Evolving Crushers. P. Hingston L. Barone L. While

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1 Evolvng Crushers P. Hngston L. Barone L. Whle School of Computer and Informaton Scence Edth Cowan Unversty Mt Lawley, WA, Australa Department of Computer Scence & Software Engneerng The Unversty of Western Australa Nedlands, WA, Australa Abstract Ths paper descrbes the use of an evolutonary algorthm to solve an engneerng desgn problem. The problem nvolves determnng the geometry and operatng settngs for a crusher n a commnuton crcut for ore processng. The ntenton s to provde a tool for consultng engneers that can be used to explore canddate desgns for varous scenaros. The algorthm has proved capable of dervng desgns that are clearly superor to exstng desgns, promsng sgnfcant fnancal benefts. Keywords: Evolutonary algorthms, evoluton strateges, engneerng desgn. I. INTRODUCTION Evolutonary algorthms are ncreasngly fndng applcatons n engneerng desgn tasks. In ths paper we descrbe a study, supported by Ro Tnto Ltd, whch uses evolutonary algorthms to optmse the performance of a commnuton crcut for ore processng. Ths study clearly demonstrates the strengths of the evolutonary approach. The performance of a processng plant has a large mpact on the proftablty of a mnng operaton, and yet plant desgn decsons are often guded more by engneerng ntuton and prevous experence than by analyss. Ths s because plants are extremely complex to model, so engneers often must rely on smulaton tools to evaluate and compare alternatve hand-crafted desgns. Ths s a tme-consumng process and the lack of an analytcal model means that there s lttle theoretcal gudance to narrow the search for better solutons. Evolutonary algorthms can be of great beneft here, provdng a means to search large desgn spaces and present the engneer wth superor desgns optmsed for dfferent operatng scenaros. In order to test the applcablty of evolutonary algorthms n ths settng, a representatve problem was chosen by Ro Tnto. The task was to fnd combnatons of desgn varables (ncludng geometrc shapes and machne settngs) to maxmse the capacty of a smple commnuton crcut, whlst also mnmsng the sze of the product. We begn the paper wth a descrpton of the problem, ncludng a bref background on crushers and commnuton crcuts. Secton III descrbes our mappng of the problem to an evolutonary algorthm, ncludng the genetc representaton, genetc operators and selecton methods. Secton IV presents some llustratve results. Fnally, we dscuss future enhancements to the system and plans to extend the work to nclude greater complexty n the smulaton model, ncludng crcuts. II. BACKGROUND Crushng and grndng of rocks and other partcles has many mportant applcatons, ncludng coarse crushng mned ore and quarry rock, fne grndng of coal for power staton bolers, and for producton of pant, ceramcs, cement and other materals. It has been estmated that several bllon tons of materal s crushed and ground annually ([1]). Thus optmsaton of crushng operatons offers large potental economc benefts. For example, n the area of energy savngs, Naper-Munn et al ([2], p1) quote a report of the U.S. Natonal Materals Advsory Board n 1981, whch estmated that realstc mprovements n crushng-related actvtes could result n energy savngs of more than 20 bllon kwh per annum. Other benefts of optmsaton of crushng and grndng n mneral processng operatons nclude reduced operatng costs, ncreased throughput and thus value producton, and mproved downstream performance. A. Crushers and Crcuts In ths secton, we provde a bref background on crushers and how they are used n commnuton crcuts. The nterested reader could consult, for example, [2] for more detaled nformaton. Commnuton refers to the collecton of physcal processes that can be appled to a stream of ore to change the sze of the partcles n the stream. Examples nclude crushng and grndng (whch break ore partcles nto smaller partcles), and screenng (whch separates ore nto several streams of dfferent partcle szes). The purpose of commnuton s to transform raw ore nto a more usable or more saleable product or to prepare t for further processng. A commnuton crcut conssts of a collecton of processng unts (crushers, screens, etc) connected together (by conveyor belts, for example), possbly contanng loops (hence the use of the word crcut ). One or more streams of ore (the feed ) enter the crcut and one or more streams of transformed materal (the product ) ext the crcut.

2 Feed Crusher Product screen Oversze (+32mm) -32mm Product Stockple Fgure 1 - The smple crcut used n ths study Fgure 1 shows the smple crcut that was used n ths study. The feed comes n on a conveyor from the top left and enters the crusher. The crushed ore s then passed through a screen that allows partcles less than 32 mm to pass through and report to product. Partcles larger than ths (the oversze ) are recycled back to the crusher. Thus the nput to the crusher s a combnaton of feed and recrculatng oversze. The type of crusher used here s a cone crusher. Fgure 2 s a schematc dagram of a typcal cone crusher. Materal s ntroduced nto the crusher from above, and s crushed as t flows downwards through the machne. The nner crushng surface, or mantle, s mounted on the concal crushng head and s drven n an eccentrc moton swvellng around the axs of the machne. The outer crushng surface, or bowl, s held statonary. Materal flows nto the crushng chamber from above, and s crushed between the two surfaces by compressve forces due to the eccentrc moton. After compresson, the chamber wdens and allows materal to flow to lower parts of the crushng chamber, and eventually to fall through and ext the machne. The gap between the bowl and the crushng head at the closest pont n the cycle s called the closed-sde settng. Ths can be reduced to obtan a narrower chamber and fner crushng. The two crushng surfaces are covered by replaceable steel lners (shaded n Fgure 2), whch can be manufactured wth dfferent cross-sectonal shapes. The eccentrc angle and speed of revoluton of the head can also be adjusted. These varables contrbute to the performance characterstcs of the crusher. B. Smulatng Crushers Ftness s evaluated usng a smulaton of a sngle cone crusher. The nputs to the smulaton are the: Physcal propertes of the feed (composton, hardness etc); Sze dstrbuton of the feed (the proporton of partcles n dfferent sze fractons); Geometry of the mantle and bowl lners; Closed-sde settng; Rotatonal speed of the head; and Eccentrc angle of the head. The fnal four of these were chosen as the desgn varables for the chosen problem. The outputs of the smulaton are the: Sze dstrbuton of the product; Power needed to crush the feed; and Maxmum amount of materal that can flow through the chamber wthout overloadng the crusher (ts capacty ). From these outputs t s possble to calculate the steadystate sze dstrbuton of the product and the capacty of a crcut that ncludes the crusher. These data are used to evaluate the ftness of proposed desgns. Each evaluaton takes approx. 300ms on a 700MHz Pentum III.

3 rpm bowl lner mantle closed-sde settng eccentrc angle Fgure 2 - Schematc dagram of a cone crusher (after [2] Fgure 6.3) III. ALGORITHM The problem descrbed above s well suted to an evolutonary algorthm approach. The problem cannot easly be descrbed analytcally, but a smulaton s avalable that can be used to evaluate canddate solutons. The search space s large too large for an exhaustve search and there s lttle to gude an engneer n determnng good desgns for a gven scenaro. We chose an evoluton strategy approach to tackle ths problem, as t has smlartes wth other problems that have been successfully handled by evoluton strateges. In partcular, canddate desgns can be descrbed usng a vector of real values, and the problem nvolves determnng geometrc shapes. Prevously reported successful applcatons of ths type nclude the desgn of a jet nozzle ([3]) and a flywheel ([4]). The basc evoluton strategy algorthm has the followng steps: 1. Create an ntal populaton of desgns. 2. Evaluate the ftness of the desgns. 3. Create a populaton of chldren by mutatng the members of the current populaton. 4. Evaluate the ftness of the chldren. 5. Select the fttest desgns from the parents and chldren together. 6. Repeat steps 3 to 5 untl done. To mplement a specfc nstantaton of the algorthm, we must specfy the representaton scheme to be used, the method of ftness evaluaton, the nature of the mutaton operators, the selecton mechansm, and the termnaton condton. It may be possble for nfeasble desgns to be generated by mutaton, n whch case we must also specfy how to deal wth these nfeasble desgns. These specfcatons are detaled n the remander of ths secton. A. Ftness The prncpal objectve that we are tryng to maxmse s the capacty of a crcut contanng a gven crusher. The placement of the crusher n a crcut s mportant because a crusher that tself has a hgh capacty may not be sutable f t generates a lot of oversze materal: the presence of ths recrculatng materal reduces the rate at whch feed can be ntroduced nto the crcut. We defne capacty rato to be the rato of the amount of materal enterng the crusher to the amount of feed enterng the crcut (at steady-state operaton). A hgher capacty rato corresponds to more recrculatng materal. The capacty of a crcut may be lmted by one of three factors. 1. The capacty of the crusher. If a crusher has capacty CAP tons/hour and capacty rato CR, the capacty of the crcut wll be lmted by CAP / CR 2. The power requrements of the crusher. A hgh rotatonal speed n partcular delvers a lot of crushng but requres a lot of power. If a crusher wth maxmum power output MP kwh requres P kwh to process a crcut feed of F tons/hour, the capacty of the crcut wll be lmted by F (MP / P) 3. The capacty of the recrculaton conveyor n the crcut. If a crusher has capacty rato CR and the conveyor has a capacty of MR tons/hour, the capacty of the crcut wll be lmted by MR / (CR 1) Each of these factors potentally lmts the capacty of the crcut, therefore the actual capacty wll be the mnmum of these values.

4 Generaton 0 Generaton 20 Generaton 100 Generaton 200 Fgure 3 - A seres of evolved lner pars Notce the potental trade-offs for the varous desgn varables. For example, a large closed-sde settng wll ncrease the capacty of the crusher, but wll also ncrease the amount of recrculatng materal, rasng the capacty rato. Smlarly, a hgh rotatonal speed wll lead to more crushng n each pass through the chamber, but wll also ncrease the power requrements of the crusher, possbly reducng the overall capacty. A secondary am of the process s to mnmse the sze of the product. Specfcally, we defne P80 to be a measure of the sze of the 80 th percentle n the product (.e. the sze k mm such that 80% of the product s smaller than k mm). For techncal reasons, a hgher value of P80 corresponds to a smaller product, so we want to maxmse P80. For the purpose of the experments reported n ths paper, we normalse both capacty and sze fgures by dvdng by the fgures for a standard desgn and settngs. The actual ftness functon that we use s: 0.05 CAP P80 where CAP s the crcut capacty, P80 s the sze measure, and the constants are chosen to equalse the varablty of the two components. Thus the ftness of the standard desgn s 1.0, and hgher ftness s better. B. Intalsaton The populaton s ntalsed wth copes of the exstng standard desgn and settngs. These copes are quckly elmnated n the frst few generatons of a typcal executon. C. Representaton The representaton of the machne settngs closed-sde settng, eccentrc angle and rotatonal speed s straghtforward, these beng real values wthn gven ranges. The best way to represent the geometrc shapes of the two lners s less clear. The shape of each lner s defned by ts vertcal cross-secton. The shape of the machne structure dctates the shape of the back of each lner, so t s only the front of each lner (the actual crushng surface) that s represented. We chose to descrbe each shape as a seres of lne segments, usng a varable-length lst of ponts, each represented by a par of coordnates. The frst coordnate par for the frst segment and the last coordnate par for the last segment are fxed, but each other coordnate s another real-valued object varable. Thus, f there are n lne segments on the mantle and m lne segments on the bowl lner, then the genotype conssts of a vector of real-valued object varables. ( n 1) + 2( 1) 3+ 2 m Fgure 3 shows a seres of lner pars evolved durng a typcal run. The frst par s a standard desgn as mght be suppled by a crusher manufacturer. D. Mutaton When a parent s mutated to produce a chld, each object varable s mutated ndependently usng self-adaptve mutaton rates as descrbed n [5]. Specfcally, each object varable s mutated usng the formula where N ( 0,1) X = X + σ N (0,1) s a normally dstrbuted random value wth mean 0 and standard devaton 1, and each strategy parameter σ s mutated usng the formula where τ σ respectvely. ( ) ( τ N(0,1) + N (0,1) ) = σ exp τ and τ are constants set to 0.25 and 0.1 N 0,1 s sampled once for each ndvdual.

5 In addton, we provded mutaton operators to ncrease or reduce the number of segments n a lner. Whether to apply these operators s determned randomly wth a fxed probablty. The operator to reduce the number of segments randomly selects two adjacent segments to merge and dscards the common end pont. The operator to ncrease the number of segments randomly selects a segment to splt nto two, usng the segment mdpont as the common end pont. Ths was done to allow the algorthm to generate more complex or smpler lner shapes as desred. E. Constrants There are a varety of feasblty constrants upon potental desgns. These can be categorsed as follows: Physcal constrants The sequences of coordnate pars must descrbe shapes that make sense operatonally. In partcular, the lners must have at least a certan thckness to be practcal. Whlst code was developed to enforce ths constrant, we found that t s volated so rarely that t s not worth the computatonal expense to do the checkng. If the fnal soluton returned volates ths constrant, the algorthm can smply be re-run. Settng constrants Each machne settng must be confned to a gven range. Ths s done by repar any value that s too low s set to the mnmum value for that settng, and any that s too hgh s set to the maxmum value. Modelng constrants The crusher smulaton s very complex and assumes (sometme mplctly) that lners have sensble shapes. To keep our desgns n the sensble regon, we mposed a heurstc constrant that the sequence of x-coordnates and the sequence of y-coordnates for each lner must both change monotoncally. Ths constrant s enforced by reparng any coordnate that volates the constrant, at the tme of creaton. Even so, the smulaton occasonally fals. In these cases, the desgn s assumed to be nonsenscal and s assgned an abysmal ftness of 0. F. Selecton Selecton s done usng the standard (λ + µ)-selecton mechansm of evoluton strateges, wth λ = µ = 1. That s, each member of the current generaton becomes the parent