SIMULATION-BASED MULTI-OBJECTIVE OPTIMIZATION OF A REAL-WORLD SCHEDULING PROBLEM

Transcription

1 Proceedngs of the 2006 Wnter Smulaton Conference L. F. Perrone, F. P. Weland, J. Lu, B. G. Lawson, D. M. Ncol, and R. M. Fujmoto, eds. SIMULATION-BASED MULTI-OBJECTIVE OPTIMIZATION OF A REAL-WORLD SCHEDULING PROBLEM Anna Persson Henrk Grmm Amos Ng Thomas Lezama Centre for Intellgent Automaton Unversty of Skövde Box 408, , SWEDEN Jonas Ekberg Stephan Falk Peter Stablum Swedsh Postal Servces, Posten AB Stockholm, SWEDEN ABSTRACT Ths paper presents a successful applcaton of smulatonbased mult-objectve optmzaton of a complex real-world schedulng problem. Concepts of the mplemented smulaton-based optmzaton archtecture are descrbed, as well as how dfferent components of the archtecture are mplemented. Multple objectves are handled n the optmzaton process by consderng the decson makers preferences usng both pror and posteror artculatons. The effcency of the optmzaton process s enhanced by performng cullng of solutons before usng the smulaton model, avodng unpromsng solutons to be unnecessarly processed by the computatonally expensve smulaton. 1 INTRODUCTION Posten AB s the Swedsh postal servces, entrely owned by the Swedsh Government. Core busness comprses dstrbuton of messages and logstcs, and Posten s one of the largest actors n these areas n the Nordc regon. As the Nordc postal market s fully deregulated, mal busness s a hghly compettve market. Facng natonal and nternatonal actors operatng n the same busness areas puts hgh demands on effcent mal operatons, and addtonal pressure arses from legal drectves that Posten s oblgated to follow, specfyng that mal operatons must be fast, relable, and cost-effcent. Every day, Posten receves over 22 mllon peces of mal and before dstrbuton to recpents, all mal s sorted n delvery order. The sortng s hghly automated, carred out usng a set of machnes that scan mal and determne destnaton address usng sophstcated optcal character readng. For sortng to be effcent, mal are dvded nto batches of 10,000-35,000 peces accordng to destnaton regon and these batches are sorted n parallel on dfferent machnes. An operaton schedule defnes for each mal batch what machne to use for sortng and on whch tme to start the sortng. Snce mal batches, as well as machnes, have dfferent characterstcs, consequences of dfferent schedules such as tme consumpton and money expenses vary a great deal. In Fgure 1, a smplfed operaton schedule s presented. Tme Machne Mal batch 03:50 04:05 04:20 05:45 05:55 06:10 06:15 06:30 06:40 IRM11 GSM7 GSM3 FSM11 BFM2 BFM6 B4 B1 B3 B8 B6 B7 B5 Fgure 1: Smplfed Mal Operaton Schedule As a convenent way to observe mal sortng operatons and consequences of dfferent operaton schedules, Posten has developed a dscrete-event smulaton model of the mal sortng process. Gven a schedule as the nput, the model can report ts performance n less than a mnute. The smulaton model, developed usng Arena smulaton software ( allows testng and analyss of dfferent schedules wthout dsruptng the real system. The smulaton model s exclusvely an evaluaton tool and supports nether generaton nor optmzaton of schedules. The establshed method for creatng schedules has so far been a manual procedure based on tral and error. As there s no gudance on how to change nput parameters between teratons, ths approach s very tme-consumng and requres many teratons and extensve effort by an expert for fndng a satsfactory schedule. Furthermore, t does not B /06/$ IEEE 1757

2 Persson, Grmm, Ng, Lezama, Ekberg, Falk, and Stablum guarantee that a vald schedule s found, but leaves the valdaton entrely n the hands of the expert, who s requred to consder and carefully control all possble constrants. As there are multple conflctng objectves to consder when creatng a schedule, manual optmzaton s practcally mpossble especally snce explct heurstcs for fndng a good schedule s mssng. Ths paper presents how the schedulng process and the resultng schedules have been mproved by mplementng an automatc smulaton-based system that supports the generaton of optmzed operaton schedules whle consderng multple objectves smultaneously. The rest of the paper s organzed as follows. The next secton presents related work n the area of smulaton-based mult-objectve optmzaton of operaton schedules. In Secton 3 the mult-objectve problem consdered s descrbed, followed by a descrpton of the optmzaton approach used for solvng t n Sectons 4 and 5. Secton 6 descrbes the smulaton-based optmzaton system mplemented and ts components. Conclusons of the paper and a descrpton of planned future work are presented n Secton 7. 