Development of a credit limit allocation model for banks using an integrated Fuzzy TOPSIS and linear programming

In this study, a credit risk concentration allocation model is developed for the banks to determine the credit risk concentration limits of their regional head’s. The proposed model is based on the Fuzzy TOPSIS (FTOPSIS) and Linear Programming (LP) approaches. FTOPSIS is easy to use and capable to keep tract of decision made in reaching the overall score by combining different types of criteria. LP combines the results of FTOPSIS and other constraints and objectives determined by the bank. Using FTOPSIS and LP together in the same model brings uniformity and a structure in credit risk concentration decisions of the banks. The developed model is tested with a real case banking application and satisfactory results are obtained. An application is also provided in the paper for illustrative purposes.     

Toward Practical Query Evaluation for Constraint Databases

Linear constraint databases (LCDBs) extend relational databases to include linear arithmetic constraints in both relations and queries. A LCDB can also be viewed as a powerful extension of linear programming (LP) where the system of constraints is generalized to a database containing constraints and the objective function is generalized to a relational query containing constraints. Our major concern is query optimization in LCDBs. Traditional database approaches are not adequate for combination with LP technology. Instead, we propose a new query optimization approach, based on statistical estimations and iterated trials of potentially better evaluation plans. The resulting algorithms are not only effective on LCDBs, but also applicable to existing query languages. A number of specific constraint algebra algorithms are also developed: select-project-join for two relations, constraint sort-join and constraint multi-join.     

Rough‐fuzzy quadratic minimum spanning tree problem

A quadratic minimum spanning tree problem determines a minimum spanning tree of a network whose edges are associated with linear and quadratic weights. Linear weights represent the edge costs whereas the quadratic weights are the interaction costs between a pair of edges of the graph. In this study, a bi‐objective rough‐fuzzy quadratic minimum spanning tree problem has been proposed for a connected graph, where the linear and the quadratic weights are represented as rough‐fuzzy variables. The proposed model is formulated by using rough‐fuzzy chance‐constrained programming technique. Subsequently, three related theorems are also proposed for the crisp transformation of the proposed model. The crisp equivalent models are solved with a classical multi‐objective solution technique, the epsilon‐constraint method and two multi‐objective evolutionary algorithms: (a) nondominated sorting genetic algorithm II (NSGA‐II) and (b) multi‐objective cross‐generational elitist selection, heterogeneous recombination, and cataclysmic mutation (MOCHC) algorithm. A numerical example is provided to illustrate the proposed model when solved with different methodologies. A sensitivity analysis of the example is also performed at different confidence levels. The performance of NSGA‐II and MOCHC are analysed on five randomly generated instances of the proposed model. Finally, a numerical illustration of an application of the proposed model is also presented in this study.     

Project scheduling under resource constraints: Application of the cumulative global constraint in a decision support framework

This paper concerns project scheduling under resource constraints. Traditionally, the objective is to find a unique solution that minimizes the project makespan, while respecting the precedence constraints and the resource constraints. This work focuses on developing a model and a decision support framework for industrial application of the cumulative global constraint. For a given project scheduling, the proposed approach allows the generation of different optimal solutions relative to the alternate availability of outsourcing and resources. The objective is to provide a decision-maker an assistance to construct, choose, and define the appropriate scheduling program taking into account the possible capacity resources. The industrial problem under consideration is modeled as a constraint satisfaction problem (CSP). It is implemented under the constraint programming language CHIP V5. The provided solutions determine values for the various variables associated to the tasks realized on each resource, as well as the curves with the profile of the total consumption of resources on time.     

A heuristic approach for identification of redundant constraints in linear programming models

Linear programming (LP) is one of the most important techniques used in modelling and solving practical optimization problems that arise in industry, commerce, and management. When formulating an LP model, systems analysts and researchers often include all possible constraints although some of them may not be binding at the optimal solution. The presence of redundant constraints does not alter the optimum solution(s), but may consume extra computational effort. Many researchers have proposed algorithms for identifying the redundant constraints in LP models. Here we propose a heuristic approach using an intercept matrix to identify redundant constraints prior to the start of the solution process. An interesting observation of the proposal technique is that the tendency of variables to pop in and pop out of the basis is eradicated after eliminating the redundancies. The eradication of pop-in and pop-out substantially reduces the number of iterations. A significant reduction in the computational effort is achieved for LP problems of different sizes.     

