Vladimir A. Bushenkov

Multicriteria DSS for River Water–Quality Planning

A decision support system (DSS) devoted to water–quality planning is described. The DSS is based on a graphic multiple–criteria technique called generalized reachable sets (GRS) method, which provides experts and decision makers with objective tradeoff curves among cost and pollution criteria. The information improves their understanding of the problem and helps to identify wastewater treatment strategies that provide reasonable balance between cost and pollution. These strategies are starting points for further negotiation between governmental agencies, private and state–owned enterprises, and regional and local authorities involved in wastewater treatment. The DSS is implemented on personal computers.

Interactive Decision Maps, with an Example Illustrating Ocean Waste Management Decisions

Interactive Decision Maps are introduced and illustrated with an ocean waste disposal example, requiring difficult pollution-cost tradeoffs. Interactive Decision Maps are a tool for quickly displaying various decision maps for three or more decision-relevant criteria. They are based on the Generalized Reachable Sets (GRS) approach developed in Russia. Animation of decision maps is also possible. Integration of Interactive Decision Maps with Pareto Race, a free search Multiple Objective Linear Programming procedure, is proposed.

A new approach to the regulator design problem

A new method for the regulator design problem is introduced. The method is based on the weak asymptotic stability theory for differential inclusions and yields some new algorithmic techniques.

Methods and algorithms for analyzing linear systems, by constructing generalized sets of attainability☆

Abstract A NEW approach to the analysis of controlled linear system is outlined, based on the construction in explicit form of all values, admissible from the point of view of the mathematical model, of the vector of indices (the generalized set of attainability). It is shown that this approach can also be used for the exact aggregation of linear models. The main attention is focussed on methods and algorithms for constructing and studying the generalized sets of attainability; the algorithms are realized as a dialog packet of POTENTIAL applied programs.

Adsorption integral equation via complex approximation with constraints: The Langmuir kernel

The relationship between the measured adsorption isotherm and unknown energy distribution function is described by so‐called adsorption integral equation, a linear Fredholm integral equation of the first kind. We consider the case of the Langmuir kernel when the equation can be reduced to the Stieltjes integral equation. A new method for solving the Stieltjes equation is developed. The method is based on the ideas of complex approximation with constraints. The numerical algorithms constructed on the base of this method allow reduction of the problem under consideration to linear or linear‐quadratic programming problems. The method is compared with the usual regularization methods. The obtained results can be useful for the evaluation of the experimental adsorption energy distribution from experimental data.

Numerical Approach to a Problem of Hydroelectric Resources Management

In this paper we consider a simplified model for a system of hydro-electric power stations with reversible turbines. The objective of our work is to obtain the optimal profit of power production satisfying restrictions on the water level in the reservoirs. Two different numerical approaches are applied and compared. These approaches center on global optimization techniques (Chen-Burer algorithm) and on Projection Estimation Refinement method (PER method) used to reduce the dimension of the problem.

Introduction to Interactive Decision Maps

In this chapter the Interactive Decision Maps (IDM) technique is introduced and its simplest application in the framework of the goal approach is described. First the screening phase of the decision making process is considered and the role of visualization in it is outlined. Then, the Pareto frontier, Edgeworth-Pareto hull, decision maps and related notions of MCDM theory are introduced using a simple regional environmental model.

Real-Life Applications

In this chapter several real-life applications of the FGM/IDM technique are considered. First, the concept of a real-life application of a decision support technique is discussed. The discussion is illustrated with the application of the FGM at the State Planning Agency of the former Soviet Union in the first part of the 1980s. Sections 2 and 3 are devoted to two decision support systems that are used by water engineers for water quality planning in river basins of Russia. Screening of water quality plans is based on application of the FGM/IDM technique. The decision support systems (DSS) helps engineers to develop water quality improvement strategies that can be used as proposals in the process of final selection of water quality improvement plans.

WATER RESOURCE CONFLICT RESOLUTION BASED ON INTERACTIVE TRADEOFFS DISPLAY

Rehabilitation of degraded water resource systems, especially large scale systems such as Danube, Mississippi or the Volga River, inevitably involve conflicts over who pays, who benefits, and how much. This paper reviews the application of computer-aided approaches to water resources conflict resolution based on the generation and interactive display of the efficient tradeoff curves among conflicting performance criteria associated with various possible decisions. Computing of efficient tradeoffs is based on a mathematical model describing the system being managed. The model is supposed to be mutually acceptable to all stakeholders. Negotiators can interactively explore the full implications of solutions that represent efficient tradeoffs among identified performance criteria. In this way they can become more informed about compromises that can be made among conflicting criteria. This approach is applied to the real-time allocation of water to agricultural and environmental users whose demand for water usually exceeds the supply. Application of these procedures using computer networks (e.g., Internet or intranets) is discussed.

Perturbations of Solution Sets of Linear Systems

This chapter is devoted to the analysis of stability and perturbations of the feasible criterion set (FCS). This problem is extremely important since the data are usually disturbed to a certain extent in real-life applications. It is required that the resulting perturbations of an FCS are not too substantial. In other words, an FCS must depend on the data disturbances in a continuous way. This chapter deals with the estimation of such perturbations in the linear case. The problem is reduced to estimating perturbations of the feasible decision set given by a system of linear inequalities and equalities. To be precise, the distance between two sets, the original set and the perturbed set is estimated.