2 RELATED WORK Mult-objectve optmzaton s an actve research area n the feld of optmzaton methodologes, partcularly usng Evolutonary Algorthms (Deb 2001). Nevertheless, the lterature reports relatvely few attempts n the area of smulaton-based mult-objectve optmzaton. Exceptons can be found n (Eskandar et al. 2005) and (Baesler and Sepúlveda 2001). Only a small fracton of the papers n the lterature, however, consder operaton schedulng problems. Almeda et al. (2001) use a smulaton-based approach for mult-objectve optmzaton of operaton schedules n a petroleum refnery. Ther proposed method s based on a genetc algorthm combned wth a mult-objectve energy mnmzng method. Usng the method the authors succeeded n fndng a schedule for a real-world refnery producton problem wth three objectves; maxmzaton of desel producton, maxmzaton of jet fuel producton, and mnmzaton of costs. Allaou and Artba (2004) propose a method based on a combnaton of smulated annealng and dspatch rules for smulaton-based mult-objectve optmzaton of flow shop schedules. In ths method, both stochastc and determnstc unavalablty of machnes are consdered n the optmzaton strategy. The authors appled ther proposed method for solvng a NP-hard schedulng problem wth the am of optmzng work n progress, job tardness, and utlzaton of resources. Gupta and Svakumar (2002) present a smulatonbased mult-objectve optmzaton method based on compromse programmng for operaton schedulng n semconductor manufacturng. The proposed method was appled for fndng a Pareto optmal soluton to a NP-hard problem of schedulng a number of ndependent jobs on a sngle machne. The objectves consdered n the optmzaton strategy were average cycle tme, average tardness, and machne utlzaton. A number of theoretcal job-shop experments was successfully carred out usng the proposed method. 3 PROBLEM DESCRIPTION Ths sectons presents the operaton schedulng problem consdered n ths paper. In general terms, the problem of fndng an optmal mal operaton schedule can be descrbed as follows. There are J non-dentcal, ndependent jobs (.e. mal batches) to be assgned to M non-dentcal, ndependent parallel machnes. No explct job prortes exst. The machnes are avalable at dfferent tmes and each machne can process only one job at a tme. Job preempton s not allowed; once a job starts on a machne t must be processed to completon. A job s ready for processng at ts release tme and must be completed before ts deadlne. The processng tme of a job depends on the machne t s assgned to and vares between dfferent machnes. Machne capacty must be respected and a job cannot be assgned to a machne n whch the capacty s below the processng requrements of the job. Jobs should be assgned to machnes n a way that s optmal accordng to a balanced relatonshp between: Total money expenses: machne usage s assocated wth money expenses for machne wear, electrcty, etc. and the total expenses should be as small as possble. Total slack tme of jobs: the tme between the completon of a job (mal batch) and ts deadlne should be as long as possble, allowng wder margns for the dstrbuton of mals to recpents. Load balancng of machnes: jobs should be dstrbuted to machnes n a way that promotes even utlzaton.. Most schedulng problems belong to a class of problems that s called NP-complete (Azzaro-Pantel et al. 1998), whch means that the tme requred for computng an optmal soluton ncreases exponentally wth the sze of the problem. Ths property also apples to the problem consdered n ths paper, as the smplfed problem of schedulng a set of J unnterruptble jobs so that the jobs are completed before ther deadlnes on machnes that are capable to process only one job at a tme, s NP-complete n the ordnary sense (Cormen et al. 2001). NP-complete problems are computatonally expensve snce guaranteeng an optmal soluton requres an exhaustve search n whch all possble solutons have to be tred and evaluated. Snce such an exhaustve search takes unreasonable computng 1758

