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Approximation and Visualization of Interactive Decision Maps Short course of lectures. Alexander V. Lotov Dorodnicyn Computing Center of Russian Academy of Sciences and Lomonosov Moscow State University.

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### Approximation and Visualization of Interactive Decision MapsShort course of lectures

Alexander V. Lotov

Dorodnicyn Computing Center of Russian Academy of Sciences and

Lomonosov Moscow State University

Lecture 8. Reasonable Goals Method for supporting the finite multi-attribute choice(database screening)

Plan of the lecture

1. The problem of database screening

2. A simple graphic description of the method

3. Software demonstration (comparison of RGM and FGNL)

4. Screening procedure

5. Several applications of the RGM/IDM technique

The problem of database screeningA database of alternatives in the form of a decision matrix is considered, i.e., table of N decision alternatives (rows) given by a finite number of attributes (columns), a part of which is used as the criteria in database screening: one or several preferable rows must be selected from the database.

The criteria, which used for selecting a small number of alternatives, are assumed to be real values. Thus, an alternative is associated with a criterion point. The method is based on visualization of the Pareto frontier of the “cloud” of criterion points.

The decision maker has to identify the goal on the Pareto frontier of the “cloud”. Such information of the DM’s preferences helps to select a small number of «good» alternatives. This study can be considered as a special form of data mining.

The alternatives can be found in multiple large lists in Web describing the selection options: real estate on sale, second-hand cars, hotels, universities, etc.

On the other hand, alternative points can be results of scientific experiments or collecting research data.

Lists of financial projects can be developed described by such attributes as discounted investment, discounted income, term of complete investment return, reliability, etc.;

Alternative variants of portfolio or of assets allocation can exist described by such attributes as dividend, income, variability, etc.;

Alternative variants of business location given in a Geographical Information System can be found;

Large by finite number of Pareto-optimal strategies for solving of environmental or technical problems can be developed by using Feasible Goals technique, etc.

For illustrative purposes, let m=2 (criterion points are displayed in the plane). Non-dominated points are given by crosses.

Pareto frontier is analyzed by user and a preferred combination of criterion values (reasonable goal) is identified

The alternatives that are close to the goal are selected combination of criterion values (reasonable goal) is identified

General combination of criterion values (reasonable goal) is identified case (m from 3 to 8)

Visualization of the Pareto frontier

is based on approximation of the CEPH and application of the Interactive Decision Mapstechniquefor the interactive analysisof the frontiers of the slices.

Software demonstration combination of criterion values (reasonable goal) is identified

RGM/IDM-based software Visual Market – 2

Example of the screening procedure combination of criterion values (reasonable goal) is identified(maximization case)

Several applications of the IDM/RGM technique combination of criterion values (reasonable goal) is identified

S combination of criterion values (reasonable goal) is identifiedelecting a location for rural health practice in Idaho

Many rural areas in the USA, compete for medical doctor, thus creating choice opportunities for those interested in practicing rural medicine. Yet, these efforts coupled with various US federal programs have had mixed results in attracting and retaining primary health care providers in rural localities. One possible cause for this is the lack of effective information tools that would aid the prospective medical doctors in screening practice locations options and learning about tradeoffs involved.

The approach based on the RGM/IDM technique allows the prospective doctors to select preferable locations based on their closeness to the goal specified by them without the difficulty of specifying criterion weights. Along with the RGM/IDM technique, the DSS applies the geographic data query and visualization module implemented in ArcViewTM 3.0.

Database of alternatives and the map of Idaho combination of criterion values (reasonable goal) is identified

Description of the database combination of criterion values (reasonable goal) is identified

Data representing health-care, social, economic, and environmental information were aggregated by 47 Primary Care Service Area (PCSA) encompassing the entire state of Idaho. The attribute database describing the PCSA provided information for evaluation criteria. The criteria were grouped into professional and personal.

Professional criteria included:

• need for physicians denoted by DOCS, this is a derived index measure: the higher the DOCS value the higher the need. DOCS can also assume negative values representing low demand for physicians or lack of thereof,

• population in 1990 (POP90),

• percent of population receiving Medicare and Medicaid (MEDICARE),

• fertility rate (FERTILITY),

• loan repayment program (LOAN_REPA),

• number of hours per week on call (ON_CALL), etc.

