult to solve by traditional methods, a fuzzy simulation-based genetic algorithm is applied. Two numerical experiments demonstrate the effectiveness of the proposed algorithm.     

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.     

多目标模糊机会约束规划的低碳多式联运路径优化

针对时间窗与需求量不确定性下的多式联运路径优化问题,运用梯形模糊数表示模糊需求量与模糊时间窗,并考虑碳排放成本、运输成本以及客户满意度,建立了多目标模糊机会约束模型。固定的交叉、变异概率会直接影响算法的收敛性,针对此问题,将自适应性与非支配排序遗传算法Ⅱ（NSGA-Ⅱ）结合,并通过与DOCPLEX和NSGA-Ⅱ的对比验证了所提模型与算法的有效性。最后,探究了碳税值与模糊需求量偏好值的变化对优化结果的影响。研究结果表明：碳税值的提出可有效促进“公转铁、公转水”,从而显著减少碳排放量,然而过高的碳税值并不一定意味着碳排放量的减少,还会对企业造成过高的成本;模糊需求量偏好值的提高会造成总成本的增加,意味着运输经济性与可靠性两者不可兼得。因此,合理设置碳税值与模糊需求量偏好值是提高多式联运环保效益与运输效益的有效方式。     

求解随机机会约束规划的混合智能算法及应用

为更有效地求解随机机会约束规划问题,提出一种基于克隆选择算法(CSA)、随机模拟技术及神经网络的混合智能算法。采用随机模拟技术产生随机变量样本矩阵训练反向传播(BP)网络以逼近不确定函数,之后在CSA中利用神经网络检验个体的可行性、计算适应度,从而得到优化问题的最优解。为保证算法搜索的快速性和有效性,CSA采用双克隆和双变异策略。仿真结果表明,与已有算法相比,混合智能算法在500代时已取得比较满意的结果,且其精度在单目标优化问题中提高了2.2%,在多目标优化问题中提高了65%;将该算法应用于求解水库优化调度的难题上,结果也表明所建立的模型及算法的可行性和有效性。     

Fuzzy mathematical programming

Fuzzy linear programming (FLP) was originally suggested to solve problems which could be formulated as LP-models, the parameters of which, however, were fuzzy rather than crisp numbers. It has turned out in the meantime that FLP is also well suited to solve LP-problems with several objective functions. FLP belongs to goal programming in the sense that implicitly or explicitly aspiration levels have to be defined at which the membership functions of the fuzzy sets reach their maximum or minimum. Main advantages of FLP are, that the models used are numerically very efficient and that they can in many ways be well adopted to different decision behaviors and contexts.     

Random fuzzy chance-constrained programming based on adaptive chaos quantum honey bee algorithm and robustness analysis

This paper proposes an adaptive chaos quantum honey bee algorithm (CQHBA) for solving chance-constrained programming in random fuzzy environment based on random fuzzy simulations. Random fuzzy simulation is designed to estimate the chance of a random fuzzy event and the optimistic value to a random fuzzy variable. In CQHBA, each bee carries a group of quantum bits representing a solution. Chaos optimization searches space around the selected best-so-far food source. In the marriage process, random interferential discrete quantum crossover is done between selected drones and the queen. Gaussian quantum mutation is used to keep the diversity of whole population. New methods of computing quantum rotation angles are designed based on grads. A proof of convergence for CQHBA is developed and a theoretical analysis of the computational overhead for the algorithm is presented. Numerical examples are presented to demonstrate its superiority in robustness and stability, efficiency of computational complexity, success rate, and accuracy of solution quality. CQHBA is manifested to be highly robust under various conditions and capable of handling most random fuzzy programmings with any parameter settings, variable initializations, system tolerance and confidence level, perturbations, and noises.     

Hybrid multilevel programming with uncertain random parameters

Multilevel programming is developed for modeling decentralized decision-making processes. For different management requirements and risk tolerances of different-level decision-makers, the decision-making criteria applied in different levels cannot be always the same. In this paper, a hybrid multilevel programming model with uncertain random parameters based on expected value model (EVM) and dependent-chance programming (DCP), named as EVM–DCP hybrid multilevel programming, is proposed. The corresponding concepts of Nash equilibrium and Stackelberg–Nash equilibrium are given. For some special case, an equivalent crisp mathematical programming is proposed. An approach integrating uncertain random simulations, Nash equilibrium searching approach and genetic algorithm is designed. Finally, a numerical experiment of uncertain random supply chain pricing decision problem is given.