一种模糊优化的全局算法及在三维水平井轨道设计中应用

本基于一种新的全局优化算法(EM)，提出一种求解模糊优化问题的全局优化算法。针对三维水平井轨道设计问题，提出两个模糊模型。最后把算法及模型应用到实际问题中，数值结果表明算法及模型是有效的、正确的。     

三维水平井轨道设计模糊最优控制模型

建立了三维水平井井眼轨道设计模糊非线性多目标最优控制模型 ,利用模糊集理论把该模型转化为非线性规划问题 ,并把该模型应用到水平井的实际生产中 ,得到满意的结果 .     

Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing

Assembly line balancing generally requires a set of acceptable solutions to the several conflicting objectives. In this study, a binary fuzzy goal programming approach is applied to assembly line balancing. Models for balancing straight and U-shaped assembly lines with fuzzy goals (the number of workstations and cycle time goals) are proposed. The binary fuzzy goal programming models are solved using the methodology introduced by Chang [Chang, C.T., 2007. Binary fuzzy goal programming. European Journal of Operational Research 180 (1), 29–37]. An illustrative example is presented to demonstrate the validity of the proposed models and to compare the performance of straight and U-shaped line configurations.     

模糊聚类分析方法在水平井开发指标预测中的应用

模糊聚类分析方法在实际中应用很广泛,采用模糊聚类的方法,以胜利油田已经大量投产的水平井的数据为基础,将同类油藏中已投产水平井进行分类,然后根据新设计井的有关参数将其归到相应类中,根据同类中已投产井的有关开发指标对新设计水平井的指标进行预测,取得了较好效果.     

Solution of a possibilistic multiobjective linear programming problem

The estimate of the parameters which define a conventional multiobjective decision making model is a difficult task. Normally they are either given by the Decision Maker who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from the past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets and several fuzzy approaches to multiobjective programming have been developed 1, 9, 10, 11. The fuzziness of the parameters gives rise to a problem whose solution will also be fuzzy, see 2, 3, and which is defined by its possibility distribution. Once the possibility distribution of the solution has been obtained, if the decision maker wants more precise information with respect to the decision vector, then we can pose and solve a new problem. In this case we try to find a decision vector, which approximates as much as possible the fuzzy objectives to the fuzzy solution previously obtained. In order to solve this problem we shall develop two different models from the initial solution and based on Goal Programming: an Interval Goal Programming Problem if we define the relation “as accurate as possible” based on the expected intervals of fuzzy numbers, as we showed in [4], and an ordinary Goal Programming based on the expected values of the fuzzy numbers that defined the goals. Finally, we construct algorithms that implement the above mentioned solution method. Our approach will be illustrated by means of a numerical example.     

Fuzzy profit measures for a fuzzy economic order quantity model

Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the fuzzy profit of the inventory model when the demand quantity and unit cost are fuzzy numbers. Since the parameters contained in the inventory model are fuzzy, the profit value calculated from the model should be fuzzy as well. Based on the extension principle, the fuzzy inventory problem is transformed into a pair of two-level mathematical programs to derive the upper bound and lower bound of the fuzzy profit at possibility level α. According to the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs to solve. By enumerating different α values, the upper bound and lower bound of the fuzzy profit are collected to approximate the membership function. Since the profit of the inventory problem is expressed by the membership function rather than by a crisp value, more information is provided for making decisions.     

Two storage inventory model in a mixed environment

Multi-item inventory models with two storage facility and bulk release pattern are developed with linearly time dependent demand in a finite time horizon under crisp, stochastic and fuzzy-stochastic environments. Here different inventory parameters—holding costs, ordering costs, purchase costs, etc.—are assumed as probabilistic or fuzzy in nature. In particular cases stochastic and crisp models are derived. Models are formulated as profit maximization principle and three different approaches are proposed for solution. In the first approach, fuzzy extension principle is used to find membership function of the objective function and then it’s Graded Mean Integration Value (GMIV) for different optimistic levels are taken as equivalent stochastic objectives. Then the stochastic model is transformed to a constraint multi-objective programming problem using Stochastic Non-linear Programming (SNLP) technique. The multi-objective problems are transferred to single objective problems using Interactive Fuzzy Satisfising (IFS) technique. Finally, a Region Reducing Genetic Algorithm (RRGA) based on entropy has been developed and implemented to solve the single objective problems. In the second approach, the above GMIV (which is stochastic in nature) is optimized with some degree of probability and using SNLP technique model is transferred to an equivalent single objective crisp problem and solved using RRGA. In the third approach, objective function is optimized with some degree of possibility/necessity and following this approach model is transformed to an equivalent constrained stochastic programming problem. Then it is transformed to an equivalent single objective crisp problem using SNLP technique and solved via RRGA. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

