Fuzzy Optimization Problem Research Articles

A successive approximation method for solving multi‐objective fuzzy optimization problems

An efficient method utilizing a “max‐pro” optimum scheme for solving the “max‐min” decision function in a fuzzy optimization environment. The proposed method significantly simplifies the “max‐min” optimum solving problem, especially in the case when the number of objectives and constraints is large. Presents illustrative examples. The technique may also have valuable applications in solving general optimization problems with a piecewise‐smoothed objective function.

Interval Methods and Fuzzy Optimization

In this paper, we describe interval-based methods for solving constrained fuzzy optimization problems. The class of fuzzy functions we consider for the optimization problems is the set of real-valued functions where one or more parameters/coefficients are fuzzy numbers. The focus of this research is to explore some relationships between fuzzy set theory and interval analysis as it relates to optimization problems.

Optimization in an intuitionistic fuzzy environment

A new concept of the optimization problem under uncertainty is proposed and treated in the paper. It is an extension of fuzzy optimization in which the degrees of rejection of objective(s) and of constraints are considered together with the degrees of satisfaction. This approach is an application of the intuitionistic fuzzy (IF) set concept to optimization problems. An approach to solving such problems is proposed and illustrated with a simple numerical example. It converts the introduced intuitionistic fuzzy optimization (IFO) problem into the crisp (non-fuzzy) one. The advantage of the IFO problems is twofold: they give the richest apparatus for formulation of optimization problems and, on the other hand, the solution of IFO problems can satisfy the objective(s) with bigger degree than the analogous fuzzy optimization problem and the crisp one.

Multiobjective fuzzy genetic algorithm optimisation approach to nonlinear control system design

Owing to the large number of free control parameters for modern nonlinear robust controllers, it is almost impossible to heuristically tune these parameters. The multiobjective fuzzy genetic algorithm optimisation is shown to provide an effective, efficient and intuitive framework for selecting these parameters. The control structure and specifications are assumed to be given. Using the concept of fuzzy sets and convex fuzzy decision making, a multiobjective fuzzy optimisation problem is formulated and solved using a genetic algorithm. The relative importance of the objective functions is assessed by using a new membership weighting strategy. The technique is applied to the selection of free control parameters for an input-output linearising controller with sliding mode control, in a remotely-operated underwater vehicle depth control system.

Paramentric orders on fuzzy numbers and their roles in fuzzy optimization problems

Two types of parametric order relations on the class of symmetric fuzzy numbers generated by shape functions are defined. The first one is same as the one defined by the present author in [3]. The notion of a “mutually nondominant” set of fuzzy numbers is introduced. A minimal solution means a solution nondominated with respect to minimizing under the fuzzy max order. A necessary and sufficient condition for a set of mutually non-dominant minimal solutions to be exhaustively detected by the order criterion of the first type is given. A necessary and sufficient condition for the same purpose as above is given for the second type one. As an application of the parametric orders, a numerical example of fuzzy shortest route problem is illustrated.

Generalized hybrid method for fuzzy multiobjective optimization of engineering systems

A generalized hybrid approach is presented for the multiobjective optimization of engineering systems in the presence of objectives and constraints that are partly fuzzy and partly crisp. The methodology is based on both fuzzy-set and Dempster-Shafer theories to capture the features of incomplete, imprecise, uncertain, or vague information that is often present in real-world engineering systems. The original partly fuzzy multiobjective optimization problem is first defuzzified into a crisp generalized multiobjective optimization problem using fuzzy-set theory. The resulting multiobjective problem is then transformed into an equivalent single-objective optimization problem using a modified Dempster-Shafer theory. The computational details of the approach are illustrated with a structural design example.

Scheduling as a fuzzy multiple criteria optimization problem

Real-world scheduling is decision making under vague constraints of different importance, often using uncertain data, where compromises between antagonistic criteria are allowed. The author explains in theory and by detailed examples a new combination of fuzzy set based constraints and iterative improvement repair based heuristics that help to model these scheduling problems. The mathematics needed for a method of eliciting the criteria's importances from human experts are simplified. The author introduces a new consistency test for configuration changes. This test also helps to evaluate the sensitivity to configuration changes. The implementation of these concepts in the fuzzy logic inference processor library FLIP++, in the fuzzy constraint library ConFLIP++, in the dynamic constraint generation library DynaFLIP++, and in the heuristic repair library Déjà Vu is described. All these libraries are implemented in a layered framework enhanced by the common user interface InterFLIP++. The benchmark application to compare the fuzzy constraint iterative improvement repair heuristic with constructive method based on classic constraints is a scheduling system for a continuous caster unit in a steel plant.

PROBO: an interactive system in fuzzy linear programming

This paper presents the analysis and design of an interactive decision support system for fuzzy optimization problems, which allows intelligent decisions according to its actuation preferences, depending on the associated model. This interactive system provides adaptation and training features by considering all the possibilities of a specific domain of fuzzy problem. The system is analyzed and their modules are shown.

A method to solve fuzzy reliability optimization problem

In this paper it is presented a method to solve the fuzzy reliability optimization problem for systems with unloaded reserve. This method can be used for systems described by possibility measures. It is considered the problem for different systems including systems with switching devices, computer systems with autonomous storage batteries.

