An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Programming Problems with Fuzzy Parameters

This paper presents an interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. The fuzzy parameters in the objective functions and the constraints are characterized by the fuzzy numbers. On the basis of the alpha-level sets of the fuzzy numbers, the concept of alpha-multiobjective nonlinear programming and alpha-Pareto optimality is introduced. Through the interaction with the decision maker (DM), the fuzzy goals of the DM for each of the objective functions in alpha-multiobjective nonlinear 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 alpha-Pareto optimal, if the DM specifies the degree alpha of the alpha-level sets and the reference membership values, the augmented minimax problem is solved and the DM is supplied with the corresponding alpha-Pareto optimal solution together with the trade-off rates among the values of the membership functions and the degree alpha. Then by considering the current values of the membership functions and as well as the trade-off rates, the DM responds by updating his reference membership values and/or the degree alpha. In this way the satisficing solution for the DM can be derived efficiently from among an alpha-Pareto optimal solution set. Based on the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the corresponding computer outputs

A Computer Program for Multiobjective Decision Making by the Interactive Sequential Proxy Optimization Technique

A new interactive multiobjective decision making technique, which is called the sequential proxy optimization technique (SPOT), has been proposed by the author. Using this technique, the preferred solution for the decision maker can be derived efficiently from among a Pareto optimal solution set by assessing his marginal rates of substitution and maximizing the local proxy preference functions sequentially. In this paper, based on the algorithm of SPOT, a computer program for multiobjective decision making with interactive procedures is presented and called ISPOT. The program is especially designed to facilitate the interactive processes for computer-aided decision making. After a brief description of the theoretical framework of SPOT, the computer program ISPOT is presented. The commands in this program and major prompt messages are also explained. An illustrative numerical example for the interactive processes is demonstrated and numerous insights are obtained

Psychological Stability of Solutions in the Multiple Criteria Decision Problems

In interactive programming, a choice behavior of the decision maker may differ depending on a proximity of current solution to satisfactory values of the objectives. An interactive approach proposed in this paper allows the decision maker to use different search principles depending on his/her perception of the achieved values of the objectives and trade-offs. While an analysis of values of the objectives may guide the initial search for a final solution, it can be replaced by trade-off evaluations at some later stages of interactive decision making. Such an approach allows the decision maker to change search principles, and to identify a psychologically stable solution of the multiple criteria decision problem

Decision-maker Trade-offs In Multiple Response Surface Optimization

The focus of this dissertation is on improving decision-maker trade-offs and the development of a new constrained methodology for multiple response surface optimization. There are three key components of the research: development of the necessary conditions and assumptions associated with constrained multiple response surface optimization methodologies; development of a new constrained multiple response surface methodology; and demonstration of the new method. The necessary conditions for and assumptions associated with constrained multiple response surface optimization methods were identified and found to be less restrictive than requirements previously described in the literature. The conditions and assumptions required for a constrained method to find the most preferred non-dominated solution are to generate non-dominated solutions and to generate solutions consistent with decision-maker preferences among the response objectives. Additionally, if a Lagrangian constrained method is used, the preservation of convexity is required in order to be able to generate all non-dominated solutions. The conditions required for constrained methods are significantly fewer than those required for combined methods. Most of the existing constrained methodologies do not incorporate any provision for a decision-maker to explicitly determine the relative importance of the multiple objectives. Research into the larger area of multi-criteria decision-making identified the interactive surrogate worth trade-off algorithm as a potential methodology that would provide that capability in multiple response surface optimization problems. The ISWT algorithm uses an ε-constraint formulation to guarantee a non-dominated solution, and then interacts with the decision-maker after each iteration to determine the preference of the decision-maker in trading-off the value of the primary response for an increase in value of a secondary response. The current research modified the ISWT algorithm to develop a new constrained multiple response surface methodology that explicitly accounts for decision-maker preferences. The new Modified ISWT (MISWT) method maintains the essence of the original method while taking advantage of the specific properties of multiple response surface problems to simplify the application of the method. The MISWT is an accessible computer-based implementation of the ISWT. Five test problems from the multiple response surface optimization literature were used to demonstrate the new methodology. It was shown that this methodology can handle a variety of types and numbers of responses and independent variables. Furthermore, it was demonstrated that the methodology can be successful using a priori information from the decision-maker about bounds or targets or can use the extreme values obtained from the region of operability. In all cases, the methodology explicitly considered decision-maker preferences and provided non-dominated solutions. The contribution of this method is the removal of implicit assumptions and includes the decision-maker in explicit trade-offs among multiple objectives or responses

Understanding Trade-offs in Stellarator Design with Multi-objective Optimization

In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial constraints may simplify the design and worsen some aspects of transport. Understanding trade-offs in stellarator designs is critical in designing high performance devices that satisfy the multitude of physical, engineering, and financial criteria. In this study we show how multi-objective optimization (MOO) can be used to investigate trade-offs and develop insight into the role of design parameters. We discuss the basics of MOO, as well as practical solution methods for solving MOO problems. We apply these methods to bring insight into the selection of two common design parameters: the aspect ratio of an ideal magnetohydrodynamic equilibrium, and the total length of the electromagnetic coils

An Interactive Fuzzy Satisficing Method Using Augmented Minimax Problems and Its Application to Environmental Systems

A new interactive fuzzy satisficing method for multiobjective nonlinear programming is presented, by considering that the decisionmaker (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 corresponding membership functions. In order to generate a candidate for the satisficing solution (Pareto optimal) after determining the membership functions, if the DM specifies his/her reference membership values, the augmented minimax problem is solved. The DM is thus supplied with the corresponding Pareto optimal solution together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM acts on this solution by updating his/her reference membership values. In this way the satisficing solution for the DM can be derived efficiently from among a Pareto optimal solution set by updating his/her reference membership values. On the basis of the proposed method, a time-sharing computer program is written to implement man-machine interactive procedures. An application to the industrial pollution control problem in Osaka City in Japan is demonstrated together with the computer output

Interactive Multiobjective Decision Making by the Sequential Proxy Optimization Technique: SPOT

In this paper, we propose a new interactive multiobjective decision making technique, which we call the Sequential Proxy Optimization Technique (SPOT), in order to overcome the drawbacks of the conventional multiobjective decision making methods. Our method combines the desirable features of both the Surrogate Worth Trade-off (SWT) method and the Multiattribute Utility Function (MUF) method. We can interactively derive the preferred solution of the decision maker efficiently by assessing his marginal rate of substitution and maximizing sequentially the local proxy preference function. A numerical example illustrates the feasibility and efficiency of the proposed method

Design space exploration of RF-circuit blocks

ii iii Acknowledgments This thesis was written in the framework of an internship at NXP Semiconductors. It describes the results of a six months master project. I was supervised by Prof. Dr. W.H.A. Schilders of NXP Semiconductors and the Technical University Eindhoven and furthermore, by Dr. ir. J. A. Croon of NXP Semiconductors. Herewith, I want to express my deep gratitude to Prof. Schilders, who has guided me during the project and for proofreading of the thesis. Furthermore, I want to thank Dr. Croon sincerely for the helpful discussions, for the detailed corrections of the thesis and furthermore for the interesting introduction to semiconductor device modeling. Additionally, I want to thank Univ.-Prof. Dipl.-Ing. Dr. H. Gfrerer of the Johannes Kepler University Linz for reviewing this work and for his useful suggestions during the project. iv vContent

Multiobjective decision making in water resources system

Call number: LD2668 .T4 1979 C525Master of Scienc