基于Vague集的模糊多目标决策方法及应用

针对目前基于Vague集多目标决策中Vague值计算困难以及确定目标满意度的下界和不满意度的上界存在主观随意性问题.提出了一种基于Vague集的模糊多目标决策方法.利用属性数学中的属性集和属性测度理论构造目标的真隶属度函数、假隶属度函数和犹豫度函数,从而可计算出目标的Vague值;采用记分函数计算方案的多目标评分值,从而可以对方案进行排序并选择出最优方案.应用实例验证了该方法的有效性和实用性.     

An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon

An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

应用模糊综合评判和灰色关联度分析评价水平井多级压裂效果

水平井多级压裂是低渗透和非常规油气田开发的有效技术手段,其压后产能评价问题已成为相关研究的热点和难点.水平井多级压裂压后产能的各项影响因素之间关系复杂,通过常规理论分析量化研究困难,压裂效果很难准确预测.本文提出应用模糊综合评判和灰色关联度分析相结合的方法,对多级压裂水平井的压裂效果进行评价.首先运用灰色理论分析影响压裂效果的各因素之间的灰色关联度,计算各影响因素在综合评判中的权重值,再结合模糊综合评判方法,对多级压裂井压后效果进行预测评价.通过目的区块24口多级压裂水平井压后效果评价与实际生产情况对比,表明模型计算准确率达到95.8%,评价结果准确可靠.     

Solving a multiobjective possibilistic problem through compromise programming

Real decision problems usually consider several objectives that have parameters which are often given by the decision maker in an imprecise way. It is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory.Here we propose a method for solving these kinds of models through a fuzzy compromise programming approach.To formulate a fuzzy compromise programming problem from a possibilistic multiobjective linear programming problem the fuzzy ideal solution concept is introduced. This concept is based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their α-cuts. The accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and a definition of discrepancy between intervals is introduced in our analysis.     

Integrated inventory problem under trade credit in fuzzy random environment

This paper is concerned with an integrated inventory problem under trade credit where both the demand rate and deteriorating rate are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The objective of this paper is to determine the optimal inventory policy by optimizing simultaneously the replenishment cycle length and trade credit period. At first, three decision criteria are given: (1) expected value criterion, (2) chance-constrained criterion and (3) chance maximization criterion. Then, after building the fuzzy random models based on the above decision criterion, a hybrid intelligent algorithm by integrating fuzzy random simulation and genetic algorithm is employed to deal with these models. At the end, three numerical examples are given to illustrate the benefits of the models and show the effectiveness of the algorithms.     

A fuzzy genetic algorithm with varying population size to solve an inventory model with credit-linked promotional demand in an imprecise planning horizon

A genetic algorithm (GA) with varying population size is developed where crossover probability is a function of parents’ age-type (young, middle-aged, old, etc.) and is obtained using a fuzzy rule base and possibility theory. It is an improved GA where a subset of better children is included with the parent population for next generation and size of this subset is a percentage of the size of its parent set. This GA is used to make managerial decision for an inventory model of a newly launched product. It is assumed that lifetime of the product is finite and imprecise (fuzzy) in nature. Here wholesaler/producer offers a delay period of payment to its retailers to capture the market. Due to this facility retailer also offers a fixed credit-period to its customers for some cycles to boost the demand. During these cycles demand of the item increases with time at a decreasing rate depending upon the duration of customers’ credit-period. Models are formulated for both the crisp and fuzzy inventory parameters to maximize the present value of total possible profit from the whole planning horizon under inflation and time value of money. Fuzzy models are transferred to deterministic ones following possibility/necessity measure on fuzzy goal and necessity measure on imprecise constraints. Finally optimal decision is made using above mentioned GA. Performance of the proposed GA on the model with respect to some other GAs are compared.     

New approach for describing transient pressure response generated by horizontal wells of arbitrary geometry

This paper is aimed at developing a methodology for studying the transient pressure behavior of horizontal wells with any curvilinear trajectory in an isotropic/anisotropic arbitrarily shaped reservoir. This methodology employs generalized functions to represent the tortuous horizontal well. A particular way of removing the singularities involved in the partial differential equation is based on reducing the original problem to the conventional solution of the homogeneous diffusivity equation under any given initial and boundary conditions. The Green function method and any standard numerical technique are combined in a single computational strategy to obtain the transient pressure response generated by a curved and twisted horizontal well in reservoirs with irregular boundaries. Analytical methods can be also used, whenever possible, to solve the reduced problem. This proposal can be easily broadened to analyze the performance of the pressure transient of any kind of reservoir sources or sinks that can be modeled using generalized functions. Some models are presented.     