Personal criteria included:

• percentage of unemployed population (UNEMPLOYED),

• percentage of population below poverty level (POVERTY),

• percentage of population with college degree (POP_DEGREE), etc.

DSS application combination of criterion values (reasonable goal) is identified

The modules supplement each other in providing decision support functions. The prospective physician can learn quickly about the location of places offering practice opportunities, their physical and socio-demographic characteristics, amenities offered by them, and relate this information to the surrounding physical environment by viewing and querying reference maps in ArcView. The information gained from spatial data query and visualization becomes useful in selecting a reasonable goal for the health practice location.

The goal selection, which is performed by the user, results in returning a list of few locations that are <<close>> to the selected goal in the sense described above. These locations can be in turn displayed and analyzed in ArcView. The process is interactive and iterative. Its intended outcome is a better-informed decision on the part of prospective health care professional about rural practice location selection.

Illustration combination of criterion values (reasonable goal) is identified

In order to illustrate the application of the method, we use five attributes for the location selection criteria:

• need for physicians (DOCS) – to be maximized;

• population in 1990 (POP90) – to be maximized;

• weekly number of hours on call (ON_CALL) – to be minimized;

• fertility rate (FERTILITY) – to be maximized

• percentage below poverty level (POVERTY) – to be minimized.

An alternative matrix of decision maps combination of criterion values (reasonable goal) is identified

Discussion combination of criterion values (reasonable goal) is identified

Actually, Nampa is the only location, which is close to the identified goal in the common sense of this word (note that the need for physicians is much higher in Nampa than it was set in the goal). Since the software does not know the preference trade-off of the user, it displays three different locations, which are not very near the goal, but may happen to be better locations from the user perspective than Nampa. Note that in Nampa the prospective physician has to spend 1.29 hours on call instead of one hour in the identified goal.

In St.Maries one has to spend only 0.92 hours on-call per week. Perhaps, the user would agree to sacrifice the population level for this advantage? Only the user can decide it. Weiser was selected since it is a little bit larger than St.Maries. Finally, Boise, the capital of Idaho, was chosen since Nampa does not meet the population level of the goal. Perhaps this is important for the user? The user has to decide whether any of the selected places is attractive enough for the location of health care practice. It is important to note that all other places in the database were further away from the identified goal, and so they were not selected.

Application to local water quality planning in Kolomna region(“Revival of the Volga River” program)

• 390625 decision alternatives were formulated;

• decision alternatives were enveloped and provided in the form of decision maps;

• reasonable goal was identified by the user;

• related alternatives were found and displayed in decision maps.

• Take into account the tradeoff rate related to minimization of the pollutant p3!

• About US\$ 5,000,000 are needed to minimize the pollution while just the same value can be obtained with the cost of US\$ 300,000

APLICACIÓN DE LA MINERÍA DE regionDATOS EN LA LOCALIZACIÓN ÓPTIMA DE INSTALACIONES PETROLERASAlberto Barrón Alcántara, PEMEX PEP SCTIDavid Alberto Salas de León, ICML de la UNAMGlicinia Valentina Ortiz Zamora ICML de la UNAMMardocheo Palma Muñoz ICML de la UNAMWiliam Bandy ICML de la UNAMCarlos Mortera ICML de la UNAMAlexander LótovCCARCRomán Efrémov URJC

Motivación region

Steps of the study region

1.- Estructuración de geobase de datos

3.- Selección de variables

4.- Extracción de conocimiento

5.- Interpretación y evaluación

Number of decision alternatives was about 9000.

para la exploración

óptima de reservas petroleras

PEMEX PEP

Ing. Alberto Barrón Alcántara

CCARC ( Centro de Computación de la Academia Rusa de Ciencias)

Dr. Alexander Lótov

Mr. Alexander Kistanov

Mr. Alexander Zaitzev

Dr. Roman Efremov

Motivación region

...

