Optimal route selection based on Monte Carlo method and adaptive amoeba algorithm under uncertain environment

The fuzzy optimal path under uncertainty is one of the basic network optimization problems. Considering the uncertain environment, many fuzzy numbers are used to represent the edge weights, such as interval number and triangular fuzzy number. Then, these fuzzy numbers are converted to real numbers directly. This converting makes the optimal path the shortest path selection problem. However, much information of uncertainty get lost when converting fuzzy numbers to real numbers. In order to ensure all the origan data complete, in this paper, a fuzzy optimal path solving model based on the Monte Carlo method and adaptive amoeba algorithm is proposed. In Monte Carlo process, a random number which belongs to the fuzzy number is generated. Then, Physarum polycephalum algorithm is used to solve the shortest path every time and record the result. After many times calculation, many shortest paths have been found and recorded. At last, by analysing the characters of all the results, the optimal path can be selected. Several numerical examples are given to illustrate the effectiveness of the proposed method, the results show that the proposed method can deal with the fuzzy optimal path problems effectively.     

不确定海流环境下水下机器人最优时间路径规划

为解决海流预测不精确条件下,现有基于确定性海流路径规划算法鲁棒性差和规划的路径有可能为不可行路径的问题,本文提出一种基于区间优化的水下机器人(AUV)最优时间路径规划算法.该算法采用双层架构,外层用蚁群系统算法(ACS)寻找由起点至终点的候选路径;内层以区间海流为环境模型,计算候选路径航行时间上下限,并分别通过区间序关系和基于可靠性的区间可能度模型将航行时间区间转换为确定性评价函数,并将评价函数值作为候选路径适应度值返回到外层算法.仿真结果表明,相对于确定海流场路径规划方案,提出的方案增强了路径规划器的鲁棒性并解决了结果路径不可行问题.     

A biologically inspired solution for fuzzy shortest path problems

By considering the uncertainty that exists in the edge weights of the network, fuzzy shortest path problems, as one of the derivative problems of shortest path problems, emerge from various practical applications in different areas. A path finding model, inspired by an amoeboid organism, Physarum polycephalum, has been shown as an effective approach for deterministic shortest path problems. In this paper, a biologically inspired algorithm called Fuzzy Physarum Algorithm (FPA) is proposed for fuzzy shortest path problems. FPA is developed based on the path finding model, while utilizing fuzzy arithmetic and fuzzy distance to deal with fuzzy issues. As a result, FPA can represent and handle the fuzzy shortest path problem flexibly and effectively. Distinct from many existing methods, no order relation has been assumed in the proposed FPA. Several examples, including a tourist problem, are given to illustrate the effectiveness and flexibility of the proposed method and the results are compared with existing methods.     

不确定条件下应急资源布局的鲁棒双层优化模型

针对非常规突发事件中应急资源布局问题,在受灾点需求不确定和应急救援过程分为多个阶段的情景下,建立了省市两级应急储备仓库定位和物资配置的鲁棒双层规划模型。运用相对鲁棒优化方法,将上述具有不确定性系数的双层规划模型转化为从者无关联的确定性线性双层规划,提出了一种混合遗传算法进行求解,实现了省市两级应急资源布局的协同优化。通过实例验证了模型及算法的可行性和有效性。     

有色冶金过程不确定优化方法探讨

有色冶金过程受原料来源多样、工况条件波动、生产成分变化等因素的影响,存在大量的不确定性,严重影响了冶炼生产的稳定性与可靠性.鉴于此,综述不同类型不确定性优化问题的描述方法,具体包括概率不确定优化问题、模糊不确定优化问题和区间不确定优化问题.通过分析有色冶金生产过程的特点与需求,以3种典型的有色冶金过程不确定优化问题为例,探讨不同类型的有色冶金过程不确定优化方法.针对氧化铝生料浆配料过程的概率不确定优化问题,采用基于Hammersley sequence sampling(HSS)的方法实现不确定模型的确定性转换;针对湿法炼锌除铜过程的模糊不确定优化问题,采用基于模糊规则的方法进行确定性评估;针对锌电解分时供电过程的区间不确定优化问题,采用基于min-max的方法求解鲁棒解.工业运行数据均验证了上述方法的有效性.     

