A Flexible Architecture for Creating Scheduling Algorithms as used in STK Scheduler

Transcription

1 A Flexble Archtecture for Creatng Schedulng Algorthms as used n STK Scheduler W. A. Fsher and Ella Herz Optwse Corporaton and Orbt Logc Incorporated fsher@optwse.com and ella.herz@orbtlogc.com Abstract A method of developng custom algorthms usng the Optwse schedulng system s presented. An overvew of the overall schedulng methodology s presented followed by a descrpton of how schedule algorthms may be customzed. Performance results for the commercal STK Scheduler regresson tests used to verfy algorthm codng enhancements and a case study are also provded. Introducton Schedulng a number of tasks to a pool of resources s a very common but dffcult problem. For example n [1] Barbulescu et al, demonstrated that a generalzed verson of the range schedulng problem s NP complete. Whle ths means that t may not be possble to construct an algorthm that can be proven to fnd the optmal soluton n fnte tme for the general problem, real world problems can have specfc condtons that make fndng good solutons possble. Most successful schedulng algorthms used n the real world explot specal condtons that allow the users to fnd good solutons. Orbt Logc and Optwse have found that a sngle algorthm for schedulng s not the best choce for all problems. By modfyng varous algorthm buldng blocks to meet both the desred soluton goals and schedulng constrants, customzed schedulng algorthms can be created that meet the needs of partcular mssons. The purpose of ths presentaton s to descrbe how the Optwse schedulng archtecture that s used n STK Scheduler can be adapted to specfc schedulng problems. An ntroducton to the Optwse algorthms was presented at the 2004 STK Users Conference [2]. An overvew of the custom algorthm nterface was ntroduced at the 2008 Copyrght 2013, All rghts reserved. STK Scheduler s Copyrght Orbt Logc Inc. STK s Copyrght Analytcal Graphcs Inc. STK Users Conference [3]. Some of that materal s updated here for completeness. Optwse and STK Scheduler STK Scheduler provdes the nterface and top level busness logc that translates a real world satellte task and resource problem nto the specfc language necessary for the Optwse algorthms to agnostcally fnd a schedule soluton. Fgure 1: STK Scheduler Task Defnton GUI STK Scheduler provdes the nterface for defnng the schedulng problem, confgurng the algorthms, as well as dsplayng the results. The user defnes resources and assocated attrbutes and then defnes tasks and ther accompanyng constrants and resource requrements and optons. Wth a seamless nterface to Systems Tool Kt (STK) the user can apply physcal constrants to the schedulng problem by selectng one or more STK computatons as resource avalablty or task schedulng constrants. The software then uses the Optwse algorthms to fnd de-conflcted, valdated schedule solutons whch can be vewed n table, Gantt, or 3D map vews. STK

2 Scheduler provdes both a graphcal and applcaton programmng nterface (API) for defnng and solvng schedulng problems and exportng the results. In the Optwse scheduler model tasks are assgned to tme slots. As shown n fgure 4a) each tme slot has an earlest start and a latest stop. The desred task duraton s assgned durng ths tme slot. The tme slot also has assocated wth t a profle. The profle s a contaner that allows one or a combnaton of resources to be defned. It s often the case that a task may be satsfed by more than one profle as shown n fgure 4 b). Fgure 2: STK Scheduler Gantt Vew Fgure 4: Tasks and profles Fgure 3: STK 3D Schedule Anmaton Wthn ths paradgm, the user can create and modfy plans manually or can employ one or many algorthms to solve the schedulng challenge. The user can also utlze the custom algorthm bulder to defne an algorthm specfc to ther schedulng problem. Regardless of the algorthm appled, a user may edt the resultng soluton f desred. Over 200 lcenses of STK Scheduler have been deployed nternatonaly supportng commercal, cvl, and mltary programs. The user lst ncludes Boeng, Harrs, Raytheon, Northrop Grumman, Booz Allen, Lockheed Martn, Honeywell, General Dynamcs, Orbtal Scences, TASC, Sctor, EADS, NASA. Pprograms supported by STK Scheduler nclude the Ar Force Satellte Control Network (AFSCN), SBIRS, SBSS, STSS, OSIRIS-REX, GLAST, WIRE, NASA Ground Network, and NFIRE. In addton, Orbtal Scences uses STK Scheduler for all launch and early orbt plannng for all of ther space launch vehcles (Taurus, Antares, Pegasus, Mnotaur). The STK Scheduler Model. In order to understand ts custom