DISTRIBUTED PRODUCTION SYSTEM: A FRAMEWORK TO SOlVE THE PRINTED CIRCUIT BOARD ROUTING

Transcription

1 Cybernetics and Systems: An Internatinal Jurnal, 21: , 1990 DISTRIBUTED PRODUCTION SYSTEM: A FRAMEWORK TO SOlVE THE PRINTED CIRCUIT BOARD ROUTING MARíA TERESA DE PEDRO ANGELA RIBEIRO JOSÉ Luís PEDRAZA Institut de Autmática Industrial (CSIC), La Pveda, Madrid, Spain Prductin systems (PSs), based n a very general idea (cnditin-actin pairs), are widely used in artificial intelligence fr mdeling intelligcnt behavir and building expert systems. Hwever, PS prgrams are very cmputatin-intensive and rn quite slwly. This precludes the use f PSs in many dmains that require real-time respnse and high perfrmance. Our apprach fr speeding up the executin f PSs is t design special message-handling machines, with architectures matched with the characteristics f the algrithms. In this line, a mdel that allws ne t describe a PS as a set f cncurrent prcesses, perating in a cperative way and cmmunicating thrugh channels, is develped. T prve its validity, the mdel is used t develp a distributed prductin system fr Printed Circuit Bard (PCB) ruting. A special machine, which efficiently supprts the defined set f prcesses, als has been designed. This prblem has been selected because it is cmplex and time cnsuming. INTRODUCTION Prductin Systems (PSs; a1scalled ru1e-basedsystems) are wide1yused in artificial intelligence (Al) fr mdeling intelligent behavir and building expert systems. They have been used n a large variety f applicatins in severa1 areas such as medicine, VLSI ruting, cmputer-aided design, and il explratin (Shrtliffe, 1976; 100bbani 1986; McDermtt, 1980; Duda, Gaschnig, and Hart, 1979). Hwever, PS prgrams are very cmputatin intensive and run quite slwly. This slw speed f executin prec1udes the This research was spnsred by the Cmisión Interministerial de Ciencia y Tecnlgía. Cpyright 1990 by Hemisphere Publishing Crpratin 181

2 DISTRIBUTED PRODUCTION SYSTEM FOR ROUTING M. DE PEDRO ET AL. 1. Match: The prductins are matched against the data structure, btaining a "cnflict set," which is cnstituted by all satisfied prductins. 2. Cnflict reslutin: The cntrl system chses a prductin f the cnflict set. 3. Act: The selected prductin is applied, s the actins n the right-hand side f the prductin are executed. The new data structure is tested t see whether the terminatin cnditins are true. The cycle f peratins is executed again until all the terminatin cnditins are satisfied, then the PS prgram finishes. Taking int accunt the exp1anatin befre, ne can divide the executin f the PS int three main independent tasks: Selectin f the mst apprpriate prductin. Applicatin f the selected prductin. Verificatin f the new data structure. These three main tasks can be perfrmed in parallel by a set f independent but cnnected prcesses, like thse shwn in Fig. 1. The three main mdules are a selectr, which selects the mst apprpriate prductin, perfrming the match step and the cnflict reslutin step; a generatr, which applies the selected prductin, executing the actins in the right-hand side f the prductin and generating new data; and a verifier, which tests the data structure, verifying if the terminatin cnditins are satisfied. The furth mdule, the rganizer, perfrms the cmmunicatin with the user and initializes the ther mdules. In this algarithmic decmpsitin the tasks executed in each mdule (selectr, generatr, and verifier) can verlap as fllws: In a first step the selectr selects the best prductin and sends a "generatin" message t the generatar thrugh the channel between them. When the generatr receives respnse and high perfr use f PSs in many dmains that require real-time mance. On the surface, PSs appear t be capable f using large amunts f parallelism (far example, it is pssible t perfrm the matching f every prductin rule in paralle1 (Stlf, 1987». Hwever, the high speed-up expected by expliting this parallelism has nt been reached (Uhr, 1987). Als, measurements and simulatins shw that the speed-up available, by using ther pssible surces f parallelism in PS prgrams, is much be10w the initial expected speed-up (Gupta, 1984). A new prpsal is made in this article: mdeling a PS by a set f independent prcesses, perating cncurrently and cmmunicating thrugh channels, and designing special-purpse message-handling machines matched with the features f the prblem. Building such special machines is nt unrealistic, since there are new tls (Hmewd, 1984) that allw cheap and easy develpment DESCOMPOSITION f these machines. OF PS ALGORITHMS PSs are able t describe several different systems n the basis f a very general idea (cnditin-actin pairs). Experts tend t express mst f their prblem-slving techniques in terms f a set f situatin-actin rules, and this suggests that a PS ught t be the methd f chice fr building expert systems and mdeling intelligent behavir. A PS cnsists f three parts: 1. A special data structure, which represents the current state f the prblem. 2. A set f prductin rules (cnditin-actin pairs). 3. A cntrl system, which drives the system's activity. SELECTOR GENERATOR VERIFIER FIGURE 1. General algrithmic decmpsitin in prductin systems. The prductin rules deal with the data structure, trying t reach a set f gal cnditins frm an initial state. The cnditin part f each prductin represents cnditins that must be present in the data structure befre a prductin can be app1ied. The actin part represents actins that change the data structure; in this way ther rules will have their cnditin part satisfied. Finally, t drive the PS activity, a cntrl system decides which prductin rule is the next ne. The cntrl system wrks by perfrming the fllwing recgnize-act cycle:

