NETWORK 2001 Transportation Planning Under Multiple Objectives

Transcription

1 NETWORK 200 Transportaton Plannng Under Multple Objectves Woodam Chung Graduate Research Assstant, Department of Forest Engneerng, Oregon State Unversty, Corvalls, OR9733, Tel: (54) , Fax: (54) , John Sessons Professor, Department of Forest Engneerng, Oregon State Unversty, Corvalls, OR9733, Emal: ABSTRACT - NETWORK 200 has been developed to provde transportaton planners wth addtonal flexblty n analyzng road systems. Whle NETWORK 2000 was lmted to mnmzng costs, NETWORK 200 can use weghted objectve functon components to mnmze road system length. Ths paper presents NETWORK 200 and the new algorthm mplemented n the program wth ts applcatons. Total open road length can be constraned whle mnmzng road and transportaton costs. Ths method can extend to nclude road deactvaton and oblteraton as optonal actvtes. Keywords: network analyss, transportaton plannng, combnatoral optmzaton NTRODUCTON The NETWORK program developed by Sessons (985) has been wdely used for solvng fxed and varable cost transportaton problems durng the last 5 years. The NETWORK algorthm n the program, whch s smlar to the Prorate Algorthm (Schnelle 980), uses a seres of rules to avod stallng n a local mnmum (Sessons 985). NETWORK 2000, developed by Chung and Sessons (2000), mproves the user nterface and enhances the problem solvng capacty. t also provdes the users wth two addtonal heurstc soluton technques; Smulated Annealng (Krkpatrck et al. 983) and Great Deluge (Dueck 993). A Geographcal nformaton System (GS) nterface s newly added to the program to help the users wth generatng a large network from GS data. Although the algorthm used n both NETWORK and NETWORK 2000 can be used for multple perod, multple product, value maxmzaton or cost mnmzaton problems, the applcatons are lmted to mnmzng costs. Consderaton of sde constrants s restrcted. Changes n forest management goals resultng from envronmental consderatons have brought new challenges to forest road system management. Multple goals and addtonal sde constrants such as open road length restrctons or road deactvatons requre a new problem solvng technque and decson makng support tool for large problems. A new verson of the NETWORK 2000 program, NETWORK 200 has been developed to provde transportaton planners wth addtonal flexblty n analyzng road systems. Whle NETWORK 2000 was lmted to mnmzng costs, NETWORK 200 can use weghted objectve functon components to mnmze road system length or other lnk attrbute. Ths paper presents NETWORK 200 and a new algorthm mplemented n the program wth the applcatons. Addtonal flexblty of the new algorthm allows users to consder multple goals and sde constrants n solvng transportaton plannng problems. The nternatonal Mountan Loggng and th Pacfc rthwest Skylne Symposum

2 ALGORTHM A new network algorthm developed by Sessons et al. (200) has been mplemented n NETWORK 200. The algorthm combnes past network heurstc approaches wth a combnatoral heurstc technque (Smulated Annealng) to provde addtonal flexblty n formulatng the objectve functon and to apply sde constrants to forest transportaton problems. The algorthm generates alternatve routes for each sale usng the route approach of the Tmber Transport Model (Sullvan 974) combned wth use of equvalent varable costs that was the foundaton of the Prorate Opton (Schnelle 980). Then, t optmzes each route usng the Smulated Annealng heurstc whle consderng multple goals and sde constrants of the problem. The basc process of the algorthm s presented n the followng four steps and llustrated n Fgure. nput data set Set k and k 2 for a block FC EVC = k VC + k2 Vol Generate k shortest paths per j Store the paths Are all blocks done? Randomly select a soluton Calculate objectve functon s ths better soluton? Accept the soluton and update the old soluton Old New Rand. < Exp Temp. Meet stop crteron? Store Enough teratons? Stop Fgure. A flowchart for the NETWORK 200 algorthm. Step. Generate k-shortest paths from each orgn to the destnaton. The k-shortest paths can ether be based on varable costs only or can nclude equvalent varable costs. We can generate blocks of k-shortest paths wth each block based upon the equvalent varables cost multpled by a weghtng factor. For example, for each orgn, develop the k-shortest paths for n The nternatonal Mountan Loggng and th Pacfc rthwest Skylne Symposum