algorthms, t s mportant frst to understand the STK Scheduler model and how Optwse Algorthms ft nto that model. For example profle 1 mght be the combnaton of satellte A and ground staton A and profle 2 s the combnaton of satellte A and ground staton B. In STK Scheduler the soluton profles are derved from real world resource constrants, such as lne-of-ste access from a satellte to a ground staton, or lmted satellte onboard memory, or the tmes when an operator s avalable n the control center. STK Scheduler uses STK to model physcal constrants, and provdes a means for non-computed constrants to be defned as well. All task and resource constrants and computatons are used to generate wndows of opportunty that could be used to accomplsh the task for a gven resource profle. In STK Scheduler these wndows are called tmeslots. The process of creatng the feasble tmeslots can be smple (a pont-to-pont STK access calculaton) or complex (multple calls to STK access calculatons wth nternal STK constrants combned wth external user-defned generated constrants). Any number of resources may be specfed n a task profle defnton usng Boolean logc to allow a varety of resource combnaton optons for any task. In STK Scheduler each vald resource combnaton s called a profle. STK Scheduler then passes to Optwse a number of profle possbltes ncludng assocated computed tmeslots. Each profle and tmeslot also has a desrablty value assocated wth t. In STK Scheduler ths s used to nclude user resource and tme preferences (for nstance, t may be more desrable to schedule the task n an early tmeslot wth a specfc resource profle). Tasks may also have several other propretes ncludng prorty, desred start tme, and duraton types. Tasks can have fxed or varable duratons. Varable duraton tasks wll only be assgned f a mnmum duraton can be assgned, but wll be expanded up to a maxmum duraton

3 f possble. Tasks can also be defned to only be allowed to use one slot or to use multple slots. When multple slots are allowed the user also has the opton to allow the task to swtch resources between assgnments f needed to acheve the desred total assgnment duraton. K dur s used to adjust the relatve weght of assgnment tmes the duraton. Thus tasks wth longer duratons wll affect the FOM more than shorter ones. K desre s used to adjust the relatve weght of desrablty of the slot assgned to the task. K early s used to adjust the relatve weght of the early bonus. The early bonus s 1.0 f the task was scheduled as early as possble and zero f as late as possble for that task. K MaxBonus s used to adjust the relatve weght of the Max duraton bonus. It s 1.0 f maxmum duraton s scheduled and 0 f mnmum duraton s scheduled. K userstart s used to adjust the relatve weght of the userstart bonus. The userstart bonus s 1.0 f the task was scheduled as close to the desred user start and zero f far away as possble for that task. UserFunc s a lnk to external user functon. (dll) Fgure 5: Resource Usage As shown n fgure 5, the resources n a profle may be used durng, allotted at the start, or replenshed at the end of tasks. It s also possble defne a resource to be use or replensh at a rate. For example a partcular task may deplete a battery resource at partcular rate, and another task may charge the battery at dfferent rate. A setup resource may be defned for use pror to the tmeslot access. Note that ths resource s used outsde the tme slot tme. It s also possble to defne a breakdown tme. All resource levels and tme values are computed wth double numerc precson. All of these propertes are defned for each profle. It s also possble to defne task to task constrants such as task A must be some amount of tme after task B. One can also defne a mnmum and maxmum between tasks that have been defne to be n a group. Model Fgure of Mert The problem nput language also allows the user to adjust parameters n the fgure of mert that s used to measure the goodness of a soluton. K FOM Pr K task K UserFunc Ua 1 : assgned, assgn Ua KdurAssgnDur KdesreSlotDesre EarlyBonus K MaxBonus early userstart ( DesredStart Start ) 0 : unassgned K assgn s used to adjust the relatve weght for pure assgnment. Ths term s complementary to the next term. max The user s able to change the values of K values n the problem defnton fle n order to adjust how much each term contrbutes to the FOM. Algorthm Heurstc Classes Before gong nto the detals of the algorthm heurstcs t s useful to take a wder vew. The algorthms used fall nto two major classes, ordered algorthms that assgn tasks by tryng tme slots n some order and the