En total, 4907 alternativas…

Soluciones factibles: otro algoritmo petroleras

y2

a(Y)

• 6

• 5

• 4

• 2

y(1)

• 1

• 2

y1

• 3

RGM for non-linear models petroleras

• First, the Pareto frontier for a non-linear model is approximated by a large number of non-dominated objective points (FGNL method);

• Then, the RGM/IDM technique is used for exploration of the Pareto frontier of the convex hull and several non-dominated points for the non-linear model.

Software demonstration petrolerasComparison of RGM/IDM technique with FGNL visualization (Pareto Front Viewer)

Applications petroleras

• Real-life. Exploration of marginal pollution abatement cost in the electricity sector of Israel (Ministry of National Infrastructures). The software system was used at the Ministry for about five years.

• Methodological. Optimization of River Basin Management Plan (Italy)

Exploration of pollution abatement cost in the Electricity Sector – Israeli case study(jointly with D. Soloveitchik and other specialists fromMinistry of National Infrastructures, Israel)

Several hundreds of pollution reduction alternatives for the Israel electricity sector were developed for the period 2003 – 2013 by application of a complicated non-linear mathematical model (FGNL does not exist that time). Then, the IDM-based screening of alternatives was applied.

Five selection criteria were used: Sector – Israeli case study

• percent of CO2 reduction (CO2_%);

• percent of NOx reduction (NOx_%);

• marginal abatement cost (NPV_DC(\$));

• percent of growing average cost of electricity (AV.C_%).

Decision map displays trade-off between CO Sector – Israeli case study2_% and NPV_D for several levels of NOx reduction as well as given levels of marginal abatement cost and percent of growing average cost of electricity

Selected alternatives Sector – Israeli case study

MULTIOBJECTIVE OPTIMIZATION FOR RIVER BASIN MANAGEMENT PLAN Sector – Israeli case studyL. Galbiati1, F.J. Elorza2, A. Udias3, F. Bouraoui1(1) JRC, Institute for Environment and sustainability. Rural, Water and Ecosystem Resources Unit (Italy).(2) D.M.A.M.I. (E.T.S.I. de Minas). Universidad Politécnica de Madrid. email: [email protected](3) D.E.I.O. (E.S. de C.C. Experimentales y Tecnología). U.R.J.C. Mostoles, Madrid (Spain).

ABSTRACT

Diffuse sources of pollution coming from agricultural practices are among the biggest problem to tackle when dealing with water management. Often the crop management is oriented to maximize production without considering the contamination caused to the ecosystem. This study is focusing on the identification of an optimize crop rotation, applying a MOEA technique coupled with a comprehensive hydrological model (ISSm) capable to take account all the components of the water cycle as well as the contamination occurring during agricultural practices and benefits from crop production. This tool has been applied to Burana-Po di Volano basin (Italy), demonstrating the effectiveness to provide tradeoff solutions that simultaneously minimize the leaching of pollutants to the groundwater and maximizes the exploitation benefits only choosing the adequate crop sequences. This methodology is an important support for policy makers and water managers, providing information about the cost-effectiveness of alternative agricultural practices.

The map of Burana-Po di Volano basin Sector – Israeli case study

Sub-basins in the watershed Sector – Israeli case study

Criteria and decision variables Sector – Israeli case study

Criteria:

• Benefit that is equal to the income minus fertilizer cost and irrigation cost;

• the average annual phosphorous yield;

• the average annual nitrogen yield.

Decision variables: allocation of crops between all sub-sub-regions for each year

After approximating the Pareto frontier by using a multi-objective evolutionary optimization algorithm, the RGM/IDM technique was used

Application of RGM/IDM in Web. multi-objective evolutionary optimization algorithm, the RGM/IDM technique was usedReasonable Goals for DataBases(RGDB)

Concept of the Web RGDB application server multi-objective evolutionary optimization algorithm, the RGM/IDM technique was used

Data input multi-objective evolutionary optimization algorithm, the RGM/IDM technique was used

Example of the RGDB display multi-objective evolutionary optimization algorithm, the RGM/IDM technique was used

Selected alternatives multi-objective evolutionary optimization algorithm, the RGM/IDM technique was used