Reference Membership Values Research Articles

Impact of Fuel Cell Power Plants on Multi‐objective Optimal Operation Management of Distribution Network

AbstractThis paper presents an interactive fuzzy satisfying method based on hybrid modified honey bee mating optimization and differential evolution (MHBMO‐DE) to solve the multi‐objective optimal operation management (MOOM) problem, which can be affected by fuel cell power plants (FCPPs). The objective functions are to minimize total electrical energy losses, total electrical energy cost, total pollutant emission produced by sources, and deviation of bus voltages. A new interactive fuzzy satisfying method is presented to solve the multi‐objective problem by assuming that the decision‐maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values until the satisfying solution for the DM can be obtained. The MOOM problem is modeled as a mixed integer nonlinear programming problem. Evolutionary methods are used to solve this problem because of their independence from type of the objective function and constraints. Recently researchers have presented a new evolutionary method called honey bee mating optimization (HBMO) algorithm. Original HBMO often converges to local optima, in order to overcome this shortcoming, we propose a new method that improves the mating process and also, combines the modified HBMO with DE algorithm. Numerical results for a distribution test system have been presented to illustrate the performance and applicability of the proposed method.

An efficient algorithm for multi-objective optimal operation management of distribution network considering fuel cell power plants

This paper presents an interactive fuzzy satisfying method based on Hybrid Modified Honey Bee Mating Optimization (HMHBMO). Its purpose is to solve the Multi-objective Optimal Operation Management (MOOM) problem which can be affected by Fuel cell power plants (FCPPs). Minimizing total electrical energy losses, total electrical energy cost, total pollutant emission produced by sources and deviation of bus voltages are the objective functions in this method. A new interactive fuzzy satisfying method is presented to solve the multi-objective problem by assuming that the decision-maker (DM) has fuzzy targets for each of the objective functions. Through the interaction with the DM, the fuzzy goals are quantified by eliciting the corresponding membership functions. Considering the current solution, the DM updates the reference membership values until the best solution can be obtain. The MOOM problem is modeled as a mixed integer nonlinear programming problem. Therefore, evolutionary methods can be used to solve this problem since they are independence of objective function’s type and constraints. Recently researchers have presented a new evolutionary method called Honey Bee Mating Optimizations (HBMO) algorithm. Original HBMO often converges to local optima and this is a disadvantage of this method. In order to avoid this shortcoming we propose a new method. This method improves the mating process and also combines the modified HBMO with a Chaotic Local Search (CLS). Numerical results on a distribution test system have been presented to illustrate the performance and applicability of the proposed method.

Optimal Multi-Objective Single-Tuned Harmonic Filter Planning

This paper presents an interactive fuzzy satisfying method for solving a general multi-objective single-tuned harmonic-filter planning problem by assuming that the decision-maker (DM) has imprecise or fuzzy goals for each of the objective functions. Through the interaction with DM, the fuzzy goals of the DM are quantified by eliciting corresponding membership functions. If the DM specifies a reference membership values, the mini-max problem is solved for generating a corresponding global noninferior solution for the DM's reference membership values. Then by considering the current values of the membership functions as well as the objectives, the DM acts on this solution by updating the reference membership values. The interactive procedure continues until the satisfying solution for the DM is obtained.

LINEAR COORDINATION METHOD FOR FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS WITH CONVEX POLYHEDRAL MEMBERSHIP FUNCTIONS

A fuzzy multi-objective decision-making with nonlinear membership functions is proposed in this paper by assuming that the decision maker has a fuzzy goal for each objective function. The fuzzy goals can be quantified by convex polyhedral membership functions, which are expressed by linguistic terms. The concept of the convex cone is used to formulate a normalized convex polyhedral penalty function, which can also be considered conversely as a convex polyhedral membership function. The most desirable value of membership functions are selected to be reference membership values of achievement of convex polyhedral membership functions that can be viewed as the extension of the idea of reference point method. The formulated model can be solved by existing linear programming solvers and can find the satisficing solution for the decision maker, which can be derived efficiently from among an M-Pareto optimal solution set together with the trade-off rates between the membership functions. The proposed model uses convex polyhedral membership functions to represent vague aspirations of the decision maker. It enriches the existing satisficing methods for fuzzy multi-objective linear programming in a more practical way with the effective method based on convex cone.