neural algorthm whch uses a competton model. In the ordered type of algorthm, tme slots (and thus the correspondng tasks) are tred n some order. As tme slots are used for a task assgnment they may block future assgnments. In the left top panel of fgure 6 just such a case has occurred (It s assumed that the task requres all capacty of a resource). The slot consderaton order s shown by the numbers near the end of the slot. By gong n a dfferent order, two other solutons result n fully assgned schedules. In Fgure 6, three examples usng dfferent orders wth one pass are shown. In the top example only one task s assgned because the assgnment of task1 to slot 1 blocks the only avalable slot for task 2. The next two examples show slot checkng orders that result n full assgnment. It s also possble to use nformaton durng the process to modfy ths slot checkng order. Multple passes can be used to add addtonal tasks that may not be schedule n a sngle pass. For example, assume the last task to be consdered (and assgned) s one whch replenshes a resource. A second pass mght allow a task unassgned durng the ntal pass to be assgned to the replenshed resource. Repar heurstcs are mplemented by removng

4 a task from a fnshed schedule and then testng f other tasks (of hgher value) may be done. A Greedy algorthm can be mplemented by selectng the next slot based on ts possble mprovement to a Fgure of Mert. Whch detaled strategy s best depends on the specfc problem. Fgure 6: Tme slots consderaton order We wll return to the detals of how the varous ordered search algorthms can be constructed after a dscusson of the other class of algorthms. Fgure 7 shows an example of a second class of algorthm used n the solver engne. Ths method evolved from an analog neural network approach for the task assgnment problem suggested by Kennedy and Chua, 1998 [5] and nvestgated n [6]. We agan begn wth a model based on tme slots. Fgure 7: Neural Competton Each tme slot represents a possble way to assgn the task and has an assgnment probablty. All tme slots start wth an assgnment probablty near zero. Each tme slot probablty s allowed to grow subject to constrants. An example of one fundamental constrant s: the sum of the probabltes of two overlappng assgnments must be less or equal to one. The algorthm s desgned to shft the start tmes of the two tasks n conflct and to reduce the probabltes to resolve the conflct. The assgn the task only once constrant s creatng by requrng the sum of probabltes for all tme slots for a partcular task to be less than or equal to one. If the sum s greater than one then all tme slots n the sum are penalzed. If there s a resource capacty volaton at a partcular tme then the tme slots probabltes are penalzed and the start tmes of the tasks are adjusted to help clear the constrant. Ths s done for all tme slots smultaneously. Fgure 7 shows ths process for a two task problem. Note that n the mddle panel (at a hypothetcal teraton 100) the frst tmeslot probablty for task one s penalzed twce whle the other two tme slots probabltes are penalzed once. These two tme slots wll outgrow the doubly penalzed tmeslot eventually forcng the frst tme slot of task 1to a zero value. Ths allows task 2 the freedom to move earler n the schedule. The order of the tme slots s no longer a factor. The soluton s drven by the problem constrants. The soluton represents a maxmzaton of an underlyng objectve functon whch s to maxmze the number of assgnments. In the model mplemented for the schedulng algorthm engne the objectve functon maxmzes total assgned duraton. Although the example above goes to the optmal soluton, t s not the case f slot 1 s gven an ntal value sgnfcantly larger than slots 2 and 3. Ths llustrates another nterestng feature of usng such an algorthm. By varyng the values of the ntal nodes randomly, t s possble to generate a famly of solutons. Notce that unlke an ordered search algorthm there s no task or resource order rules; the constrants are feedback loops that constran the soluton space. Regresson Tests Results Optwse and Orbt Logc mantan a lbrary of over two hundred past problems that test the feature space of the scheduler. The regresson tests demonstrate the complexty and speed wth whch STK Scheduler and varous algorthms solve these problems. By runnng a varety of algorthms on a varety of problems, t s clear that one algorthm s not best for all problems. Most of the regresson tests contan less than 100 tasks and solve n less than a second wth most of the algorthms. They are mportant, but yeld lttle nformaton for evaluatng performance. Here we dscuss four of the most complex tests from a computaton pont of vew and two smaller test problems. All soluton tmes n ths secton were benchmarked on a 64 bt Intel Core GHz processor. The names have been replaced n the four customer derved cases. Table 1 gves an overvew of the dmenson