遺伝的アルゴリズムによるファジィ信頼性の最適設計問題の一解法(ファジィと遺伝的アルゴリズム)

遺伝的アルゴリズムによるファジィ信頼性の最適設計問題の一解法(ファジィと遺伝的アルゴリズム)

MIXED-DISCRETE FUZZY PROGRAMMING FOR NONLINEAR ENGINEERING OPTIMIZATION

Abstract Engineering optimization often contains a mix of continuous, integer and discrete types of design variables. The design domain and constraints frequently are fuzzy and cannot be defined precisely. This paper proposes an algorithm of mathematical programming in which the A-formulation of fuzzy optimization combines the modified branch-and-bound with max-partial derivative branching techniques for solving mixed discrete fuzzy optimization problems. The construction of a membership function of a design goal is extremely important in order to obtain the true optimum. The paper proposes a strategy to construct and select the preferred objective membership function. Optimal designs of a reinforced concrete beam and a pressure vessel illustrate this strategy. The numerical results and the feasibility of the proposed methodology are presented and discussed.

On Multi-Objective Fuzzy Optimization of Ship Structures

In order to solve the multi-objective fuzzy optimization problems of ship structures, two approaches, known as the maximum level method and the linear weighted sum method, based on the different forms of fuzzy decision-making are presented. In these methods, the membership functions are constructed for the subsets of the fuzzy goals subject to the fuzzy constraints, and then the multi-objective fuzzy optimization problem is transformed into the single-objective ordinary optimization problem, which can be solved by using nonlinear programming techniques. The proposed approaches are illustrated by two numerical examples in the application of ship structural design.

Multi-objective fuzzy optimization of structures based on generalized fuzzy decision-making

In order to find a satisfactory solution for the multi-objective fuzzy optimization problem of structures, the membership functions are constructed for the subsets of the fuzzy objectives subject to the fuzzy constraints, and three approaches are presented by using the different types of generalized fuzzy decision-making. Two illustrative numerical examples given show that in creating the user-oriented design environment in computer-aided design systems the application of generalized fuzzy decision-making to multi-objective fuzzy optimization of structures looks promising.

Fuzzy genetic algorithm and applications

In this paper we introduce fuzzy genetic algorithms to (approximately) solve fuzzy optimization problems. We argue that this technique can produce good approximate solutions by applying it to solve a fuzzy optimization problem. Other applications of fuzzy genetic algorithms to fuzzy optimization, the fuzzy maximum flow problem, fuzzy regression, and tuning a fuzzy controller are also presented.

A fuzzy-based optimal reactive power control

A mathematical formulation of the optimal reactive power control problem using fuzzy set theory is presented. The objectives are to minimize real power losses and improve the voltage profile of a given system. Transmission losses are expressed in terms of voltage increments by relating the control variables to the voltage increments in a modified Jacobian matrix. This formulation does not require Jacobian matrix inversion, and hence it will save computation time and memory space. The objective function and the constraints are modeled by fuzzy sets. Linear membership functions of the fuzzy sets are defined and the fuzzy linear optimization problem is formulated. The solution space is defined as the intersection of the fuzzy sets describing the constraints and the objective functions. Each solution is characterized by a parameter that determines the degree of satisfaction with the solution. The optimal solution is the one with the maximum value for the satisfaction parameter. Results for test systems reveal the advantages of the approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Concurrent engineering: Robust design in fuzzy environment

The question of robust designis formulated and solved as fuzzy optimization problem. The process equations are equality constraints. The nonequality constraints are the criteria resulting from the “house of quality” method. A numerical example is presented to illustrate the basic idea of the robust design with fuzzy parameters.

Optimal control of biotechnological processes described by fuzzy sets

Abstract Fuzzy set theory is applied to extend the optimal control problem for complex objects such as biotechnological processes. It allows inclusion of all possible and admissible process states in the problem formulation. A new approach for model representation with convenient fuzzy sets taking into account expert experience is proposed. Bellman-Zadeh's approach is applied to transform a fuzzy optimal control problem ot a deterministic one which is solved numerically. Optimal control of a real-life fermentation process is determined and a better solution is reached due to more realistic and flexible problem formulation.

ROBUST DESIGN OF ACTIVELY CONTROLLED STRUCTURES USING COOPERATIVE FUZZY GAMES

Abstract The combined structural and control optimization problem for flexible space structures is formulated as a multiple objective optimization (MOO) problem. An improvement in robustness of active controlled structures through structural modifications is also addressed. The structural weight, controlled system energy, and robustness indices are considered as objective functions of the integrated structure/control design problem with cross-sectional areas of members treated as design variables. To model vague and imprecise information in the problem formulation, the tools of fuzzy set theory are employed. A new methodology for solving the resulting MOO problem, referred to herein as a cooperative fuzzy game theoretic approach is presented. It is shown that existing techniques for solving crisp and fuzzy optimization problems are special cases of the fuzzy game theoretic formulation. The computational procedure is demonstrated via an application to a twelve member ACOSS-FOUR space structure. The qualita...

A coupled knowledge based system using fuzzy optimization for advisory control

AbstractA knowledge based system is described that is designed to generate on‐line advice for operators regarding the proper distribution of hydrogen resources in a refinery. The system uses a coupled architecture incorporating numerical computing in a knowledge based system environment. This arrangement allows for powerful and flexible problem solving. One portion of the coupled system formulates an optimization problem that is subsequently solved by an external routine. This application is particularly concerned with uncertainty that is present in some of the constraints. To deal with this uncertainty, a fuzzy approach to the optimization is taken. A method is presented that solves the fuzzy optimization problem using standard mathematical programming techniques. The results of the fuzzy optimization allow the crisp solution to be expanded into a neighborhood of solutions that is considered acceptable. Although this work examines a specific problem, the concepts presented are general.

Fuzzy optimal control

The problem of fuzzy optimal control of nonlinear systems is formulated and solved on the basis of fuzzy mathematical programming. The fuzzy optimal control problem is extended to the case of multicriteria optimal control. A particular case of fuzzy optimal control with fuzzy objective function and crisp transversality conditions is also considered.