An interactive fuzzy satisfying method based on evolutionary programming technique for multiobjective short-term hydrothermal scheduling

Abstract This paper presents an interactive fuzzy satisfying method based on evolutionary programming technique for short-term multiobjective hydrothermal scheduling. The multiobjective problem is formulated considering two objectives: (i) cost and (ii) emission. Assuming that the decision maker (DM) has fuzzy goals for each of the objective functions, evolutionary programming technique based fuzzy satisfying method is applied for generating a corresponding optimal noninferior solution for the DM’s goals. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values until the satisfying solution for the DM can be obtained. A multi-reservoir cascaded hydroelectric system with a nonlinear relationship between water discharge rate, net head and power generation is considered. The water transport delay between connected reservoirs is taken into account. Thermal plants with nonsmooth fuel cost and emission level function are also taken into consideration. Results of the application of the proposed method are presented.

An interactive fuzzy satisficing method for multiobjective nonconvex programming problems with fuzzy numbers through coevolutionary genetic algorithms

In this paper, by considering the experts' fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective nonconvex nonlinear programming problems with fuzzy numbers are formulated and an interactive fuzzy satisficing method through coevolutionary genetic algorithms is presented. Using the alpha-level sets of fuzzy numbers, the corresponding nonfuzzy alpha-programming problem is introduced. After determining the fuzzy goals of the decision maker, if the decision maker specifies the degree alpha and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems for which the coevolutionary genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, the revised GENOCOP III is proposed by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented together with an illustrative numerical example.

An interactive fuzzy satisficing method for multiobjective nonconvex programming problems through floating-point genetic algorithms

In this paper, we focus on multiobjective nonconvex nonlinear programming problems and present an interactive fuzzy satisficing method through floating point genetic algorithms. After determining the fuzzy goals of the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the augmented minimax problems for which the floating point genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, we propose the revised GENOCOP III by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented together with an illustrative numerical example.

An interactive fuzzy satisficing method for multiobjective block angular linear programming problems with fuzzy parameters

In this paper, by considering the experts’ imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, large-scale multiobjective block-angular linear programming problems involving fuzzy parameters characterized by fuzzy numbers are formulated. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced. The fuzzy goals of the decision maker for the objective functions are quantified by eliciting the corresponding membership functions including nonlinear ones. Through the introduction of an extended Pareto optimality concept, if the decision maker specifies the degree α and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig–Wolfe decomposition method is applicable. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented along with an illustrative numerical example.

Economic emission load dispatch through an interactive fuzzy satisfying method

Abstract The economic emission load dispatch (EELD) problem treats economy, emission and security as competing objectives for optimal dispatch, which requires some form of conflict resolution to arrive at a solution. This paper presents an interactive fuzzy satisfying method for solving an EELD problem assuming that the decision maker (DM) has imprecise or fuzzy goals for each of the objective functions. The fuzzy goals are quantified by defining their corresponding membership functions and the DM is then asked to specify the reference (desirable) membership values. Numerical results for an example system have been presented to illustrate the performance and applicability of the proposed method.

An interactive fuzzy-norm satisfying method for multi-objective reactive power sources planning

An interactive fuzzy-norm (FN) satisfying method for multi-objective reactive power sources planning is presented, by considering that the decision-maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. After determining the membership functions to solve a candidate for the satisfying solution, which is also a noninferior solution, if the DM specifies the reference membership values, the FN approach is applied for generating a corresponding global noninferior solution for the DM's goals. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values. In this way the satisfying solution for the DM can be obtained. Results of the application of the proposed method are also presented.

An interactive fuzzy satisficing method for multiobjective nonconvex programming problems through floating point genetic algorithms

In this paper, we focus on multiobjective nonconvex nonlinear programming problems and present an interactive fuzzy satisficing method through floating point genetic algorithms. After determining the fuzzy goals of the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the augmented minimax problems for which the floating point genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, we propose the revised GENOCOP III by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented together with an illustrative numerical example.

An interactive fuzzy satisficing method for multiobjective optimal control problems in linear distributed-parameter systems

In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method.

An interactive fuzzy satisficing method for multiobjective 0–1 programming problems with fuzzy numbers through genetic algorithms with double strings

Abstract In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective 0–1 programming problems involving fuzzy numbers are formulated. Using the a-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced. The fuzzy goals of the decision maker (DM) for the objective functions are quantified by eliciting the corresponding linear membership functions. Through the introduction of an extended Pareto optimality concept, if the DM specifies the degree α and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems through genetic algorithms with double strings. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the DM efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.