5 of the problems wth regard to the number of tasks, resources and tmeslots that are covered. name #tasks #resources #slots 15T2R OL-Ex Cust Cust Cust Cust Table 1: Regresson Test Dmensons The 15T2R test was desgned to have many tradeoffs nvolvng tasks resource conflcts. Wth ths setup, the Neural algorthm performs very well. However, despte what was desgned to be a stressng problem, the Random algorthm wth one tral found a full assgnment soluton. A more detaled analyss n [7] showed that the probablty of gettng a full soluton wth one run of Neural was 72 % and wth one run of random t was 48 %. All cases took less than a second to run. The FOM was programmed to reward total task duraton and earlest start. For fully assgned solutons hgher FOM measures how early the tasks were scheduled. Algorthm # assgned FOM OPS Sequental MPS Neural(1) Neural(100) Random(1) Random(100) Table 2: 15T2R Regresson Test Results The OL-Ex10 test contans 120 tasks and 30 resources usng four task types wth varyng fxed duraton tmes. STK accesses were obtaned for 10 hours assumng smultaneous access to a ground staton and some elevaton constrants. By usng a 10 hour tme perod, the total resource avalablty was reduced to a pont where the schedulng algorthms needed to do some real work. Ths problem s an example of one that s solved well by the Algorthm # assgned FOM OPS Sequental MPS Neural(1) Neural(100) Random(1) Random(100) Table 3: OL-ex10 Regresson Test Results Sequental algorthm. Only the Neural algorthm was capable of gettng a full soluton pror to the nventon of the Sequental algorthm. Notce that the Sequental algorthm has the hghest FOM score. That s because t has the tghtest packng of the tasks. The next four examples are all large problems derved from customer problems. All examples nclude varable duraton tasks whch can be expanded, but have lmted or no handover tasks. They are 1 or 2 day schedule perods wth mnmum duratons as small as 2 mnutes and maxmum duraton rangng from 5 mnutes to unlmted. In the regresson test each of the standard algorthms s run. The Neural and Random algorthms are run wth number of tres of 1 and 5. Table 4 shows the number of assgnments for each customer derved case wth each type of algorthm. Case OPS Seq MPS Neural Neural Ran Ran (1) (5) (1) (5) Table 4: Customer Regresson Test Results (Assgnments) Notce that no one algorthm stands out as best for these problems. The Random algorthm wth 5 tres appears to be the best. The MPS method s next n terms of performance. Note here that performance s analyzed based on the number of assgned tasks. Ths s not unusual when nteractng wth the STK Scheduler customer base. More tasks seem always to trump even the best constructed FOM score. Based on customer feedback t s clear that customers place a premum on predctablty. Unless one of the algorthms has found a soluton wth a much hgher assgnment percentage they wll use one pass or sequental. Both these algorthms were desgned to follow typcal human strategy. Case OPS Seq MPS Neural (1) Neural (5) Ran (1) Ran (5) Table 5: Customer Regresson Test Results (Soluton Tme) The most nterestng thng to note n the tme to solve metrc s that the Neural algorthm takes sgnfcantly longer than the rest for large problems. The Neural algorthm must set up a feedback network based on the number of tmeslots. In the case 2 and case 3 that s and tmeslots, respectvely. In ths problem most those nodes have no nteracton wth most of the other

6 nodes. Because these problems have weak nteractons between the resources most of the neural computaton s summng zeros. In ths case, the Neural algorthm s a bad choce. Whle not yet n the regresson test but under current development, we have done one problem whch had a request for 29,745 tasks to be assgned over a 24 hour perod usng 33 resources. There were an astoundng 1,710,462 possble accesses (tme slots). Usng a modfed verson of the nput routne and a custom algorthm very smlar to the Sequental algorthm (no expand) we were able to fnd a soluton wth 20,706 assgnments n 161 seconds. That s over 120 assgnments per second. Ths s an example a smple but extremely large problem. It llustrates effcency of the underlyng code and the ablty of the algorthm to handle large problems. The results of