3 DISTRIBUTED PRODUCTION SYSTEM FOR ROUTlNG M. DE PEDRO ET AL. ture). The blck verifier is shared amng all generatin prcesses, because the end cnditin in a MS (like that in a BS) is that the data structures reach crnmn states. When the verifier detects that tw r mre data structures have reached the same state, it will send a "cllisin" message t each f the selectin prcesses invlved in that cllisin. If a selectr receives a cllisin message, it builds up the sequence f prductins that were selected t reach the crnmn state, and it sends this sequence t the rganizer in a "slutin" message. The prblem will be slved when the rganizer has all the sequences f prductins jining all terminal states amng themselves. If the number f terminal states is k, it will be pssible t at least achieve a k + 1 speed-up rate This speed-up rate will be achieved when the sum f the run time f the selectin prcess and the run time f the generatin prcess is equal t k times the run time f the testing prcess. S, a substantial reductin in running time can be achieved by implementing the multidirectinal strategy in a parallel way whenever each selectr-generatr pair wrks driven crrecdy int a subspace f the glbal space f ptential slutins. Ntice that all these subspaces are independent f each ther. On the ther hand it is assumed that there are nt verheads related t the crnmunicatin amng the cncurrent A MULTIDIRECTIONAL prcesses. PS TO PCB ROUTING The Ruting Prblem Representatin In a PCB, a cnnectin is a path jining several terminals t themselves. T rute a PCB is t find all the cnnectins s that all f them are electrically independent and verifying the design cnditins. The physical bard space will be cnstituted by a n-sided quadrangular grid (whse size, step, and number f sides depend n the specific prblem). The slutin path is cmpsed f chains f hrizntal and vertical segments cntained in the grid, as in mst ruting methds. Our ruter prcedure will be a MPS, in which search prcesses (segment chains serving as terrninals) must be cnnected. The jint f all these chains is the desired cnnectin. Taking int accunt that tw different cnnectins cannt have cmmn pints, search prcedures must find paths n the free physical bard space. This cnditin cannt be satisfied if the PS des nt knw the free ndes in the grid. Thus, bth a data structure t cntain the grid ccupatin and a state space t cntain all the ptential slutins are needed. the generatin message, it perfrms the actins in the prductin and then sends a "testing" message t the verifier and a "new data" message t the selectr. S, while the verifier is testing the new data structure, the selectr is able t select a new prductin. In this way, it is pssible t duplicate the speed, at mst This lw speed-up rate will be adequate nly if the characteristics f the prblem cnsidered wuld allw explitatin f ther surces f parallelism. Finally, it is desirable that there be little crnmunicatin amng the prcesses. Therefre, the PS is fitted t distribute the knwledge amng all the prcesses. In ur case, it is cnvenient t have selectin, generatin, and test knwledge. Each kind f knwledge is related t a mdule such as that in Fig. 1. Prblems that permit decmpsitin int a larger set f prcesses are thse in which a bidirectinal strategy (BS) can be applied t slve them. In this case, it is pssible t g frm the initial state t the gal state using a set f prductins, called direct prductins, and simultaneusly, t g frm the gal state t the initial state using inverse prductins. In the mst general case, when there are tw r mre initial states and tw r mre gal states, the prblem can be slved using a multidirectinal strategy (MS). In this case, a structure f independent prcesses like the ne shwn in Fig. 2 is prpsed. Ntice that there is a selectr and a generatr fr each terminal state, initial state, and gal state, because independence amng all generatin prcesses is assumed (each selectr-generatr pair must have its wn data struc- FIGURE 2. General decmpsitin in prductin systems with multidirectinal strategy. G2 v D D

