Optimization Techniques for Natural Resources

Transcription

1 Optmzaton Technques for Natural Resources SEFS 540 / ESRM 490 B Lecture 1 (3/27/2017)

2 About the Instructor Teachng: nspre stuents to be curous but crtcal learners who can thnk for themselves an nurture creatve eas Research: quantfy resource traeoffs an proucton possbltes to a natural resource management ecson Tranng: forest engneerng, operatons research an forest management scence

3 The ecson makng process n natural resources management Natural Scence Management Scence Socal scence Delph-process Nomnal Group Technque Data collecton Data processng Decson tools to generate management alternatves Demonstraton/ vsualzaton of alternatves & traeoffs Consensus Bulng Remote Sensng Fel Surveys Permanent Plots Questonnares Optmzaton Smulaton Economcs Fnance Decson Montorng Implementaton

4 Management Alternatves an Consensus Bulng Proft (mllon $) Mature forest habtat (ha)

5 Moels to Solve Natural Resource Problems Descrptve moels What s there? patterns What s happenng? processes Spatal an temporal nteractons Measurements, montorng Statstcal moels

6 Moels to Solve Natural Resource Problems (cont.) Prectve moels What happens f we o ths vs. that? Smulaton, stochastc moel, scenaro analyses, etc. Prescrptve moels What s the best course of acton? Optmzaton

7 How o escrptve, prectve an prescrptve moels work together? Descrptons Prectons Where are the nsects? Where are the amage trees? Intensty of amages Host selecton behavor Populaton ynamcs Stan susceptblty an rsk Projecte spatal spersal Epecte nsect an host response to treatments Prescrptons Image source: Mark McGregor, USDA Forest Servce, Bugwoo.org

8 The role of ecson moels

9 Moels an Moel Bulng Funamentals

10 Moels Abstract representatons of the real worl Lack nsgnfcant etals Can help better unerstan the key relatons n the system/problem Useful for forecastng an ecson makng

11 Moel types Scale moels (e.g., moel arplane) Pctoral moels (photographs, maps) Flow charts: llustrate the nterrelatonshps among components Mathematcal moels

12 f (5ac) (12ac) a (5ac) b (4ac) e (9ac) c (6ac) f c A B C D E F a b e A B C D E 1 0 F 1

13 A a (5ac) (12ac) E e (9ac) B b f (5ac) (4ac) c (6ac) Objectve: Mamze fnancal return from cuttng the stans 1. Decson varables : Let (where = a, b, c, or e) enote the ecson whether stan shoul be cut or not. 2. Objetve : Let f stan s to be cut, an 0 otherwse; {0,1}. Let c enote the fnancal return from cuttng stan. Ma Z c c c c c c c N a a b b c c e e f f, where N={a,b,c,,e,f}

14 3. Constrants : Ajacent stans are not allowe to be cut. Ma Z c N subject to: a e a b b b c c c e e f b c b c e 1 1 a (5ac) f (5ac) (12ac) b (4ac) e (9ac) c (6ac) A B C D E F A B C D E 1 0 F 1

15 A mathematcal program: a (5ac) f (5ac) (12ac) b (4ac) e (9ac) c (6ac) Ma Z b c b c e c N subject to: a a e f {0,1} Objectve functon(s) Constrants

16 Mathematcal moels The most abstract Concse Can be solve by effcent algorthms usng electronc computers, Thus, very powerful.

17 Goo Moelng Practces The qualty of nput ata etermnes the qualty of output ata The nature of the management problem etermnes the choce of the moel (not the other way aroun) Ask: Is the moel to be use to smulate, evaluate, optmze, or escrbe the system or phenomenon?

18 Goo Moelng Practces (cont.) What s the scale, resoluton an etent of the problem? What are the outputs (results) of the moel? What are these results use for? Who wll use them?

19 Optmzaton Moels Determnstc vs. probablstc optmzaton Conve vs. non-conve problems Constrane vs. unconstrane optmzaton Eact vs. a-hoc (heurstc) optmzaton Statc vs. sequental (ynamc) ecsons Sngle vs. mult-objectve optmzaton Sngle vs. multple ecson makers Sngle vs. multple players (games)