3 blocks of k-shortest paths where the equvalent varable cost of road segment (EVC ) s calculated usng the followng equaton: EVC = k Fxed Cost( FC ) Varable Cost( VC ) + k2 Volume over segment (Eq ) Step 2. Solve the combnatoral optmzaton problem of assgnng the best route to each orgn (sale) to mnmze the sum of fxed and varable costs usng a heurstc. Multple goals are formulated nto the objectve functon and addtonal sde constrants are used to determne the feasblty of solutons. Step 3. Usng the volumes over each road segment resultng from the assgnment n Step 2, recalculate the equvalent varable costs for each road segment. Step 4. f the number of desred cycles has not been completed, return to Step usng the equvalent varable costs calculated from Step 3. Our ntal computatonal experence s that ths algorthm can fnd the optmal soluton for a set of test problems and wth some expermentaton wth weghtng factors and block szes has yelded superor solutons over NETWORK (Sessons 985) for a large problem. However, t s not wthn the scope of ths paper to compare ths algorthm wth other possble network algorthms. APPLCATONS Advantages of the NETWORK 200 algorthm are that ts objectve functon s more flexble than NETWORK and sde constrants can be easly added. Alternatve objectve functons such as mnmzng total road length, mnmzng cost subject to an open road length constrant, and ncludng decommssonng costs can be readly accommodated. Ths paper presents two approaches to constranng total open road length usng NETWORK 200. Approach consders the road length constrant as part of the objectve functon goal (Equaton 2), whle Approach 2 consders road length as a subject to constrant (Equaton 3). Approach Mn. ( VC Vol + FC X ) + ( RL X ) = = TL n (Eq. 2) Approach 2 Mn. st. = = ( VC Vol + FC X ) ( RL X ) AML (Eq. 3) where, VC : varable cost on lnk The nternatonal Mountan Loggng and th Pacfc rthwest Skylne Symposum

4 FC Vol : fxed cost on lnk : volume transported over lnk X : bnary varable ( f lnk s used, otherwse 0) RL TL n AML : road length of lnk : target road length : total number of lnks n a network problem : weghtng factor : allowable maxmum road length The objectve functon n the Approach conssts of two weghted components: devaton from a target length and total road system costs. Approach penalzes objectve functon not only when total road length exceeds the target but also when t s lower than the target (two way goal). The advantage of ths approach s that the users can generate alternatve solutons resultng from trade off between two components by applyng dfferent weght factors. Relaxng the road length constrant may decrease road costs. t also permts nvestgaton of nfeasble areas of the soluton space. n Approach 2, the road length constrant determnes feasblty of soluton, but t does not affect qualty of the soluton. Ths approach can be used when the open road densty n a management area s tghtly fxed. Approach 2 does not permt the nvestgaton of part of the soluton space that volates the constrant. Other components rather than road length can also be ncluded n the formulaton of transportaton plannng problems. Snce t s hard to express envronmental consderatons n terms of economc values, some user-defned ndces could be ntroduced. The ndces could represent envronmental hazard level such as potental sol eroson, sol sedment producton rate, or other quantfable values related to envronmental consderatons of road segments. NETWORK 200 allows the users to modfy the formulaton of objectve functon and to add sde constrants n order to consder multple management goals n the plannng area. EXAMPLE The nput and results from a sngle perod network (Fgure 2) modfed from Sessons (985) are shown n Tables, 2, and 3. For ths example, each lnk s assgned to an arbtrary road length. Approach was used to mnmze total project costs whle consderng total open road length constrant. Three dfferent cases were tested: Case ) wthout road length constrant, Case 2) wth target = 0 mles and weght factor (n) =0, and Case 3) wth target = 0 mles and weght factor = 00. NETWORK 200 found the mnmum total cost $506,234 and total open road length 4.6 mles wthout road length constrant (Case ). The results from the three cases showed total open road length can be close to the target at the expense of the project costs (Table 3). Fgure 2 llustrates alternatve solutons found by NETWORK 200 for each case. The nternatonal Mountan Loggng and th Pacfc rthwest Skylne Symposum