4 DISTRIBUTED PRODUCTION SYSTEM FOR ROUTING M. DE PEDRO ET AL. terminal is cnnected), whereas the multidirectinal methd cnnects all terminals at nce. Fr this reasn the slutin zne is defined fr each search as fllws: Fr the unidirectinal case, the slutin zne is the smallest rectangle cntaining the previus unin. In the case f simultaneus searches, the slutin zne is defined as the smallest rectangle that cntains all the rest f the terminals in the cnnectin. We have already seen that dividing the base f knwledge int selectin knwledge, generatin knwledge, and verificatin knwledge allws us t build a cperative MPS. Besides, this distributed representatin has anther advantage. In fact, the slutin space is cnstituted by all pssible hrizntal and vertical segments cntained in the grid, but the óccupatin matrix prevents the creatin f a segment thrugh an ccupied pint f the reticle. A cnsequence f this is that creatin f cincident segments is impssible, s the slutin space becmes reduced and, mst imprtantiy, becmes a tree f segments. This same explanatin assures us that all search subspaces are disjinted. In ther wrds, prblem representatin requires that every search explre different avenues. Frm an efficiency pint f view, the parallel MPS is much faster than the crrespndent unidirectinal PS. This is because the first generates fewer ndes than the secnd, withut paying in cmputatinal verheads. COMPUTER ARCHITECTURE TO THE ROUTING MPS Taking int accunt that the ruting prcedure can be cnsidered t be like a set f prcesses, each ne dealing with its private data, a message-based multiprcessr appears adequate fr running the MPS ruter. The system architecture is designed t be very clse t the algrithmic partitin f PS and als t the prblem characteristics, s the blck diagram f Fig. 1 can shw the uter level f system architecture. It is related t the three steps f an Al algrithm, named here search, ruter, and verifier, respectively. The rganizer is the mdule that cmmunicates with the user, prducing the set f messages t initialize the ther mdules and t start every cnnectin. Searcher The partitin f searcher int elemental search prcesses is based n the pssibility f ding heuristic searches, independentiy, simultaneusly, and in different directins frm each ther, as we have already explained. Fr each The space f ptential slutins is divided int subspaces, which act as terminal s in the cnnectin, s that every search prcess wrks with a subspace. The grid ccupatin is represented by a matrix in which null elements crrespnd t free ndes and nnnull elements crrespnd t ccupied ndes. Ruting Prcedure The previus sectin describes, frm an algrithmic pint fview, the distributin f a PS in prcesses f selectin, generatin, and verificatin. Gn the ther hand the prpsed representatin f a ruting prblem allws ne t divide the base f knwledge int selectin knwledge (distributed amng all the search subspaces), generatin knwledge (cntained in the ccupatin matrix), and verificatin knwledge (cntained in ne verificatin matrix). In summary, the distributed ruting prblem representatin allws that the selectin, generatin, and verificatin prcesses are executed cncurrentiy and cperatively, accrding t the prpsed MPS mdel. Hwever, in this case we have nly a generatin prcess, because the ruting space is unique: It is an ccupatin matrix. Abstracting the fact that the search culd be unidirectinal r multidirectinal, the specific PS behavir, ruting a PCB, is as fllws: Initial step: Segments are created, frm each terminal, as lng as pssible. Cyclic steps: Cl. Created segments are put in the search space. C2. The slutin test is dne. If the cnnectin is cmpleted with the new segments, the prcedure will end successfull y. C3. All existent segments are evaluated in rder t chse the best ne. If the expansin f all segments has been exhausted, the prcedure will end withut a slutin. C4. Successrs f the chsen segment are generated frm its predecessr and are nrmal t it. The successrs g tward the slutin zne when pssible. The MPS used t rute the PCB is based n a Al algrithm with a unidirectinal heuristic search, which we have built befre. There are sme differences between the systems. The main ne is that the unidirectinal methd cnnects terminals sequentially (the first tw terminals are cnnected; afterward the third is cnnected t the previus unin, and s n until the last