3 Persson, Grmm, Ng, Lezama, Ekberg, Falk, and Stablum tme for most complex schedulng problems, a common and acceptable practce s to sacrfce optmalty for effcency by heurstcally gudng the search and evaluatng only a fracton of all confguratons (Arnaout and Rabad 2005). 4 MULTI-OBJECTIVE OPTIMIZATION In general mult-objectve optmzaton problems, there exst no sngle best soluton wth respect to all objectves as mprovng performance on one objectve deterorate performance of one or more other objectves (Srnvas and Deb 1995). Ths s also the case for the mult-objectve optmzaton problem consdered n ths paper. As t s not possble to obtan solutons whch maxmze performance of all objectves at the same tme, the optmal solutons to the problem are consdered to be the Pareto optmal set. The Pareto optmal solutons are the set of solutons strctly superor to the other solutons consderng all objectves but possbly nferor to other solutons consderng one or a subset of the objectves (Srnvas and Deb 1995). Any of the Pareto optmal solutons s an acceptable soluton, snce none of them s absolutely superor to any others (Srnvas and Deb 1995). 4.1 Two-Stage Artculaton of Preferences Varous methods for smulaton-based mult-objectve optmzaton can be categorzed accordng to the tmng of when the artculaton of the requred preference nformaton occurs relatve to the optmzaton (Evans et al. 1991). Ths tmng can be: Before the optmzaton (pror artculaton of preferences) Durng the optmzaton (progressve artculaton of preferences) After the optmzaton (posteror artculaton of preferences) None of these alternatve approaches s generally better than another for solvng mult-objectve problems, but they all have varous strengths and weaknesses (Evans et al. 1991). In ths paper, we use a combnaton of pror and posteror artculaton of preferences; beneftng the strengths of both these approaches. We do not make use of progressve artculaton of preferences as t s consdered too tme-consumng for the decson maker to be nvolved durng the entre optmzaton process. Whle many multobjectve optmzaton methods are based on ether pror or progressve artculaton of preferences, only a few attempts have been made based on posteror artculaton of preferences (Medagla et al. 2004). Pror to the optmzaton, the decson maker s asked to express tradeoff preferences regardng the varous objectves by assgnng a weght value to each objectve specfyng ts relatve mportance a hgher value means that the objectve s consdered more mportant. From a total amount of 100% the decson maker allots each objectve a percentage value and the total weghtng assgned must sum up to 100%, as shown n the example n Table 1. Ths tradeoff nformaton s used to determne the drecton of the optmzaton strategy, makng the optmzaton process more effcent. Table 1: Example of Objectves Weghtng Objectve Weght Mnmze total money expenses 50 Maxmze slack tme of jobs 30 Maxmze machne load balancng 20 Posteror to the optmzaton, all dentfed Pareto optmal solutons are presented to the decson maker wth nformaton of ther achevement level of the varous objectves. The decson maker may then choose the most desrable one from the soluton set usng some other hgherlevel nformaton based on hs/her doman knowledge. 4.2 Integratng Multple Objectves The varous objectves are weghted by the decson maker pror to the optmzaton and aggregated nto a sngle objectve through a weghted sum functon (Wegert et al. 2000): n v = wu, where = 1 n w = 1, w 0, (1) and where u s the subutlty produced through objectve, w s the relatve mportance of objectve, and n s the number of objectves. The goal of the optmzaton strategy s to maxmze v consderng all problem constrants. = Normalzaton of Objectves The varous objectves consdered are all represented usng dfferent measurement unts. To allow a far comparson between performance of the dfferent objectves, all objectve measurements are normalzed to values between 0 and 1: out o s the meas- where ured output value of o, o worst u = best worst u s the utlty of objectve o, worst s the worst possble value 1759