these regresson tests show that across a wde varety of schedulng problems wth dfferent performance crtera, there s no sngle best n the standard set of algorthm. Solver Archtecture and Custom Algorthms Next, we turn our attenton to the custom algorthm feature. The methodology that s used to fnd a schedule soluton s embedded n a solver engne that has been desgned from the ground up to be adaptable. It uses a run tme nterpreted scrpt language to defne the algorthm. scrpt, track solutons generated by the soluton scrpt and provde output back to the clent program (In ths case STK Scheduler). The hgh level manager s also the place n the code where strategy s added. Examples of such strategy wll emerge later n the dscusson. Each box ndcates the logcal flow of a typcal problem. The scrptng language parallels ths flow. These blocks also roughly ndcate the ndependence of the underlyng computaton. The code n some of these routnes has been optmzed over the past 10 years to allow near real tme turnaround for many typcal problems. Each component has also been desgned to be modfed. The basc structure of a soluton scrpt s shown n fgure 9. A soluton strng s a xml format fle that contans one or more tral specfcaton. A tral specfcaton contans steps and modfers. Steps are order specfc, modfers are not. At a mnmum, a tral must have a search step. All other parameters are optonal. Typcally a scrpt that uses an ordered search wll also have a sort step. Fgure 9: Soluton Scrpt Structure Fgure 8: Hgh Level Manager The job of the hgh level manager shown n fgure 8 s to parse the nput problem descrpton and nput soluton The archtecture allows up to three sort levels, each wth a parameter that defnes the preference for sortng. Sort parameters can be set to lst, prorty, early start, desrablty, slack, or random. For lst, prorty, and desrablty, the sort parameter can be set to ascendng or descendng. For random sorts, the randomzaton can be by task, profle, or tme slot. A randomzer allows a random choce from remanng slots f all the pror sort crtera are equal. The randomzer name determnes whether the randomzaton wll occur over all slots, slots assocated wth tasks or slots assocated wth profles. Use of a randomzer nstructs the manger to loop over the tral by the named varable number of tmes, randomzng the fnal varable. Ths allows a Monte-Carlo lke search

7 strategy to be mplemented. The soluton wth the best fgure of mert s chosen. Multple modfers can be selected and are not order dependent. The frst modfer s the use of Prorty Groups. If the Prorty Groups modfer s selected, slots are frst placed nto as many groups as there are unque prortes. Ths allows multple passes to be made over the slots n the group to obtan maxmum group assgnment before movng on to another prorty group. Whether or not prorty groups have been chosen as an opton, a sngle or multple dmensonal sort of the slots s avalable. The next two modfers deal wth the Fgure of Mert. Wth a Greedy Fgure of Mert modfer enabled, each tme an assgnment attempt s completed, the Fgure-of-Mert (FOM) s checked for all possble assgnments assumng success. The slot wth the largest possble ncrease n FOM s checked next. Ths mmcs a classc greedy heurstc but wth a user defnable FOM. The External Fgure-of-Mert modfer drects the engne to call an external method wthn a user modfable dll to calculate the Fgure of Method (FOM). There are a number of expand modfers because expand s a computatonally expensve operaton and expandng a task early n the assgnment process wll tend to block later assgnments. Havng the ablty to frst assgn the mnmum duraton requred to meet the task requrement and later expand duraton f t s possble has resulted n ablty to have maxmum task assgnment and extremely hgh resource usage. Expand modfers are: Expand after Each Try, Expand After Each Task, Expand Handover Task Up Front, and pre-assgn and Expand Soft Tasks. The pre-assgn and Expand Soft Resources modfer nstructs the manager to fnd tasks that use soft resources and assgn them frst. Soft resources are typcally rate resource that are consumed by some data tasks and replenshed by other. The resource also has a soft lmt to how much they can be replenshed. A typcal example s a battery recharge operaton from a solar collector. When the battery s full the chargng operaton s turned off automatcally at ts lmt. The easest way to model t s to have a task that s always on whenever there s sun access. The onboard system knows when the battery s full and soft resources fulfll the same functon. Fndng these tasks and makng sure they