Solution of fuzzy multi-objective project crashing problem

Project management is a very important field employed for scheduling activities and monitoring the progress, in competitive and fluctuating environments. The feasible duration time required to perform a specific project is determined using critical path method. However, because of competitive priorities, time is important and the completion time of a project determined using critical path method should be reduced to meet a deadline requested. In this situation, project crashing problem arises. Project crashing analysis is concerned with shortening the project duration time by accelerating some of its activities at an additional cost. In general, the parameters of the problem are accepted as certain and the project crashing problems are solved using deterministic solution techniques. In reality, because of uncertain environment conditions, incomplete or unobtainable information, there can be ambiguity in the parameters of the problem. The uncertainty in the parameters can be modeled via fuzzy set theory. Using fuzzy models gives the chance of better project management decisions with more stability under uncertain environmental factors. In the literature, various authors solved different fuzzy versions of project management problems via transforming them into their crisp equivalents. In this study, a fuzzy multi-objective project crashing problem with fuzzy parameters is handled. The fuzzy project crashing problem is solved with a direct solution approach based on fuzzy ranking methods and the tabu search algorithm.     

Optimisation of mixed-model assembly line balancing problem under uncertain demand

Assembly lines play a crucial role in determining the profitability of a company. Market conditions have increased the importance of mixed-model assembly lines. Variations in the demand are frequent in real industrial environments and often leads to failure of the mixed-model assembly line balancing scheme. Decision makers have to take into account this uncertainty. In an assembly line balancing problem, there is a massive amount of research in the literature assuming deterministic environment, and many other works consider uncertain task times. This research utilises the uncertainty theory to model uncertain demand and introduces complexity theory to measure the uncertainty of assembly lines. Scenario probability and triangular fuzzy number are used to describe the uncertain demand. The station complexity was measured based on information entropy and fuzzy entropy to assist in balancing systems with robust performances, considering the influence of multi-model products in the station on the assembly line. Taking minimum station complexity, minimum workload difference within station, maximum productivity as objective functions, a new optimization model for mixed-model assembly line balancing under uncertain demand was established. Then an improved genetic algorithm was applied to solve the model. Finally, the effectiveness of the model was verified by several instances of mixed-model assembly line for automobile engine.     

Robust scheduling on a single machine to minimize total flow time

In a real-world manufacturing environment featuring a variety of uncertainties, production schedules for manufacturing systems often cannot be executed exactly as they are developed. In these environments, schedule robustness that guarantees the best worst-case performance is a more appropriate criterion in developing schedules, although most existing studies have developed optimal schedules with respect to a deterministic or stochastic scheduling model. This study concerns robust single machine scheduling with uncertain job processing times and sequence-dependent family setup times explicitly represented by interval data. The objective is to obtain robust sequences of job families and jobs within each family that minimize the absolute deviation of total flow time from the optimal solution under the worst-case scenario. We prove that the robust single machine scheduling problem of interest is NP-hard. This problem is reformulated as a robust constrained shortest path problem and solved by a simulated annealing-based algorithmic framework that embeds a generalized label correcting method. The results of numerical experiments demonstrate that the proposed heuristic is effective and efficient for determining robust schedules. In addition, we explore the impact of degree of uncertainty on the performance measures and examine the tradeoff between robustness and optimality.     

动态环境下基于蚁群算法的实时路径规划方法*

提出了一种实现移动机器人在复杂动态环境下进行实时路径规划的新方法。该方法首先利用模糊逻辑来描述机器人局部环境模型;然后采用改进的蚁群系统算法快速地搜索出局部最优路径,并在此路径的引导下,结合机器人滚动规划方法,实现移动机器人在复杂动态环境下的实时路径规划。该方法不仅能克服传感器测量误差等引起环境信息的模糊性和不确定性的影响,还可以充分发挥蚁群算法的群体智能优势来保证系统规划的实时性。仿真结果表明该算法的有效性和可行性。     

Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

In designing phase of systems, design parameters such as component reliabilities and cost are normally under uncertainties. This paper presents a methodology for solving the multi-objective reliability optimization model in which parameters are considered as imprecise in terms of triangular interval data. The uncertain multi-objective optimization model is converted into deterministic multi-objective model including left, center and right interval functions. A conflicting nature between the objectives is resolved with the help of intuitionistic fuzzy programming technique by considering linear as well as the nonlinear degree of membership and non-membership functions. The resultants max–min problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Finally, a numerical instance is presented to show the performance of the proposed approach.     

