Theory of Multiobjective Optimization

Mechanical stability of the in vivo lumbar spine: implications for injury and chronic low back pain

This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first-order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.

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Water quality modeling: A review of the analysis of uncertainty

TOPSIS for MODM

: One use of spectral analysis of time series is to determine if two different time series are realizations from the same process This thesis develops the theory behind Krishnaiah and Schuurmann's theoretical work reported in their report Approximations to the Distributions of the Traces of Complex Multivariate Beta and F Matrices We take the trace of a test statistic calculated from the spectral density matrices of the time series and test it The thesis applies the theory to two small sample simulations (Author)

Spectral Analysis of Time Series.

This book focuses the methodology of decision analysis and support related to the principle of reference point optimization (developed by the editors of this volume and called also variously: aspiration-led decision support, quasi-satisfying framework of rationality, DIDAS methodology etc.). 

The selection principle applied for this volume was to concentrate on advances of theory and methodology, related to the focusing theme, to supplement them by experiences and methodological advances gained through wide applications and tests in one particular application area - the programming of development of industrial structures in chemical industry, and finally to give a very short description of various software products developed in the contracted study agreement.

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Aspiration Based Decision Support Systems

1: Theory and Methodology.- Decision Support Systems Using Reference Point Optimization.- Decision Support Systems of DIDAS Family (Dynamic Interactive Decision Analysis & Support).- Modern Techniques for Linear Dynamic and Stochastic Programs.- A Sensitivity Method for Solving Multistage Stochastic Linear Programming Problems.- Regularized Decomposition and Augmented Lagrangian Decomposition for Angular Linear Programming Problems.- Dynamic Aspects of Multiobjective Trajectory Optimization in Decision Support Systems.- Mathematical Programming Package HYBRID.- Safety Principle in Multiobjective Decision Support in the Decision Space Defined by Availability of Resources.- Nonlinear Optimization Techniques in Decision Support Systems.- Nonlinear Computer Models - Issues of Generation and Differentiation.- Issues of Effectiveness Arising in the Design of a System of Nondifferentiable Optimization Algorithms.- A Methodological Guide to the Decision Support System DISCRET for Discrete Alternatives Problems.- A Generalized Reference Point Approach to Multiobjective Transshipment Problem with Facility Location.- Solving Multiobjective Distribution-Location Problems with the DINAS System.- Towards Interactive Solutions in a Bargaining Problem.- 2: Applications and Experiences.- MIDA: Experience in Theory, Software and Application of DSS in the Chemical Industry.- Basic Model of an Industrial Structure.- Multiobjective Evaluation of Industrial Structures.- Hierarchical Multiobjective Approach to a Programming Problem.- Spatial Allocation and Investment Scheduling in the Development Programming.- Architecture and Functionality of MIDA.- 3. Short Software Descriptions.- IAC-DIDAS-L - A Dynamic Interactive Decision Analysis and Support System for Multicriteria Analysis of Linear and Dynamic Linear Models on Professional Microcomputers.- HYBRID - A Mathematical Programming Package.- IAC-DIDAS-N - A Dynamic Interactive Decision Analysis and Support System for Multicriteria Analysis of Nonlinear Models.- DISCRET - An Interactive Decision Support System for Discrete Alternatives Multicriteria Problems.- DINAS - Dynamic Interactive Network Analysis System.- MCBARG - A System Supporting Multicriteria Bargaining.- POSTAN 3 and PLP - Extension of MINOS for Postoptimal Analysis.

Aspiration Based Decision Support Systems: Theory, Software and Applications

The purpose of this paper is to report on the progress made in the System and Decision Sciences (SDS) research group at IIASA on the development of the decision support system DIDASS (Dynamic Interactive Decision Analysis and Support System). This system is based on methodology derived from the paradigm of satisficing decision making and the methodology of linear and nonlinear programming. The mathematical background to this approach (based on aspiration formation and the concept of scalarizing functions) is outlined in Section 2. Methods of implementation and computational aspects are discussed in Section 3. The fourth section summarizes three applications of DIDASS, and the paper ends with some conclusions.

DIDASS — Theory, Implementation and Experiences

This paper presents the methodological framework for the Group Decision Support System named SCDAS. The system supports a group of decision makers working together on selecting the best alternative from a given, finite set of alternatives. The framework utilizes aspiration-led and quasisatisficing paradigms for eliciting user's preference, and the achievement function for ranking alternatives. Possible implementation of the system within the framework of a computerized teleconferencing system is discussed. Also, previous experience in applying the SCDAS system is presented.

SCDAS — Decision support system for group decision making: Decision theoretic framework

This paper studies the reference point approach of Wierzbicki for multiobjective optimization. The method does not necessarily aim at finding an optimum under any utility function but rather it is used to generate a sequence of efficient solutions which are interesting from the decision maker's point of view. The user can interfere via suggestions of reference values for the vector of objectives. The optimization system is used to find (in a certain sense) the nearest Par-to solution to each reference objective. 

The approach is expanded for adaptation of information which may accumulate on the decision maker's preferences in the course of the interactive process. In this case any Pareto point is excluded from consideration if it is not optimal under any linear utility function consistent with the information obtained. Thus, the pareto points being generated are the "nearest" ones among the rest of the pareto points. 

Wierzbicki's approach is implemented on an interactive mathematical programming system called SESAME and developed by Orchard-Hays. It is now capable of handling large practical multicriteria linear programs with up to 99 objectives and 1000 to 2000 constraints. The method is tested using a forest sector model which is a moderate sized dynamic linear program with twenty criteria (two for each of the ten time periods). The approach is generally found very satisfactory. This is partly due to the simplicity of the basic idea which makes it easy to implement and use.

A. Lewandowski

Papers

Aspiration Based Decision Support Systems

Aspiration Based Decision Support Systems: Theory, Software and Applications

DIDASS — Theory, Implementation and Experiences

SCDAS — Decision support system for group decision making: Decision theoretic framework

An Implementation of the Reference Point Approach for Multiobjective Optimization