Interval Evaluations in the Analytic Hierarchy Process By Possibility Analysis

Since a pairwise comparison matrix in the Analytic Hierarchy Process (AHP) is based on human intuition, the given matrix will always include inconsistent elements violating the transitivity property. We propose the Interval AHP by which interval weights can be obtained. The widths of the estimated interval weights represent inconsistency in judging data. Since interval weights can be obtained from inconsistent data, the proposed Interval AHP is more appropriate to human judgment. Assuming crisp values in a pairwise comparison matrix, the interval comparisons including the given crisp comparisons can be obtained by applying the Linear Programming (LP) approach. Using an interval preference relation, the Interval AHP for crisp data can be extended to an approach for interval data allowing to express the uncertainty of human judgment in pairwise comparisons.     

An overview on fault diagnosis and nature-inspired optimal control of industrial process applications

Fault detection, isolation and optimal control have long been applied to industry. These techniques have proven various successful theoretical results and industrial applications. Fault diagnosis is considered as the merge of fault detection (that indicates if there is a fault) and fault isolation (that determines where the fault is), and it has important effects on the operation of complex dynamical systems specific to modern industry applications such as industrial electronics, business management systems, energy, and public sectors. Since the resources are always limited in real-world industrial applications, the solutions to optimally use them under various constraints are of high actuality. In this context, the optimal tuning of linear and nonlinear controllers is a systematic way to meet the performance specifications expressed as optimization problems that target the minimization of integral- or sum-type objective functions, where the tuning parameters of the controllers are the vector variables of the objective functions. The nature-inspired optimization algorithms give efficient solutions to such optimization problems. This paper presents an overview on recent developments in machine learning, data mining and evolving soft computing techniques for fault diagnosis and on nature-inspired optimal control. The generic theory is discussed along with illustrative industrial process applications that include a real liquid level control application, wind turbines and a nonlinear servo system. New research challenges with strong industrial impact are highlighted.     

Sensitivity analysis of LP-MPC cascade control systems

Model predictive control (MPC) has found wide application in the chemical process industry as well as other industrial sectors. Commercial MPC systems are typically implemented in conjunction with a steady-state linear or quadratic programming optimizer, whose key functions are to track the economic optimum and to provide feasible set-points to the model predictive controller. The two-level system is complementary to real-time optimization which typically utilizes more complex models and is executed less frequently. Despite the widespread adoption of LP-MPC systems, occurrences of poor performance have been reported, where large variations in the computed set-points were observed. In this paper, we analyze the sensitivity of the LP solution to variation in the LP model bias, through which feedback to the LP layer occurs. We consider both multi-input, single-output (MISO) and multi-input, multi-output (MIMO) systems. Principles are illustrated through graphical representation as well as case studies. The performance of the two-level LP-MPC closed-loop system is evaluated and explained using results of the LP sensitivity analysis.     

敏捷供应链静态调度模型及其贪婪算法

针对确定性市场需求下的敏捷供应链(ASC)调度具有批量和时间双重约束的问题,根据供应层级关系建立多级供应链结构模型(SCSM),在此基础上设计调度问题的线性规划(LP)模型及其两阶段求解算法：第一阶段的最短响应时间调度贪婪算法判定供应链系统对需求批量和时间约束满足与否;第二阶段的精益调度贪婪算法求解以最小化供应链库存成本为目标的最优调度方案。最后通过算例验证了模型和算法的实用性和有效性。     

Modeling uncertain processes with interval random vector functional-link networks