5 Lnk dentfer (From) (To) Table. Network nput for Example. Round Trp Haul Cost ($/truck/lnk) Road Cost ($/lnk) , , , , , , , , , , , , , , Road length (Mles) Table 2. Harvest nput for Example (Sngle Perod). Harvest de Destnaton de Harvest Volume Year 0 4, , ,200 0 CONCLUSON A computer program, NETWORK 200, has been developed for optmzng large fxed and varable cost transportaton problems under multple objectves. The new algorthm mplemented n NETWORK 200 has been dscussed. A technque for the formulaton of the multple objectves and constrants n transportaton plannng problems has been presented. NETWORK 200 has the ablty to formulate multple road system management goals. t can allow the users to explore solutons satsfyng multple objectves and sde constrants arsng The nternatonal Mountan Loggng and th Pacfc rthwest Skylne Symposum

6 from envronmental consderatons and requrements. NETWORK 200 s easy to understand by both feld personnel and analysts and can be learned quckly. ts nteractve capablty and GS nterface are also advantages of ths program. Table 3. Total project costs and open road length n solutons found by NETWORK 200. Case Total costs ($) Total open road length (mles) $506, $532, $546, Mll 9 0 Mll 9 0 Mll 9 Drecton Case Case 2 Case 3 Fgure 2. Solutons found by NETWORK 200 for three dfferent road length constranng cases. There are lmtatons to NETWORK 200. The greatest lmtaton s that t s a heurstc algorthm and the soluton may not be optmal. Furthermore, addtonal objectves and sde constrants usually ncrease complexty of the problems. Fndng good solutons to a complex transportaton plannng problem requres the user s effort to explore the soluton space n order to better understand the problem to be solved and the trade offs between goals. LTERATURE CTATONS Chung, W. and J. Sessons NETWORK 2000: a program for optmzng large fxed and varable cost transportaton systems. n Proc. of the Eghth Symposum on Systems Analyss n Forest Resources, Arthaud, G.J. (ed.). Sept 28-30, Aspen, Colorado, Kluwer Press (n press) The nternatonal Mountan Loggng and th Pacfc rthwest Skylne Symposum

7 Dueck, G New optmzaton heurstcs: the Great Deluge and Record-to-Record Travel, J. of Computatonal Physcs 04: Krkpatrck, S., C. Gellat, and M. Vecch Optmzaton by smulated annealng. Scence 220: Schnelle, B MNCOST users nstructons. USDA Forest Servce Report, rthern Regon, Dv. of Engneerng, Mssoula, MT. Sessons, J A heurstc algorthm for the soluton of the fxed and varable cost transportaton problem. n Proc. of the 985 Symposum on Systems Analyss n Forest Resources, Dress and Feld (eds.). Socety of Amercan Foresters, Dec 9-, Athens, GA. p Sessons, J., W. Chung, and H.R. Henmann New algorthms for solvng large scale harvestng and transportaton problems ncludng envronmental constrants. n Proc. of the FAO/ECE/LO workshop on new trends n wood harvestng wth cable systems for sustanable forest management n mountan forests, June 8-24, Ossach, Austra. (n press) Sullvan, E. C Network User s Gude. Spec. Rep. nst. Transport and Traffc Eng. Berkeley, Unv. of Calforna. The nternatonal Mountan Loggng and th Pacfc rthwest Skylne Symposum