Approximation and Visualization of Interactive Decision Maps Short course of lectures

1. 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

2. 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

3. 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.

4. Features of the problem 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.

5. Possible sources of the alternatives 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.

6. Example: real estate on sale

7. A simple graphic description of the method

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

9. Enveloping the criterion points

10. Approximating the Edgeworth-Pareto hull of the convex hull (the so-called CEPH)

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

12. The alternatives that are close to the goal are selected

13. General 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.

14. Software demonstration RGM/IDM-based software Visual Market – 2

15. Example of the screening procedure(maximization case)

16. Several applications of the IDM/RGM technique

17. Selecting 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.

18. Database of alternatives and the map of Idaho

19. Description of the database 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.

20. DSS application 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.

21. Illustration 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.

23. An alternative matrix of decision maps

25. Discussion 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.

26. 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.

27. 390625 decision alternatives were considered and evaluated

28. Initial decision map

29. How it is dangerous to use simple pollution minimization! • 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

30. Decision map with restricted cost

31. Decision map with the goal

32. Selected alternatives that are close to the goal

33. APLICACIÓN DE LA MINERÍA DE DATOS 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

34. Motivación

35. Steps of the study 1.- Estructuración de geobase de datos 2.- Filtrado de datos 3.- Selección de variables 4.- Extracción de conocimiento 5.- Interpretación y evaluación Number of decision alternatives was about 9000.

36. Decision alternatives

37. Matrix of decision maps

38. Selected decision map

39. Selected alternatives

40. Aplicación de la Minería de Datos 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

41. Motivación

42. Criterios para determinar la ubicación de las instalaciones petroleras ... En total, 4907 alternativas…

43. Criterios para determinar la ubicación de las instalaciones petroleras

44. Soluciones factibles: otro algoritmo y2 a(Y) • 6 • 5 • 4 • 2 y(1) • 1 • 2 y1 • 3

45. RGM for non-linear models • 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.

46. Software demonstrationComparison of RGM/IDM technique with FGNL visualization (Pareto Front Viewer)

47. Applications • 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)

48. 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.

49. Five selection criteria were used: • percent of CO2 reduction (CO2_%); • percent of NOx reduction (NOx_%); • additional total cost (NPV_D); • marginal abatement cost (NPV_DC($)); • percent of growing average cost of electricity (AV.C_%).

50. Decision map displays trade-off between CO2_% 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