4 Persson, Grmm, Ng, Lezama, Ekberg, Falk, and Stablum of o, best s the best possble value of o and an optmal value of u s 1. 5 OPTIMIZATION ALGORITHM The mult-objectve optmzaton strategy s based on a Genetc Algorthm (GA). GAs are populaton based search algorthms nspred by theores from natural evoluton. The basc dea behnd these algorthms s that a populaton of ndvduals represents possble solutons of a gven problem. Through recombnaton of solutons, offsprng are created, formng a new generaton of the populaton. Some of the solutons are better suted for the problem and these are gven more opportuntes to reproduce and pass ther desrable behavor to the next generaton, smlar to natural selecton. New generatons of the populaton are evolved untl a suffcently good soluton s found. GAs have been proven to be very flexble and relable n searchng for global solutons (Baesler and Sepulveda 2000) and also capable of solvng complex schedulng problems (Azzaro-Pantel et al. 1998). Ther characterstcs makng them sutable for solvng mult-objectve smulaton-based problems (Eskandr et al. 2005) and they can easly be coupled wth any dscrete-event smulaton models, n contrast wth some other heurstc methods whch are more sutable only to certan problems (Azzaro-Pantel et al. 1998). The rest of ths secton descrbes the GA mplemented for solvng the mult-objectve optmzaton problem consdered n ths paper. The mplementaton was based on GAlb ( whch s a C++ lbrary of GA components Representaton of Solutons The GA encodes possble solutons as genomes and each genome nstance represents a sngle soluton to the problem n ths case an operaton schedule. In many applcatons, the effcency of GAs s determned manly on how the doman problem s encoded n the genome and the representaton has therefore been consdered carefully n ths study. For ths problem, the set of jobs s consdered to be J= { j1, j2, K, j k } and the set of machnes M = { m1, m2, K, m n }. A genome conssts of n lsts of varable length, (( j ) ( ) 1 ) 1,1, j 1,2, K, j 1,, K, jn,1, jn,2, K, j, where each lst represents schedulng nformaton for a specfc machne. Each n, n lst entry represents a job scheduled on the machne (e.g., jobs j1,1, j1,2, K, j 1, are scheduled on machne 1). The genome s a permutaton of all jobs,.e., each job s present n 1 one and only one of the lsts. When generatng a schedule from a genome, each job lst s sorted frst by startng tme and subsequently by deadlne. The assumpton behnd ths approach s that a job wth an earler startng tme has an earler deadlne and thus there s no reason to schedule an early job after a late job. When a lst has been sorted, jobs are scheduled on the machne n the sorted order. Fgure 3 shows an example of a smplfed genome wth and fourteen jobs scheduled on four machnes. m 1 j 9 j 1 Fgure 3: Example of Genome An advantage of ths representaton s that the genetc materal used to represent a soluton (.e. an operaton schedule) s kept small, reducng the sze of the search space and thus mprovng performance of the algorthm. A drawback, on the other hand, s that t may represent nfeasble solutons however ths s handled by the evaluaton functon, gvng only partal credt to nfeasble solutons Genetc Operators m 2 j 14 j 13 j 3 j 5 m 3 j 7 j 2 j 4 j 12 j 11 m 4 j 6 j 8 j 10 A frst populaton of 50 canddate solutons s randomly created. In the ntalzaton procedure, a heurstc functon s used to make sure that jobs are only scheduled on machnes wth enough capacty. Durng each successve generaton of the GA, a proporton of the exstng populaton s selected to breed a new generaton. Indvdual solutons are chosen for matng through roulette wheel selecton, n whch the probablty for selecton s proportonal to the ftness of the soluton. Thus, solutons wth hgher ftness values are more lkely to be selected, but a small number of solutons wth less ftness values have some probablty of beng selected as well n order to keep a large dversty of the populaton. From the pool of selected solutons, two solutons are chosen as parents and through matng two new solutons are formed accordng the procedure outlned n Fgure 4. Ths process, called crossover, takes place wth a probablty of 0.9. foreach j n J do machne1 WhchMachne( parent1, j) machne2 WhchMachne( parent2, j) wth probablty 0.1do Swap( machne1, machne2) end AddToLst( chld1[ machne1], j) AddToLst( chld2[ machne2], j) end Fgure 4: Crossover Functon 1760