are on and fully expanded always mproves the changes of gettng tasks that wll requre the resource on. There are three possble search optons, ordered, neural and DS1MPS. No sort step s requred for the neural or DS1MPS. DS1MPS mplements code that mmcs the performance of the orgnal algorthms. It requres the manager to set up some specal trackng snce nternally t s equvalent to dong multple trals wth dfferent presorts. The fnal step opton s an output step. Whle t seems ths s essental, for STK Scheduler t s not needed because STK Scheduler s able to read the soluton strng from the Optwse schedulng object drectly wthout fle I/O. You mght want an output step f you wsh to have an addtonal fle wrtten at the end of a seres of trals. The fle format can be a tradtonal flat fle or xml and you can select from the last completed try from a tral (current) or the best soluton found thus far. Buldng Custom Algorthms Whle t s possble to create the custom scrpts by hand edtng, a GUI Algorthm Bulder s avalable from wthn STK Scheduler. The user can smply select the sort parameters from a lst, and chose behavor modfers from check boxes. A screenshot s shown n fgure 10. Fgure 10: STK Scheduler Custom Algorthm Bulder GUI The process s smple. Select a 1 2 or 3 dmensonal sort, use pull down lst to select a sort parameter (an A or D at the end of the parameter names means ascendng or descendng sort), select any modfers that are needed, f a randomzer or neural s used select the number of tres to use, select a maxmum tme to allow for a search, and select a output type f needed. When the add Tral to Soluton button s press an xml strng s added to the exstng soluton. You can have multple trals n a soluton. Example Soluton Strngs The soluton strng s a smple xml format strng. Each soluton strng can have one or more trals. If there s more than one tral than the manager keeps track of the best soluton based on the FOM. Note: the order of modfers s not mportant but step order s. A search s the only requred step. Slots wll reman n the order they were lsted n the nput descrpton fle f the sort step s omtted. It s possble to output a name value formatted or xml formatted outfle at the end of each tral. The nterface of the software module also allows the callng clent to retreve the soluton data wthout fle I/O. For example the

8 soluton strng that corresponds to the One Pass Algorthm n STK Scheduler s: <?xml verson= 1.0 encodng=utf-8?> <SolnProc> <Tral> <modfer> useprgrps </modfer> <modfer> expandalltasksatend </modfer> <step> Sort1(desreA) </step> <step> Search(ordered) </step> </Tral> </SolnProc> In the One Pass algorthm task are passed nto prorty groups and sorted by slot desrablty. If a slot has an dentcal prorty and slot desrablty then the lst order n the nput descrpton s used. Thus, f there are a number of tasks wth equal prorty and all slots have equal desrablty, then the frst task and slot n the nput fle lst order wll be tred. Snce the slots assocated wth a task tend to be wrtten n a group typcally the one pass algorthm wll search all slots for a partcular task before movng on to the next task. It s not a requrement that all slots for a task be wrtten at one tme, t s a tendency of most users. In STK Scheduler the desre parameter s used to adjust slot desrablty based on prorty of the resources n the profle and schedulng preferences. If default values are chosen then t s the same for all tme slots. It s however another way to adjust the algorthm performance. Makng one change to the strng; replacng Sort1(desreA) to Sort1(earlyStartA) changes the algorthm to match the Sequental Algorthm n the standard algorthms lsted n STK Scheduler. In the sequental algorthm slots are agan placed nto prorty groups. But now snce there s a sort(earlystarta) slots are sorted by ther slot start tme n ascendng order. Thus, the task wth the earlest possble slot start wll be tred frst. If the task assgnment s blocked, then whchever task that has the next earlest slot tme wll be tred. What happens f there are multple slots wth the same tme? The lst order of the slots s used. Ths algorthm s a drect mappng of a customer request. Many problems can be solved wth ths frst avalable approach and t tends to match a strategy that human schedulers are comfortable wth. The strng for the MultPass Algorthm s very smple: <Tral> <step> Search(DS1MPS) </step> <modfer> expandalltasksatend </modfer> </Tral>. The multpass algorthm was a frst generaton algorthm that used multple tres wth dfferent presorts to fnd the best soluton. Dependng on the number of resources n the