This paper presents a new approach to building an interval model for an industrial process with uncertainty that employs an interval neural network (INN), which can solve problems such as model structure demands and complexity limitations in the conventional unknown but bounded (UBB) errors method. A new architecture for an interval random vector functional-link network (IRVFLN) and its learning algorithm with penalty factors are proposed, to solve the problems such as the local minima, slow convergence, and very poor sensitivity to learning rate settings in the interval feed-forward neural networks with error back-propagation (IBPNNs). As an application case study, the IRVFLN is used to model the glutamic acid fermentation process under the condition of bounded-error data, and the test results indicate that the accuracy of the IRVFLN model meets the manufacturing requirements. The comparison is performed with IBPNN, and the results demonstrate that the proposed network outperforms IBPNN both on effectiveness and efficiency. Also, a comparison is given with a crisp (point-valued) approach using RVFLN, and the results show that the crisp approach is less reliable when existing uncertainties in measuring or process.     

Parameter dependent H∞ control by finite dimensional LMI optimization: application to trade‐off dependent control

In this paper, we consider the design of an H_∞ trade‐off dependent controller, that is, a controller such that, for a given Linear Time‐Invariant plant, a set of performance trade‐offs parameterized by a scalar θ is satisfied. The controller state space matrices are explicit functions of θ. This new problem is a special case of the design of a parameter dependent controller for a parameter dependent plant, which has many application in Automatic Control. This last design problem can be naturally formulated as a convex but infinite dimensional optimization problem involving parameter dependent Linear Matrix Inequality (LMI) constraints. In this paper, we propose finite dimensional (parameter independent) LMI constraints which are equivalent to the parameter dependent LMI constraints. The parameter dependent controller design is then formulated as a convex finite dimensional LMI optimization problem. The obtained result is then applied to the trade‐off dependent controller design. A numerical example emphasizes the strong interest of our finite dimensional optimization problem with respect to the trade‐off dependent control application. Copyright © 2005 John Wiley & Sons, Ltd.     

有约束多目标多自由度优化的可行性分析及软约束调整

有约束多目标多自由度优化是从复杂工业过程优化控制的实际应用背景出发而提 出的.文中讨论了它的可行性问题,并将其规范成一线性规则问题,给出了判断可行性及调整 软约束的统一算法.     

Evolutionary trajectory planning for an industrial robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator (AdeptOne XL robot) in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE), have been used for the optimization. Two methods (normalized weighting objective functions and average fitness factor) are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.     

模糊非线性规划对称模型基于遗传算法的模糊最优解*

本文基于扩展原理，借助于隶属函数，对具有一般形式的Ｆｕｚｚｙ数，提出了描述和表达Ｆｕｚｚｙ目标和Ｆｕｚｚｙ约束条件的方法，将一类具有Ｆｕｚｚｙ目标／资源约束非线性规划的对称模型转化为确定性的非线性规划。基于遗传自救的思想提出了Ｆｕｚｚｙ环境下求解非线性规划对称模型的Ｆｕｚｚｙ最优解方法。     

Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization

In this paper, a fuzzy multi-objective programming problem is considered where functional relationships between decision variables and objective functions are not completely known to us. Due to uncertainty in real decision situations sometimes it is difficult to find the exact functional relationship between objectives and decision variables. It is assumed that information source from where some knowledge may be obtained about the objective functions consists of a block of fuzzy if-then rules. In such situations, the decision making is difficult and the presence of multiple objectives gives rise to multi-objective optimization problem under fuzzy rule constraints. In order to tackle the problem, appropriate fuzzy reasoning schemes are used to determine crisp functional relationship between the objective functions and the decision variables. Thus a multi-objective optimization problem is formulated from the original fuzzy rule-based multi-objective optimization model. In order to solve the resultant problem, a deterministic single-objective non-linear optimization problem is reformulated with the help of fuzzy optimization technique. Finally, PSO (Particle Swarm Optimization) algorithm is employed to solve the resultant single-objective non-linear optimization model and the computation procedure is illustrated by means of numerical examples.     