5 Persson, Grmm, Ng, Lezama, Ekberg, Falk, and Stablum To mantan the genetc dversty from one generaton to the next, some of the offsprng solutons are mutated. In the mutaton procedure, all jobs are terated through and a job s moved to a random lst wth a probablty of 0.1. Smlar to the ntalzaton procedure, a heurstc s used when mutatng solutons to make sure that jobs are only scheduled on machnes wth enough capacty. 5. If a the stoppng crteron s met, the search s termnated and the set of Pareto optmal solutons are returned otherwse the process s repeated from step Ftness Functon A ftness functon quantfes the qualty of solutons by assgnng a ftness value to each of them correspondng to ther performance. The ftness value assgned s based on a combnaton of two propertes of a soluton: Objectves: Credt s gven based on the achevement of the objectves; the hgher the level of achevement, the hgher the credts. Delay: If the processng of a job s completed after ts deadlne a penalty s gven. Based on these two propertes, the formula to calculate the ftness of soluton s: f = v dw d (2) where v s the result of the weghted sum functon n Equaton (1), d s the number of delays, and w s the weght d for property d Evolutonary Process The overall GA evoluton process works as descrbe below. A flow dagram of the process s also presented n Fgure 4: 1. A frst populaton of canddate solutons (.e. operaton schedules) s created. These ntal solutons are randomly generated n order to enable a wde range of solutons. To acheve faster mprovement of the algorthm t s also possble to nsert user-defned solutons known to have good performance n the ntal populaton. 2. Performance of solutons are evaluated and a ftness value s assgned to each of them usng the formula descrbed n Equaton (2). 3. The solutons wth hghest ftness are selected and by applyng genetc operators, offsprng are created from these solutons, formng the new, mproved generaton of the populaton. 4. Some of the solutons n the new generaton are arbtrary mutated to mantan the genetc dversty. Fgure 5: Optmzaton Strategy 6 DESIGN AND IMPLEMENTATION Ths secton descrbes the realzaton of a smulaton-based system that supports the automatc generaton of optmzed operaton schedules. 6.1 Archtectural Desgn The suggested soluton s based on the archtecture shown n Fgure 6. The decson maker specfes optmzaton objectve preferences and nputs these to a clent applcaton, whch ntates the optmzaton process and sends the objectves to an optmzaton component. A canddate soluton to the problem s automatcally generated by the optmzaton component and sent to the evaluaton component. The evaluaton component quantfes the performance of the suggested soluton and notfes the optmzaton component of the results. Based on ths feedback, the optmzaton component generates an mproved soluton and sends ths new soluton to the evaluaton component. The generate-and-evaluate process s then repeated untl the stoppng crtera s met and when ths happens the resultng set of Pareto optmal solutons s sent back to the clent component, where the results are presented to the decson maker. The archtecture s based on the prncple of encapsulaton wth low couplngs between components; components only know about each others nterfaces (.e. nput and output) wth mnmal knowledge of ther nternal detals. 1761