problem t tres up to 32 dfferent presorts ncludng a phase n whch slots are randomze by profle. In order to be able to exactly match the orgnal algorthm performance, any step based sort parameters are gnored. MultPass nspred the custom algorthm approach. Rather than havng the presort selecton rules fxed n logc, t s now possble for the end user to create ther own. Somethng smlar to MPS could be created n a custom algorthm by usng multple trals. The strng neural algorthm s very smlar to the MPS strng: <Tral numtres= 5> <step> Search(DS1MPS) </step> <modfer> expandalltasksatend </modfer> </Tral>. As descrbed above the neural algorthm does not search n any order so a sort step s gnored. Notce that a new varable s now defned n the tral header, numtres=5. Ths nstructs the engne to do 5 runs of the neural scheduler usng random startng condtons each tme. Agan the best soluton based on the FOM s saved. Neural works best on problems n whch many tasks usng the same resources at nearly the same tmes. The fnal algorthm n the standard set of algorthms s STK Scheduler s Random. It was orgnally wrtten to be a base case for judgng performance. It turned out to be a great algorthm for problems where there were multple smlar resources and unform usage was desred. Such resources tended to have smlar but not qute dentcal access tmes. The soluton strng for random s <Tral numtres=30> <modfer> expandalltasksatend </modfer> <step> Sort1(ranDS1) </step> <step> Search(ordered) </step> </Tral>. The key dfference s that there s one sort parameter, rands1, whch s a specal verson of the random sort. rands1 exactly matches the way that slots were randomzed n the frst generaton random algorthm. It s most smlar to ranslot. The dfference s n how slots are randomzed. There are now many more optons for controllng how much a when randomzaton s appled. Randomzaton of the fnal varable s one example of a schedulng strategy that s added at the manager level of the software. The manager smply makes multple loops over a tral randomzng the varable and checkng the FOM. Repar as descrbed n [8] [9] can also be mplemented by modfyng ths level of codng. For repar the hgh level manager uses some method to select a porton or portons of a schedule soluton to freeze and then schedules around the partal soluton. The routnes that expand the task duraton at the end of the schedule are an example of repar behavor. Those routnes are clever enough to be able to move a task later n tme that s constranng the duraton expanson of a prmary task. NASA Case Study Example Next consder an example of a problem we nvestgated as part of a proposal to demonstrate the applcaton of STK Scheduler to the NASA Ground Staton Problem. For the problem we modeled a two week perod durng whch 41 spacecraft wth multple vew requests were assgned to one of 20 ground staton antennas. Snce each spacecraft msson was assgned a unque prorty, there were 41 prortes levels. Based on desred the number of desred

9 events per msson and the avalablty of the resources the feasblty modelng of STK Scheduler generated 4452 possble tasks and 158,069 tme slots. The customer also defned two goals. The prmary goal was to assgn the largest number of events to the hghest prorty mssons frst f possble. The secondary goal was to maxmze assgnment and match target resource usage as defne n an external spreadsheet. The purpose of the spreadsheet calculaton was to penalze solutons n whch an ndvdual resource dd not match contractually oblgated resource usage levels for some resources. Over usage ncurred addtonal charges whle under usage mpled wasted contract tme. The spread sheet calculaton computed a composte whch tred to capture these two goals but dd not strctly enforce the frst goal. The proposed fgure of mert was FOM = 1 + (100* A -1000*B - C)/D, where A = (number of events over desred), B = (number of events under desred), C = (ndvdual resource usage penalty), and D = ((501-pr)*number desred events). The sums are over the mssons except for C whch s over the resources. For the STK Scheduler modelng of ths problem, the number of tasks s equal to the number of desred events. It s not possble to assgn more than the desred number of events and A wll always be zero. The resultng FOM n form s 1- δ/k - C/K. (δ= 1 f a task s assgned and 0 f not). K s a new constant that correctly scales between the reduced form and the correct spreadsheet formula. The key pont s that δ s an avalable term n the exstng FOM. The C/K (penalty) term must be computed externally. Fgure 11 shows data beng exported from STK Scheduler