5 DISTRIBUTED PRODUCTION SYSTEM FOR ROUTING 189 cnnectin in the bard, each searcher will create and handle a tree f segments related.t each terminal, selecting a segment f that tree in each iteratin. The selectin will be made by means f an evaluatin functin, previusly determined frm the prblem heuristic. When the verifier mdule f the system finds a cllisin pint, it sends this pint t the searchers invlved in the cllisin. Then each searcher will answer by giving the sequence f segments that link the cllisin pint t the rt 01' its tree (i.e., the terminal). The dispsitin f elemental prcesses fr the searcher is shwn in Fig. 3. U. > ~ as : 'g :: :g] u.. '" ~E.s S OIJ '"ti - ;.:a.j:>.~ C,) I '" < '" Q eu) f; ;, u Bu... :: ::..ci :I: «~ '" ~ '" u... ~... ~ ;>, Ruter The ruter task is generating the sllccessrs 01' the segrnent selected by an elemental searcher. It acts in the rllwing way: When it receives a generatin inquiry frrn the searcher, it answers by sending the set f successrs f the requested segrnent. T carry Ollt that runctin, the ruter expands each successr f the requested segrnent until it finds an bstac1e. The set f successr segments is sent t bth the searcher and the verifier. There are tw ways f dividing the ruter blck in elemental prcesses: the hrizntal methd, which assigns a ruter prcess t a zne f the bard, and.the vertical methd, which assigns a ruter prcess t each side f the bard. The hrizntal the divisin explits a gemetric parallelism, and the vertical explits an event parallelism. We have chsen the last ne, because it is mre efficient. Figure 4 shws the blck ruter decmpsitin. prcess is t drive a generatin message t a specific ruter. The task f "assign" :I: C,) «U) 1 ::>... :I: C,) «U) Verifier The wrk f this blck is t d.a cllisin test, t verify whether the paths btained frm different searches jin each ther. Figure 5 shws the descmpsitin f the verifier blck. In this case the decmpsitin cnsidered is the hrizntal ne. It is interesting t bserve that the decmpsitin f bth the ruter and verifier mdules in elemental prcesses is related t the characteristics f the prblem and nt t the mdel prpsed fr the PS, whereas the decmpsitin f the searcher mdel is related t the multidirectinal strategy. 188 :: N Z«el

6 : ASStGN ~ ~ B FIGURE 5. Prcesses structure fr the verifier, hrizntal decmpsitin... lo.. I!'.. lo HORIZONTAL SEARCH ASSIGN HORIZONTAL VERIFtER VERTl CAL VERTICAL FIGURE 4. Prcesses structure fr the ruter, vertical decmpsitin.

7 .> DISTRIBUTED PRODUCTION SYSTEM FOR ROUTING M. DE PEDRO ET AL. REFERENCES Duda, R. 0.,1. G. Gaschnig, and P. E. Hart, Mdel design in the PROSPECTOR cnsultant system fr mineral explratin, in Expert Systems in the Micr Electrnic Age, Edinburgh University Press, Edinburgh, Sctland, Gupta, A., Parallelism in Prductin Systems: The Surces and the Expected Speedup, tech rep., Cmput. Dep., Carnegie-Melln Univ., Hmewd, M., D. Mau, D. Shepherd, and R. Shepherd, The IMS T800 Transputer. IEEE Micr, Vl. 7(5) 10-26, Jbbani, R., and D. P. Siewirek, Wearver: A Knwledge-Based Ruting Expert, 22nd Design Autmatin Cnference IEEE, McDermtt, J., Rl: A Rule-Based Cnfigurer f Cmputer Systems, tech rep., Cmput Dep., Carnegie-Melln Univ., Pittsburgh, PA., Shrtliffe, E. H., Cmputer-Based Medical Cnsultatins: MYCIN, Nrth-Hlland, Amsterdam, Stlf, S. J., Initial Perfrmance f the DAD02 Prttype, Cmputer IEEE, Vl. 20(1), 75-83, Uhr, L., Multi-Cmputer Architeáures fr Artificial lntelligence: Tward Fast, Rbust, ParaUel Systems, Wiley, New Yrk, SYSTEM IMPLEMENTATION AND RESULTS The parallel architecture explained befre has been implemented emplying transputers as prcessing elements. In practice, blck diagrams shwn befre have been adapted in rder t accmmdate and explit the specific features f transputers. Actually, a prttype f the special-purpse machine has been built up with five transputers. Cnsidering the cmputing needs, the assigning f prcesses t prcessrs has been dne as fllws: ne fr the rganizer, ne fr the ruter, ne fr the verifier, and tw fr the searcher. Presently, the machine slves nly a cnnectin. The speeding up btained with the experimental results ranges frm 8 t 40 times. This encuraging result allws us t expect higher acceleratins with the current prttype, which will slve the glbal ruting. DISCUSSION In rder t explit efficiently the ptential reductin in cmputer time that the algrithms with a multidirectinal strategy ffer, strategies are needed t influence the searches s that the terminatin ccurs early. This will be achieved if each search is well driven int a different subspace f the glbal ptential slutins space. On the ther hand a substantial reductin in running time can be btained by implementing the multidirectinal strategy in parallel. Hwever, all this des nt mean that a multidirectinal strategy, implemented in a parallel way, runs faster than its crrespnding unidirectinal strategy. There are tw causes f cmputatinal verheads, ne due t the multidirectinality and the ther due t the parallelism. The first cause lies with the fact that, nrmally, additinal cmputatins are needed t guarantee that ndes belnging t every search tree are different. The secnd cause is related t the cmmunicatins needed amng the cncurrent prcesses. Evidently, these tw causes are related t each ther. In the situatin that we have explained here, the generatin knwledge guarantees the independence f the search subspaces; every search tree has different ndes. This fact avids cmputatinal verhead due t the multidirectinality.