6 Persson, Grmm, Ng, Lezama, Ekberg, Falk, and Stablum Clent Component Fgure 6: Archtectural Desgn The low couplng between components allows for a flexble mplementaton where components can be changed wthout nfluencng each other, assumng that the nterface s unchanged. It also fts well nto a dstrbuted and parallel computng platform where dfferent components can be run on separate computers. The archtecture s easy to use, as the user only nteracts wth a smple nterface and does not need to have any knowledge of the optmzaton strategy. The user s replaced n the problem-solvng process by the optmzaton component and besdes specfcaton of optmzaton objectve preferences, no manual effort s requred. 6.2 Implementaton Ths secton descrbes how the system presented n the prevous secton has been mplemented Clent Component The clent component was mplemented usng Excel and Vsual Basc for Applcatons (VBA), as Excel was the already exstng nterface for the Arena smulaton model. When the clent s started, t prompts the user to nput detals about optmzaton objectve preferences. The user then starts the optmzaton process by clckng a button. When the optmzaton process s ntated, a VBA scrpt generates a text fle specfyng optmzaton objectves tradeoffs, sends ths fle n a call to the optmzaton component, and wats for the optmzaton component to send back the set of Pareto optmal schedules. The resultng schedules are presented to the user n the Excel nterface together wth summary results and statstcs Evaluaton Component The evaluaton component conssts of two subcomponents; a Smplfed Model and an Arena smulaton model. The dea of ntroducng a Smplfed Model, and not only usng a smulaton model as n ordnary smulaton optmzaton approaches, s to reduce the overall tme consumpton needed for evaluaton of solutons. The smulaton model s the man bottleneck n the process and avodng unnecessary use of t wll enhance the system effcency. The Smplfed Model performs a rough estmaton of solutons and does not consder stochastc events n the system. Solutons sent to the evaluaton component are frst processed by the Smplfed Model, whch performs cullng of unpromsng solutons and acts as flter to the smulaton subcomponent. The Smplfed Model approxmates the tme consumpton of each job n a schedule and estmates f all deadlnes are met,.e. f a schedule s vald. If a soluton s consdered as nvald by the Smplfed Model, t s not sent to the tme-consumng smulaton for further evaluaton, but feedback s returned to the optmzaton component mmedately. As the Smplfed Model s an approxmaton of the smulaton there s an nherent rsk that solutons are msclassfed. A false-postve classfcaton (.e. when an nvald soluton s classfed as vald) cause no harm on the optmzaton results but only add some extra tme to the process. A false-negatve classfcaton (.e. when a vald soluton s classfed as nvald), on the other hand, has the consequence that promsng solutons may not proceed n the optmzaton process. To reduce the number of false-negatve classfcatons, the classfcaton procedure of the Smplfed Model s made optmstc. Solutons consdered as vald by the Smplfed Model are sent to the Arena smulaton model for detaled evaluaton of processng tmes, money expenses, and other propertes dependng on complex nterrelatonshps between dfferent parts of the system, often nfluenced by stochastc events. Before the Arena smulaton model was nserted n the system t was carefully verfed and valdated, snce the correctness of the smulaton model s of crtcal mportance for the optmzaton results to be useful n realty Optmzaton Component The optmzaton component, based on the optmzaton strategy descrbed n Secton 5, uses the evaluaton component for performance quantfcaton of solutons. The optmzaton component s not aware of n what way solutons are evaluated, but only receves performance quantfcatons. 6.3 Results The mplemented system was tested usng real-world scenaros and so far the results look very promsng. Evaluaton of results from the tests show that the system s successful n fndng good schedules accordng to optmzaton objectves preferences specfed by the decson maker. Doman experts have compared the generated schedules wth ther own manually created schedules and see a great potental n the system. Compared to the manual approach of creatng schedules, the system mplemented has consderable advantages. Snce no manual control or nterventon n the optmzaton process s necessary, a lot of tme and effort are saved for the expert responsble for creatng schedules. The system 1762

7 Persson, Grmm, Ng, Lezama, Ekberg, Falk, and Stablum also makes t easy to obtan schedules wth certan focuses, such as for example low money expenses, as the decson makers preferences are consdered n the optmzaton process. It s worth to notce, however, that from the results t s not clear how well the optmzed solutons compare wth the achevable values of the objectves, as the deal values are not known. By performng cullng of solutons before the tmeconsumng smulaton takes place, a reduced tme consumpton for the total evaluaton process can be acheved. As shown n the chart presented n Fgure 8, the number of unpromsng solutons tend to be large, especally n the begnnng of the optmzaton process (results are an average of ten runs). An explanaton of ths s that the GA starts from a set of random solutons and performs a broad search over the whole search space. Note that not all ndvduals n the populaton are evaluated for each generaton because some solutons reman unchanged from one generaton the next. Number of Solutons Generaton Vald Invald Fgure 8: Number of Vald and Invald solutons as Classfed by the Smplfed Model 7 CONCLUSIONS AND FUTURE WORK Ths paper presents a successful applcaton of smulatonbased mult-objectve optmzaton of a complex real-world operaton schedulng problem. A two-stage artculaton of the decson makers optmzaton objectve preferences was used n the mult-objectve approach. Expressng preferences pror to the optmzaton enables the drecton of the optmzaton strategy to be nfluenced, makng the search process more effcent. Presentng the complete set of the resultng Pareto optmal solutons posteror to the optmzaton enables the decson maker to choose the preferred one and hence results n a fnal soluton that s desrable from the decson maker s perspectve. As there may be qute many Pareto optmal solutons, t s mportant to present the set of solutons n a way that ads the decson maker n the task of analyzng all solutons to fnd the best one. In Persson et al. (2006) we descrbe how ths support can be provded and present deas of a graphcal user nterface for analyss of solutons. The overall process was made more effcent by performng a rough estmaton of solutons before evaluatng them usng the tme-consumng smulaton. Potental s seen n ths approach of avodng unpromsng solutons to be unnecessarly evaluated. However, the cullng of solutons requres further studes, whch are ncluded n planned future work. To mprove optmzaton results further, future work also ncludes studyng how doman expert knowledge can be captured and ncorporated n the optmzaton process. A human expert may have extensve knowledge valuable for the optmzaton, and ncorporatng ths knowledge n the optmzaton strategy may be a way to obtan faster and more accurate optmzaton results. ACKNOWLEDGEMENT Ths work s done wthn the OPTIMIST project whch s partally fnanced by the Knowledge Foundaton (KK Stftelsen), Sweden. It uses GAlb developed by Matthew Wall at the Massachusetts Insttute of Technology. REFERENCES Allaou, H., and A. Artba Integratng smulaton and optmzaton to schedule a hybrd flow shop wth mantenance constrants. Computers & Industral Engneerng 47: Almeda, M. R., S. Hamacher, M. A. C. Pacheco, and M. B. R. Velasco Applyng Genetc Algorthms to the Producton Schedulng of a Petroleum Refnery. In MIC'2001-4th Metaheurstcs Internatonal Conference, Arnaout, J-P. M., and G. Rabad Mnmzng the Total Weghted Completon Tme on Unrelated Parallel Machnes wth Stochastc Tmes. In Proceedngs of the 2005 Wnter Smulaton Conference. Pscataway, NJ: Insttute of Electrcal and Electroncs Engneers. Azzaro-Pantel, C., L. Bernal-Haro, P. Baudet, S. Domenech, and L. Pbouleau A two-stage methodology for short-term batch plant schedulng: dscreteevent smulaton and genetc algorthm. Journal of Computers and Chemcal Engneerng 22(10): Baesler, F. F., and J. A. Sepúlveda Mult-Objectve Smulaton Optmzaton for a Cancer Treatment Center. In Proceedngs of the 2005 Wnter Smulaton Conference. Pscataway, NJ: Insttute of Electrcal and Electroncs Engneers. Cormen, T. H., C. E. Leserson, R. L. Rvest, and C. Sten Introducton to Algorthms. 2 nd edton. USA: MIT Press. 1763

