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 paper presents a review of methodological principles, mathematical theory, variants of implementation and various applications of decision support systems of DIDAS family, developed by the authors and many other cooperating researchers during the years 1980–1986 in cooperation with the Systems and Decision Sciences Program of the International Institute for Applied Systems Analysis. The purpose of such systems is to support generation and evaluation of alternative decisions in interaction with a decision maker that might change his preferences due to learning, while examining a substantive model of a decision situation prepared by experts and analysts. The systems of DIDAS family are based on the principle of reference point optimization and the quasisatisficing framework of rational choice.

Decision Support Systems of DIDAS Family

The purpose of this paper is to describe recent developments in DIDASS methodology and implementation. The DIDASS system, which is based on the paradigm of satisficing decision making and the theory of multiple criteria optimization, has been the subject of numerous papers and reports. The principles of the method and selected applications were presented by Grauer et al. (1984).

A Trajectory-Oriented Extension of DIDASS and Its Applications

The Interactive Decision Analysis Project is concerned, among other things, with the development of software for solving multiple-criteria decision problems. 

In this paper the authors describe some recent modifications to an interactive decision-support system previously developed at IIASA: the new package is more user-friendly and more efficient but less portable. All the new options are defined in full in a technical appendix.

MM-Minos - An Integrated Interactive Decision Support System

Industrial development can be seen as the process of changing the production structure by means of investment over the course of time. To control this development to the benefit of society while maintaining the profitability of the industry, decision makers must learn how socioeconomic changes and market conditions affect the static and dynamic properties of the production structure. This paper reports on the progress of collaborative research into the design of tools which could help decision makers to control development in the chemical industry. 

The basic approach is to formulate a model of the equilibrium state of the industry or, in the case considered here, of a particular subsector of the industry. The development process is initially described by a static multiobjective optimization problem, from which a dynamic multiobjective optimization problem is then derived. An example illustrating the use of this method for the pesticide-producing sector is given. 

The optimization problem and method for controlling industrial development put forward in this paper were worked out as part of the research program on Growth Strategy Optimization Systems (GSOS), sponsored by the Ministry of the Chemical Industry in Poland. This program is actually carried out at the Institute for Control and Systems Engineering (ICSE), part of the Academy of Mining and Metallurgy (AMM) in Cracow. 

The multiobjective optimization method for generating efficient alternatives and the related software were developed by the System and Decision Sciences Area at IIASA. 

This collaborative research was carried out within the framework of the agreement on scientific cooperation cosigned by IIASA and the AMM in June 1980.

A. Lewandowski

Papers

Decision Support Systems of DIDAS Family

A Trajectory-Oriented Extension of DIDASS and Its Applications

MM-Minos - An Integrated Interactive Decision Support System

Generating Efficient Alternatives for Development in the Chemical Industry

A Program Package for Linear Multiple Criteria Reference Point Optimization - Short User Manual