to and Excel macro for calculaton of the NASA FOM. Fgure 11:NASA Case Study Archtecture The frst test was to try the exstng standard algorthms and gnore the penalty term and use data exported from STK to calculate the FOM. The best standard algorthm was the Sequental Algorthm. The second test was to use Algorthm Bulder to create a custom algorthm agan gnorng the penalty term. The best custom algorthm found was to add randomze profles to the sequental algorthm wth 50 tres. For the thrd test an external FOM was coded that was used to select the best soluton from the multple tres. Fnally, the greedy opton wth the external FOM was tred whch checks the delta FOM of all possble slots to choose the next slot to try. The external NASA FOM had to be modfed slghtly to allow a better delta FOM to be calculated. Table 6 shows how each algorthm fared wth regard to number of assgnments, FOM score, and the penalty score. It also shows the number of prorty assgnments mssed relatve to the best soluton at a specfc prorty level. Algorthm Assgned FOM Penalty # mssed relatve best at pr= Sequental at pr=16 Sequental wth random profle nternal FOM 50 tres Sequental wth random profle external FOM 200 tres Greedy External FOM 30 tres Table 6:NASA Case Study Results at pr= Best case prmary crtera at pr=6 It turns out the best soluton from a FOM pont of vew does not meet the prmary goal: assgn hgher prorty tasks before lower prorty f possble. The best FOM case of found wth Greedy, results n 2 fewer tasks assgned at prorty level = 6 than a case wth a FOM= To get the better FOM, assgnments were made to meet the target usage levels at the cost of total tasks because that s what the FOM sad was the trade-off. A human operator would probably not bump a hgher prorty task n order or take a lower total number of assgnments to obtan better resource usage. Another pont of comparson s tme to solve. All algorthms took around 10 seconds per try to solve the problem except for the Greedy FOM whch was sgnfcantly slower at over 300 seconds per try. Tryng to

10 add code that could search for very small mprovements n the external FOM was very expensve computatonally. On the other hand method 3 whch loosely coupled the external FOM but allowed for random searchng of the soluton space found the best soluton from the prmary goal pont of vew usng less computaton tme. Concluson In ths paper we have shown how creatng customzed algorthms usng STK Scheduler can be used to ncrease the value of schedule solutons. Optwse provdes the underlyng archtecture wth a flexble algorthm scrptng language and solver engne. On top of the Optwse archtecture, STK Scheduler provdes GUIs and APIs that allow the user to defne tasks and resources that can be ted to physcal constrants, buld specalzed algorthms, adjust the fgure-of-mert, run the algorthms, and vsualze the schedule results n a varety of formats. The value of the custom algorthm was shown n a NASA case study where a varety of custom algorthms were developed and compared wth regard to how well each soluton met a varety of specfc crtera. It s the desgn synergy between adaptable algorthms, schedule data management, flght dynamcs computatons and user nterfaces whch s requred to meet the aerospace schedulng challenges of today and tomorrow. [7] Fsher W. The Optwse Corporaton Schedulng Algorthms (As used n STK/Scheduler) In STK Scheduler product documentaton. [8] Zweben M. Davs E. Daun B. and Deale M. Schedulng and Reschedulng wth Iteratve Repar IEEE Transactons on Systems, Man Cybernectcs, Vol 23 No [9] Chen S., Knght R., Stechert A., Sherwood R., and Rabdeau G. Usng Iteratve Repar to Improve the Responsveness of Plannng and Schedulng Proceedngs of the Ffth Internatonal Conference on Artfcal Intellgence Plannng and Schedulng References [1] Barbulescu L., Watson J. Whtley L. and Howe A. Schedulng Space-Ground Communcatons for the Ar Force satellte Control Network Journal of Schedulng, Vol. 7, 2004 [2] Fsher W. Schedulng Algorthm Technology STK/Scheduler 2004 AGI Users Conference, July 2, 2004 [3] Fsher W. STK/Scheduler Next Generaton Schedulng Algorthms Under the Hood Presentaton 2008 AGI Users Conference, Oct 9, [4] Zegler,I. and George D. STK Scheduler Onlne Product Documentaton. http//orbtlogc.com/support/scheduler/frame.htm [5] Kennedy M. and Chua L., Neural Networks for Nonlnear Programmng, IEEE Transactons on Crcuts and Systems, Vol. 35, No.5, May 1988 [6] Fsher W., Fujmoto R., and Smthson R, A Programmable Analog Neural Network Processor, IEEE Transactons on Neural Networks, Vol. 2, No. 2, March 1991