An interactive fuzzy satisficing method for structured multiobjective linear fractional programs with fuzzy numbers

In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem formulation process, multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers are formulated. Using the a-level sets of fuzzy numbers, the corresponding nonfuzzy a-multiobjective linear fractional programming problem is introduced. The fuzzy goals of the decision maker for the objective functions are quantified by eliciting the corresponding membership functions including nonlinear ones. Through the introduction of extended Pareto optimality concepts, if the decision maker specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method and Ritter's partitioning procedure are applicable. Then a linear programming-based interactive fuzzy satisficing method with decomposition procedures for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

多目的整数計画問題に対する遺伝的アルゴリズムによる対話型ファジィ満足化手法

This paper deals with multiobjective integer programming problems by considering fuzzy goals of the decision maker for objective functions. After determining the fuzzy goals of the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the augmented minimax problem which becomes an integer programming problem. For solving the problem, decoding algorithms for 0-1 programming problems are revised and ringed double strings are also introduced. Then an interactive fuzzy satisficing method is presented together with an illustrative numerical example.

AN INTERACTIVE FUZZY SATISFICING METHOD FOR MULTIOBJECTIVE LINEAR FRACTIONAL PROGRAMS WITH BLOCK ANGULAR STRUCTURE

In this paper, we focus on multiobjective linear fractional programming problems with block angular structure. By considering the vague nature of human judgments, we assume that the decision maker may have a fuzzy goal for each of the objective functions. Having elicited the corresponding membership functions including nonlinear ones, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method and Ritter's partitioning procedure are applicable. Then a linear programming-based interactive fuzzy satisficing method with decomposition procedures for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

<特集>線形分布定数系における多目的最適制御問題に対する対話型ファジィ満足化手法(ファジィ意思決定)

Abstract In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method.

Fuzzy Programming for Large-Scale Multiobjective Linear Programming Problems with Fuzzy Parameters

In this paper, a large-scale multiobjective block-angular linear programming problem involving fuzzy parameters is formulated by considering the experts' vague understanding of the nature of the parameters in the problem-formulation process. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced and the fuzzy goals of the decision maker are quantified by eliciting the membership functions. Through the introduction of an extended Pareto optimality concept, if the decision maker specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method is applicable. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker from an extended Pareto optimal solution set is presented.

Interactive fuzzy satisfying method for optimal multi-objective VAr planning in power systems

The paper presents an interactive fuzzy satisfying method for solving a multi-objective VAr planning problem by assuming that the decision maker (DM) has imprecise or fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting corresponding membership functions. If the DM specifies the reference membership values, the minimax problem is solved for generating a corresponding global noninferior optimal solution for the DM's reference membership values. Then, by considering the current values of the membership functions as well as the objectives, the DM acts on this solution by updating the reference membership values. The interactive procedure continues until the satisfying solution for the DM is obtained. The minimax problem can be easily handled by the simulated annealing (SA) approach which can find a global optimal solution even for the solution space which is nonconvex and the objective functions which are nondifferentiable. Results of the application of the proposed method are presented.

Interactive fuzzy decision making for generalized multiobjective linear fractional programming problems with fuzzy parameters

In this paper, we focus on multiobjective linear fractional programming problems with fuzzy parameters and present a new interactive fuzzy decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method. The fuzzy parameters in the description of the objective functions and the constraints, which reflect the expert's ambiguous understanding of the nature of the parameters in the problem-formulation process, are characterized by fuzzy numbers. The concept of α-multiobjective linear fractional programming and M-α-Pareto optimality is introduced based on the α-level sets of the fuzzy numbers. Through the interaction with the DM, the fuzzy goals of the DM for each of the objective functions in α-multiobjective linear fractional programming are quantified by eliciting the corresponding membership functions. After determining the membership functions, in order to generate a candidate for the satisficing solution which is also M-α-Pareto optimal, if the DM specifies the degree α of the α-level sets and the reference membership values, the minimax problem is solved by combined use of the bisection method and the linear programming method, and the DM is supplied with the corresponding M-α-Pareto optimal solution together with the trade-off rates among the values of the membership functions and the degree α. By considering the current values of the membership functions and α as well as the trade-off rates, the DM acts on this solution by updating his/her reference membership values and/or the degree α. In this way, the satisficing solution for the DM can be derived efficiently from among an M-α-Pareto optimal solution set. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated.