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Frequently Asked Questions (FAQS);faqs.060 John Beasley has posted information on his OR-Lib, which contains various optimization test problems. Send e-mail to umtsk99@vaxa.cc.imperial.ac.uk to get started. Or have a look in the Journal of the Operational Research Society, Volume 41, Number 11, Pages 1069-72. There are various test sets for NLP (Non-Linear Programming). Among those I've seen mentioned are - ACM TOMS (Transactions on Mathematical Software), V13 No3 P272 - publications (listed in another section of this list) by Schittkowski; Hock & Schittkowski; Floudas & Pardalos; Torn; Hughes & Grawiog. Many of the other references also contain various problems that you could use to test a code. The modeling language GAMS comes with about 100 test models, which you might be able to test your code with. -------------------------------------------------------------------------- 5. "What is MPS format?" A: MPS format was named after an early IBM LP product and has emerged as a de facto standard ASCII medium among most of the various commercial LP codes. You will need to write your own reader routine for this, but it's not too hard. The main things to know about MPS format are that it is column oriented (as opposed to entering the model as equations), and everything (variables, rows, etc.) gets a name. MPS format is described in more detail in Murtagh's book, referenced in another section. Here is a little sample model, explained in more detail below: NAME METALS ROWS N VALUE E YIELD L FE L MN L CU L MG G AL L SI COLUMNS BIN1 VALUE 0.03 YIELD 1. BIN1 FE 0.15 CU .03 BIN1 MN 0.02 MG .02 BIN1 AL 0.7 SI .02 BIN2 VALUE 0.08 YIELD 1. BIN2 FE .04 CU .05 BIN2 MN .04 MG .03 BIN2 AL .75 SI .06 BIN3 VALUE 0.17 YIELD 1. BIN3 FE .02 CU .08 BIN3 MN .01 AL .8 BIN3 SI .08 BIN4 VALUE 0.12 YIELD 1. BIN4 FE .04 CU .02 BIN4 MN .02 AL .75 BIN4 SI 0.12 BIN5 VALUE 0.15 YIELD 1. BIN5 FE .02 CU .06 BIN5 MN .02 MG .01 BIN5 SI .02 AL .8 ALUM VALUE 0.21 YIELD 1. ALUM FE .01 CU .01 ALUM AL .97 SI .01 SILCON VALUE 0.38 YIELD 1. SILCON FE .03 SI .97 RHS ALOY1 YIELD 2000. FE 60. ALOY1 CU 100. MN 40. ALOY1 MG 30. AL 1500. ALOY1 SI 300. BOUNDS UP PROD1 BIN1 200.00 UP PROD1 BIN2 750.00 LO PROD1 BIN3 400.00 UP PROD1 BIN3 800.00 LO PROD1 BIN4 100.00 UP PROD1 BIN4 700.00 UP PROD1 BIN5 1500.00 ENDATA MPS is an old format, so it is set up as though you were using punch cards, and is not free format. Fields start in column 1, 5, 15, 25, 40 and 50. Sections of an MPS file are marked by so-called header cards, which are distinguished by their starting in column 1. Although it is typical to use upper-case throughout the file (like I said, MPS has long historical roots), many MPS-readers will accept mixed-case for anything except the header cards, and some allow mixed-case anywhere. The NAME card can be anything you want. The ROWS section defines the names of all the constraints; entries in column 2 or 3 are E for equality rows, L for less-than ( <= ) rows, G for greater-than ( >= ) rows, and N for non- constraining rows (the first of which would be interpreted as the objective function). The largest part of the file is in the COLUMNS section, which is the place where the entries of the A-matrix are put. All entries for a given column must be placed consecutively, although within a column the order of the entries (rows) is irrelevant. Rows not mentioned for a column are assumed to have a coefficient of zero. The RHS section allows one or more right-hand-side vectors to be defined; most people don't bother having more than one. In the above example, its name is ALOY1, and has non-zero values in all 7 of the constraint rows of the problem. Rows not mentioned are assumed to have a right-hand-side of zero. The optional BOUNDS section lets you put lower and upper bounds on individual variables (no * wildcards, unfortunately), instead of having to define extra rows in the matrix. All the bounds that have a given name in column 5 are taken together as a set. Variables not mentioned in a BOUNDS set are taken to be non-negative. There is another optional section called RANGES that I won't go into here. The final card must be the ENDATA, and yes, it is spelled funny. For comparison, here is the same model written out in equation format. Minimize VALUE: 0.03 BIN1 + 0.08 BIN2 + 0.17 BIN3 + 0.12 BIN4 + 0.15 BIN5 + 0.21 ALUM + 0.38 SILCON Subject To YIELD: BIN1 + BIN2 + BIN3 + BIN4 + BIN5 + ALUM + SILCON = 2000 FE: 0.15 BIN1 + 0.04 BIN2 + 0.02 BIN3 + 0.04 BIN4 + 0.02 BIN5 + 0.01 ALUM + 0.03 