Dynamic estimation of optical flow field using objective functions

Optical flow (image velocity) fields are computed and interpreted from an image sequence by incorporating knowledge of object kinematics. Linear and quadratic objective functions are defined by considering the kinematics, and the function parameters are estimated simultaneously with the computation of the velocity field by relaxation. The objective functions provide an interpretation of the dynamic scenes and, at the same time, serve as the smoothness constraints. The computation is initially based on measured perpendicular velocity components of contours or region boundaries which, due to the ‘aperture problem’, are theoretically not the true perpendicular velocity components. This difficulty is alleviated by introducing a dynamic procedure for the measurement of the perpendicular components. Experiments on using objective functions for synthetic and real images of translating and rotating objects generated velocity fields that are meaningful and consistent with visual perception.     

Linear programming software tools on UNIX System

Linear programming(LP) is one of the most widely used Operations Research/Management Science/Industrial Engineering techniques. Recently, multiple criteria decision making or multiple objective linear programming has been well established as a practical approach to seeking satisfactory solutions to real-world decision problems.

In this paper we develop software tools for solving various linear programming problems such as a traditional LP problem, bicriteria LP problem, and multi-criteria LP problem on UNIX system. In a phase for reading data of various LP problems, we define a BNF(Backus-Nauel form) of various LP problems and implement BNF rules by using the C programming language.

In a phase for computing various LP problems, we use efficient methods for solving LP problems, develop various software tools on UNIX system, and combine each LP tool corresponding to an user request in which the Shell programming is used.

We also demonstrate some real-world LP problems by using LP software tools developed here on an UNIX System. Sanyo MPS 020.     

Learning indistinguishability from data

 In this paper we revisit the idea of interpreting fuzzy sets as representations of vague values. In this context a fuzzy set is induced by a crisp value and the membership degree of an element is understood as the similarity degree between this element and the crisp value that determines the fuzzy set. Similarity is assumed to be a notion of distance. This means that fuzzy sets are induced by crisp values and an appropriate distance function. This distance function can be described in terms of scaling the ordinary distance between real numbers. With this interpretation in mind, the task of designing a fuzzy system corresponds to determining suitable crisp values and appropriate scaling functions for the distance. When we want to generate a fuzzy model from data, the parameters have to be fitted to the data. This leads to an optimisation problem that is very similar to the optimisation task to be solved in objective function based clustering. We borrow ideas from the alternating optimisation schemes applied in fuzzy clustering in order to develop a new technique to determine our set of parameters from data, supporting the interpretability of the fuzzy system.     

The identification of binding constraints: A directional derivative heuristic approach

A heuristic procedure to identify binding constraints in linear programming (LP) problems is based upon an examination of the orientation of the constraining closed half spaces with respect to the orientation of the objective function. The constraints with the minimum difference will be classified as binding. An experiment to test the usefulness of this procedure in solving LP problems is also developed and discussed.     

A multi-item transportation problem with fuzzy tolerance

This paper presents the recently introduced modified subgradient method for optimization and its effectiveness in a fuzzy transportation model. Here a multi-item balanced transportation problem (MIBTP) is formulated where unit transportation costs are imprecise. Also available spaces and budgets at destinations are limited but imprecise. The objective is to find a shipment schedule for the items that minimizes the total cost subjected to imprecise warehouse and budget constraints at destinations. The proposed model is reduced to a multi-objective optimization problem using tolerances, then to a crisp single-objective one using fuzzy non-linear programming (FNLP) technique and Zimmermann's method. The above fuzzy MIBTP is also reduced to another form of deterministic one using modified sub-gradient method (MSM). These two crisp optimization problems are solved by Genetic Algorithm (GA). As an extension, fuzzy multi-item balanced solid transportation problems (STPs) with and without restrictions on some routes and items are formulated and reduced to deterministic ones following FNLP and Zimmermann's methods. These models are also solved by GA. Models are illustrated numerically, optimum results of fuzzy MIBTP from two deductions are compared. Results are also presented for different GA parameters.