Fuzzy coefficient volatility (FCV) models with applications

Recently, Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers. In this paper, we propose a class of FCV (Fuzzy Coefficient Volatility) models and study the moment properties. The method used here is very similar to the method used in Appadoo et al. [S.S. Appadoo, M. Ghahramani, A. Thavaneswaran, Moment properties of some time series models, Math. Sci. 30 (1) (2005) 50–63]. The proposed models incorporate fuzziness, subjectivity, arbitrariness and uncertainty observed in most financial time series. The usual forecasting method does not incorporate parameter variability. Fuzzy numbers are used to model the parameters to incorporate parameter variability.     

THE OPTIMAL CONTROL SYSTEM OF 3D HORIZONTAL WELL AND ITS APPLICATION

A multi-objective optimal control model for nonlinear multilevel dynamicalsystem is built in this paper. The existence of the solutions to this systemand the controllability and the polykeys of the control are discussed. In orderto obtain the global optimal solution, Uniform Design method is introducedto select initial1 feasible points, then an improved Hooke-jeeves algorithm isproposed. The new algorithm and its corresponding software we developed hasvalidated in more than 12 horizontal wells, which show their advantages suchas less length of trajectory designed, more accuracy of target hitting and lesstime-consuming comparison with present conventional method.     

Model Based Trajectory Control of an Overhead Travelling Crane

Until now, most papers concerning control of overhead travelling cranes have only focussed on position control of the translational degrees of freedom, see for example [1], [3], [4], and [5]. With more advanced robotic applications envisaged, however, there is a demand for both trajectory control in six degrees of freedom and active damping of the weakly damped load oscillations due to the rope suspension [2]. Hence, a model based trajectory control is presented for an overhead travelling crane that has been upgraded with an orientation unit providing three additional axes. Starting from a central multibody model, decentralised design models are derived for each crane axis. By this, couplings between the axes are identified and appear as disturbance inputs in these decentralised design models. Each decentralised axis controller consists of linear state feedback, feedforward control, and observer based disturbance compensation and is derived in symbolic form. This allows for an adaptation of the complete control structure employing the gain scheduling technique with respect to varying system parameters like rope length and load mass. Couplings between the crane axes are compensated by feedforward control, whereas the e.ects of nonlinear friction forces are counteracted by combination of feedforward control and disturbance estimation. Experimental results, taken at a 5 t ‐ bridge crane, show the bene.ts of the proposed control scheme as regards control performance and steady‐state accuracy.     

Projective codes which satisfy the chain condition

Binary linear codes with length at most one above the Griesmer bound were proven to satisfy the chain condition by Helleseth et al. [1]. Binary linear projective codes with length two above the Griesmer bound which satisfy the chain condition are found. Necessary conditions for binary linear codes for which the two-way chain condition holds are derived.     

基于灰色关联法的水平井压裂参数优化研究

针对低渗透薄互砂岩油藏A油田C9区块水平井井区储层物性差、非均质性强、开发难度大等问题,为改善水平井井区开发效果、提高水平井单井产能,应用灰色关联法,结合数值模拟软件,分析影响压裂水平井产能的主要因素,开展水平井压裂参数优化研究,结果表明裂缝半长和裂缝间距是影响压裂水平井产能的主要因素,优选出水平井压裂方案:裂缝半长为...     

考虑基岩向井筒供气的气藏压裂水平井产能预测模型

基于等效井径模型,综合考虑各裂缝不同参数、裂缝变质量入流和井筒变质量流动等因素的影响,建立并求解了基岩和压裂缝同时向井筒供气的井筒与气藏耦合的压裂水平井产能预测模型.研究分析了压裂水平井产能敏感因素.结果表明:压裂水平井的产能随裂缝条数、裂缝半长、裂缝间距的增加而增加;为获得较高的产能,压裂时应尽可能保持裂缝与井筒垂直;压裂缝条数一定时,裂缝越长、间距越大,压裂缝产能贡献越大,而裂缝越短、间距越小时,基岩向井筒供气的贡献越大,压裂缝贡献相对较小.研究成果为气藏压裂水平井设计提供了科学依据.