Robust fuzzy stabilisation of interval plants

The paper deals with the problem of stabilisation of interval systems. To this end, by using Takagi–Sugeno fuzzy mechanism, a Mamdani-type PID-like fuzzy controller is modified and extended to develop a new PID-like Takagi–Sugeno fuzzy stabilising controller for the plant described by an interval system. Indeed, a PID-like Takagi–Sugeno fuzzy controller and an interval plant are considered in the forward path of a unity feedback system, and parameters in Takagi–Sugeno fuzzy controller are determined so that the stability of the closed-loop system is assured. The closed-loop system has a multilinear uncertainty structure. Therefore, based on the Zero Exclusion Condition for multilinear uncertain systems, a new theorem presenting sufficient conditions for the Takagi–Sugeno fuzzy controller to be robust stability guaranteed is also derived. An example is given to illustrate the application and the effectiveness of the proposed controller.     

Multitask-oriented manufacturing service composition in an uncertain environment using a hyper-heuristic algorithm

One of the most important issues in cloud manufacturing involves obtaining an optimal manufacturing service composition solution. However, traditional manufacturing service composition methods either focused on single-task-oriented service composition or optimized solutions under a deterministic environment. In the study, a multitask-oriented manufacturing service composition (MMSC) model with two stages in uncertain environment is proposed. It handles the problem of multitask scheduling and also deals with the inherent uncertainty and ambiguity in cloud manufacturing including the occurrence of urgent task requests and the delayed delivery time of raw materials. In order to solve the MMSC model, a new genetic based hyper-heuristic algorithm (GA-HH) with adjustable length of chromosome is proposed. The GA-HH contains a set of low-level heuristics that directly operate on the solution domain that are organized by the high-level heuristic (i.e., genetic algorithm). Finally, the proposed GA-HH is proved as an efficient, effective, and robust algorithm to solve the MMSC model with considerations of multitask and uncertainty, by comparing it with other well-known meta-heuristic algorithms such as the genetic algorithm and particle swarm optimization.     

基于LMI方法的网络闭环控制系统离散鲁棒模糊控制

针对网络闭环控制系统中时延和不同步等不确定因素,将时延的不确定性转换为系统状态方程系数矩阵的不确定性,提出了一种新的网络闭环控制系统建模方法———具有时滞的不确定离散模糊T-S模型;并在此模型的基础上,利用并行分布补偿原理和Lyapunov理论及LMI方法,证明了通过状态的静态反馈模糊控制,使闭环系统稳定的充分条件等价于求解一组LMI。仿真示例验证了该控制方法的有效性.     

一种区间数-二元联系数转换的模糊决策改进算法

针对准则值和准则权重以二元或三元区间数形式给出的模糊决策问题,提出一种区间数-二元联系数转换改进算法.利用区间数的偏好值和上下限取值范围,将区间数转换为二元联系数.将区间数的偏好值作为联系数的同一度,并将区间数上下限到偏好值的距离作为联系数的差异度,使得转换过程中区间模糊信息中的确定性增大,不确定性减小.在此基础上,使用同一度和差异度重新定义联系数的正负理想解,并确定联系数间的距离公式,进而提出一种改进的基于联系数的TOPSIS模糊决策算法.最后,结合实例表明所提出算法的有效性和合理性.     

A robust optimization approach for imprecise data envelopment analysis

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it’s supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.     

基于信息结构的区间值决策信息系统鲁棒不确定性度量

现阶段基于单值的信息系统的不确定性度量研究较多,而少有关于区间值决策信息系统的不确定性和噪声标签对系统不确定性影响的研究.因此,文中提出基于信息结构的区间值决策信息系统鲁棒不确定性度量.利用KL散度定义区间值之间的相似度,构造区间值模糊相似关系,并提出区间值决策信息系统的信息结构.为了降低噪声决策对系统不确定性度量的影响,引入K近邻点计算样本关于决策的隶属度,提出2种基于信息结构的鲁棒不确定性度量方法.实验表明文中不确定性度量的有效性和合理性.     