of one chld, and the best ndvduals selected from the combned parents and chldren become the next generaton. IV. RESULTS AND DISCUSSION In ths secton, we descrbe an example set of runs of the algorthm that s ndcatve of the performance attaned on test problems. We ran the system ten tmes wth a populaton sze of 50 for 200 generatons on each run. Table 1 shows the performances of the best desgns from these runs. The results show an average ncrease n capacty of around 140%, and around 10% n P80. TABLE 1 - PERFORMANCES OF THE BEST DESIGNS FROM TEN RUNS RELATIVE TO THE STANDARD DESIGN. Run Capacty P80 Ftness Fgure 4 shows how the ftness values and the two components, P80 and capacty, evolve durng a typcal run, Run 10. Improvements n capacty have been scaled down by a factor of 19 to reflect the ftness functon scalng. It can be seen that mprovements tend to be made by favourable tradeoffs between the two components. Fgure 3 shows the best lner pars from selected generatons evolved durng another run. It can be seen that the evolved shapes are dstnctly dfferent from the standard desgn. Whlst engneers can provde a post-hoc ratonale for the revsed desgn, and ths provdes confdence n the valdty of the desgns, t s vrtually mpossble to predct n advance the effect of a change n shape, much less to ntut a hgh qualty desgn for a specfc scenaro. It s worth notng that each run takes only around 30 mnutes. In a real desgn exercse, a runnng tme of several hours (or even days) would stll be very acceptable, so there s plenty of scope for ncreased task complexty n the future. V. FUTURE WORK The work reported here s stll n the early stages of ts development. Whle the results obtaned so far are excellent, many enhancements and extensons are envsaged. The problem descrbed n ths study could be extended to nclude other objectves. Work has begun on a mult-objectve algorthm based on Pareto optmalty, usng the prncples outlned n [6]. Planned enhancements to the crusher smulaton are lkely to make t run an order of magntude slower. We may then need to develop specal strateges to speed up the evolutonary algorthm. One possblty s to use faster, more approxmate models early n the search, usng a scheme smlar to the njecton sland genetc algorthm descrbed n [4].

6 Capacty / P80 / Ftness Capacty P80 Ftness Generaton Fgure 4 - Graph showng ftness evoluton durng Run 10 from Table 1 Another am s to nclude, as part of the task, the desgn of the crcut tself that s, to co-evolve crushers, screens and other processng unts and ther settngs, as well as the pattern of conveyors connectng them together. Ths brngs n elements of network desgn, another applcaton area n whch evolutonary algorthms have been successful (see e.g. [7]). The concurrent desgn of ths network and the machnes wthn t wll be challengng, but the potental rewards are huge. VI. CONCLUSION In ths paper we have descrbed a study n the applcaton of evolutonary algorthms to a dffcult practcal engneerng desgn problem. Our system determnes the lner profles and operatng settngs for a commnuton crcut n an ore processng plant. Intal results are very promsng and ndcate sgnfcant fnancal benefts. In many ways, ths problem s an deal applcaton for evolutonary algorthms. The pay-off s hgh; the problem s too complex to solve analytcally; the search space s too large to explore unaded; we have a well-defned evaluaton functon and a straghtforward representaton scheme, sutable for manpulaton by genetc operators. Many challenges reman n ncorporatng more realsm n the problem defnton (for example, ncludng varety n feed propertes, nteractons wth other plant, etc) and valdatng the predcted performance wth feld trals. VII. ACKNOWLEDGEMENTS Ths work was supported by Ro Tnto Research Grant BTC005. The authors would lke to acknowledge the support and assstance of Ro Tnto Techncal Servces. VIII. REFERENCES [1] F. J. Horns, "Wear measurements n sze reducton machnery," Chemcal Process Engneerng, pp , [2] T. J. Naper-Munn, Morrell, S., Morrson, R.D. & Kojovc, T., Mneral Commnuton Crcuts. Brsbane: Julus Kruttschntt Mneral Research Centre, [3] J. S. Klockgether, H-P., "Two-phase Nozzle and Hollow Core Jet Experments," presented at 11th Symposum on Engneerng Aspects of Magnetohydrodynamcs, [4] D. Eby, Averll, R.C., Punch, W.F. & Goodman, E.D., "Optmal Desgn of Flywheels Usng an Injecton Island GA," Artfcal Intellgence for Engneerng, Desgn, Analyss and Manufacturng, vol. 13, pp , [5] T. Back, Ulrch, H. & Schwefel, H-P., "Evolutonary Computaton: Comments on the Hstory and Current State," IEEE Transactons on Evolutonary Computaton, vol. 1, pp. 3-16, [6] D. Veldhuzen, & Lamont, G, "Multobjectve Evolutonary Algorthms: Analyzng the State-of-the-Art," Evolutonary Computaton, vol. 8, pp , [7] B. Gross, Hammel, U., Maldaner, P., Meyer, A., Roosen, P. & Schutz, M., "Optmzaton of Heat Exchanger Networks by Means of Evoluton Strateges," presented at The Sxth Conference on Parallel Problem Solvng from Nature, 1996.