8 Persson, Grmm, Ng, Lezama, Ekberg, Falk, and Stablum Deb, K Mult-objectve Optmzaton Usng Evolutonary Algorthms. Chchester: John Wley & Sons. Eskandar, H., L. Rabelo, and M. Mollaghasem Multobjectve Smulaton Optmzaton Usng an Enhanced Genetc Algorthm. In Proceedngs of the 2005 Wnter Smulaton Conference. Pscataway, NJ: Insttute of Electrcal and Electroncs Engneers. Evan, G., Stuckman, M. and Mollaghasem, M Multple response smulaton optmzaton. In Proceedngs of the 1991 Wnter Smulaton Conference. Pscataway, NJ: Insttute of Electrcal and Electroncs Engneers. Gupta, A. K., and A. I. Svakumar Smulaton based Multobjectve Schedule Optmzaton n Semconductor Manufacturng. In Proceedngs of the 2002 Wnter Smulaton Conference. Pscataway, NJ: Insttute of Electrcal and Electroncs Engneers. Medagla, A. L., S. B. Graves, and J. L. Rnguest Multobjectve evolutonary approach for lnearly constraned project selecton under uncertanty. Techncal Report No. COPA , Department of Industral Engneerng, Unversty of Los Andes, Colomba. Persson, A., H. Grmm, and A. Ng On-lne Instrumentaton n Smulaton-based Optmzaton. In Proceedngs of the Wnter Smulaton Conference Pscataway, NJ: Insttute of Electrcal and Electroncs Engneers. Srnvas, N., and K. Deb Multobjectve Optmzaton Usng Nondomnated Sortng n Genetc Algorthms. Evolutonary Computaton 2(3): Wegert, G., S. Werner, D. Hampel, H. Henrch and W. Sauer Mult Objectve Decson Makng Solutons for the Optmzaton of Manufacturng Processes. In Proceedngs of the 10th Internatonal Conference on Flexble Automaton and Intellgent Manufacturng (FAIM2000), AUTHOR BIOGRAPHIES ANNA PERSSON s a Ph.D. canddate at Unversty of Skövde, Sweden and De Montfort Unversty, U.K. She holds a Master s degree n Computer Scence from Unversty of Skövde. Her research nterests nclude artfcal ntellgence, smulaton-based optmzaton, and effcency enhancement technques for smulaton-based optmzaton. Her e-mal address s <anna.persson@hs.se>. AMOS H. C. NG s a Senor Lecturer at the Unversty of Skövde, Sweden. He holds a B.Eng. degree and a M.Phl. degree, both n Manufacturng Engneerng from the Cty Unversty of Hong Kong and a Ph.D. degree n Computng Scences and Engneerng from De Montfort Unversty, Lecester, U.K. He s a member of the IEE and a Chartered Engneer n the U.K. Hs research nterests nclude agent-based machne control systems, vrtual engneerng for manufacturng machnery and machne systems as well as smulaton-based optmzaton. Hs e-mal address s <amos.ng@hs.se>. THOMAS LEZAMA s a Lecturer at the Unversty of Skövde. He holds a B.Sc. n Automaton from Unversty of Skövde, Sweden and a M.Sc. n Computer Integrated Manufacturng from Loughborough Unversty, Loughborough, U.K he receved a Ph.D. degree n Computng Scence and Engneerng from De Montfort Unversty, Lecester, U.K. Hs e-mal address s <thomas. karlsson@hs.se>. JONAS EKBERG works wthn the Logstcs Development Department at Posten AB. He has 7 years of experence from process development wth smulaton- and optmzaton tools, ncludng development, project management, analyss and tranng. He holds an M.Sc. n Systems Engneerng from the Royal Insttute of Technology n Stockholm. Hs e-mal address s <jonas.ekberg@posten.se>. STEPHAN FALK s Project Manager at Posten AB where he s responsble for among others smulaton tools for the producton. Hs professonal background concerns prmarly operatonal development and busness development responsbltes wthn Ercsson and Emerson. He holds a BScEE and a MBA degree. Hs e-mal address s <stephan.falk@posten.se>. PETER STABLUM works wthn the Logstcs Development Department n Posten AB. The last couple of years, supply chan smulaton and optmzaton have been hs man tasks. He holds an M.Sc. n Industral Engneerng and Management from Luleå Unversty of Technology. Hs e- mal address s <peter.stablum@posten.se>. HENRIK GRIMM s a Systems Developer at the Unversty of Skövde, Sweden. He receved hs BSc and MSc degrees n Computer Scence from Unversty of Skövde. Hs research nterests nclude computer smulaton, artfcal ntellgence, and dstrbuted systems. Hs e-mal address s <henrk.grmm@hs.se>. 1764