Multi-objective genetic programming approach for robust modeling of complex manufacturing processes having probabilistic uncertainty in experimental data

In this paper, a multi-objective uniform-diversity genetic programming (MUGP) algorithm deployed for robust Pareto modeling and prediction of complex nonlinear processes using some input-output data table. The uncertainties included in measured data are considered to obtain more robust models. The considered benchmarks are an explosive cutting and forming processes, in which the nonlinear behavior between the input and output of processes are detected using MUGP. For both case studies, a multi-objective modeling and prediction procedure firstly performed using deterministic data. Secondly, the same identification procedure carried out using probabilistic uncertainty in the experimental input-output data. The objective functions considered are namely, training error, prediction error and number of tree nodes (complexity of models) in the deterministic approach. Accordingly, the mean and standard deviation of training error and prediction error are considered in robust Pareto modeling and prediction of such processes. In this way, Pareto front of such modeling and prediction is first obtained for both explosive cutting and forming processes with deterministic data. Such Pareto front is then obtained using experimental input-output-data having probabilistic uncertainty in input parameters through a Monte Carlo simulation (MCS) approach. In addition, it has been shown that for both cases, the trade-off models obtained from deterministic data have significant biases when tested on data with probabilistic uncertainty. Finally, the obtained results of such multi-objective robust model identification show promising results in terms of compensating uncertainty in the experimental input-output-data.     

基于区间二型模糊摩擦补偿的鲁棒自适应控制

针对不确定机械系统中普遍存在的摩擦力,由于其非线性和不确定性,传统基于摩擦模型的补偿控制方法难以达到满意的系统性能要求.本文提出基于自适应区间二型（Type-2）模糊逻辑系统对系统摩擦进行补偿建模,并在该摩擦补偿方法的基础上设计出鲁棒自适应控制器,保证系统输出精度,且对摩擦环境的变化具有较强自适应性.区间二型模糊逻辑系统相对于传统一型模糊逻辑系统具有较强的处理不确定性问题的能力,在本文中使用自适应区间二型模糊逻辑系统不断逼近摩擦力,根据李雅普诺夫稳定性理论求出自适应律并证明系统跟踪误差的有界性.在不同摩擦环境下的仿真结果验证了本文所提摩擦建模方法与控制策略的有效性与实用性.     

Discrete Interval Type 2 Fuzzy System Models Using Uncertainty in Learning Parameters

Fuzzy system modeling (FSM) is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty. Conventional FSM techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system. However, since type 1 fuzzy sets express the belongingness of a crisp value x' of a base variable x in a fuzzy set A by a crisp membership value mu_A(x'), they cannot fully capture the uncertainties due to imprecision in identifying membership functions. Higher types of fuzzy sets can be a remedy to address this issue. Since, the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set, the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades. In this paper, we propose a black-box methodology that can identify robust type 2 Takagi-Sugeno, Mizumoto and Linguistic fuzzy system models with high predictive power. One of the essential problems of type 2 fuzzy system models is computational complexity. In order to remedy this problem, discrete interval valued type 2 fuzzy system models are proposed with type reduction. In the proposed fuzzy system modeling methods, fuzzy C-means (FCM) clustering algorithm is used in order to identify the system structure. The proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of FCM, known as the level of membership, and its variation over a specific set of values which generate the uncertainty associated with the system structure     

基于小波包变换和块模糊分类的自适应水印算法

提出了在WPT域上基于块模糊分类的新的自适应水印算法。首先用m-序列来控制对原始图像进行小波包变换的分解结构,将适当的小波系数组成小波子块。然后根据人类视觉系统(HVS)模型和能量模型,对小波子块进行模糊分类。最后,根据分类结果,将不同强度的二值水印嵌入到不同的小波子块中。实验结果表明,提出的算法能抵抗各种图像处理的攻击,具有较好的鲁棒性。