SILCON <= 60 MN: 0.02 BIN1 + 0.04 BIN2 + 0.01 BIN3 + 0.02 BIN4 + 0.02 BIN5 <= 40 CU: 0.03 BIN1 + 0.05 BIN2 + 0.08 BIN3 + 0.02 BIN4 + 0.06 BIN5 + 0.01 ALUM <= 100 MG: 0.02 BIN1 + 0.03 BIN2 + 0.01 BIN5 <= 30 AL: 0.7 BIN1 + 0.75 BIN2 + 0.8 BIN3 + 0.75 BIN4 + 0.8 BIN5 + 0.97 ALUM >= 1500 SI: 0.02 BIN1 + 0.06 BIN2 + 0.08 BIN3 + 0.12 BIN4 + 0.02 BIN5 + 0.01 ALUM + 0.97 SILCON <= 300 and 0 <= BIN1 <= 200 0 <= BIN2 <= 750 400 <= BIN3 <= 800 100 <= BIN4 <= 700 0 <= BIN5 <= 1500 -------------------------------------------------------------------------- 6. "What software is there for non-linear optimization?" A: I don't claim as much expertise in this area, but the question is frequent enough to be worth addressing. If I get enough feedback, this section might grow large enough to need to be split off as a separate FAQ list. It's unrealistic to expect to find one general NLP code that's going to work for every kind of nonlinear model. Instead, you should try to find a code that fits the problem you are solving. Nonlinear solution techniques can be divided into various categories, such as unconstrained, linearly constrained, convexly constrained, or general. If your problem doesn't fit in any category except "general", or you insist on a proven optimal solution (except when there no chance of multiple local minima), you should be prepared to have to use a method that boils down to exhaustive search, i.e., you have an intractable problem. See the comments in the MIP section on Simulated Annealing and Genetic Algorithms. Several of the commercial LP codes referenced above have specialized routines, particularly for Quadratic Programming (QP, linear constraints with a quadratic objective function). Many nonlinear problems can be solved (or at least confronted) by application of a sequence of LP or QP approximations. There is an ACM TOMS routine for QP, #587, available from the netlib server, in directory /netlib/toms. See the section on test models for detail on how to use this server. There is a directory, /netlib/opt, on the netlib server containing a collection of optimization routines. At my last check, I saw - "praxis" (unconstrained optimization, without requiring derivatives) - "tn" (Newton method for unconstrained or simple-bound optimization) - "ve08" (optimization of unconstrained separable function). - "simann" (unconstrained optimization using Simulated Annealing) - "vfsr" (constrained optimization using Simulated Annealing) Again, see the section on test models for detail on how to use this server. Here is a summary of codes mentioned in newsgroups in the past year, not sorted into categories. - MINOS - Stanford University, Office of Technology Licensing, 415-723-0651. This code is often used by researchers as a "benchmark" for others to compare with. - NPSOL - Stanford University, Office of Technology Licensing, 415-723-0651. - QPSOL - Stanford University, Office of Technology Licensing, 415-723-0651. - NAG Library routine E04UCF. - IMSL routine UMINF and UMIDH. - Harwell Library routine VF04. - Hooke and Jeeves algorithm - reference? - MINPAK I and II - Contact Steve Wright, wright@mcs.anl.gov - GENOCOP - Genetic algorithm, Zbigniew Michalewicz, zbyszek@mosaic.uncc.edu said to be available by ftp at unccsun.uncc.edu (152.15.10.88). - DFPMIN - Numerical Recipes (Davidon-Fletcher-Powell) - Amoeba - Numerical Recipes - Brent's Method - Numerical Recipes - FSQP - Contact Andre Tits, andre@src.umd.edu. Said to be free of charge to academic users. - CONMIN - Vanderplaats and Associates, Goleta CA - NOVA - DOT Products, Houston TX - GRG2 - Leon Lasdon, University of Texas, Austin TX - GINO - LINDO Systems, Chicago, IL -------------------------------------------------------------------------- 7. "What references are there in this field?" A: Too many to count. Here are a few that I like or have been recommended on the net. I have *not* reviewed them all. General reference [1] - Nemhauser, Rinnooy Kan, & Todd, eds, Optimization, North-Holland, 1989. (Very broad-reaching, with large bibliography. Good reference; it's the place I tend to look first. Tough sledding for beginners.) LP - Chvatal, Linear Programming, Freeman, 1983. (I find it hard to whole- heartedly recommend any one LP textbook, but this is one I'd probably use in teaching an undergraduate course.) - Hughes & Grawiog, Linear Programming: An Emphasis on Decision Making, Addison-Wesley, 1973. - Luenberger, Introduction to Linear and Nonlinear Programming, Addison Wesley, 1984. (Updated version of an old standby.) - Murtagh, B., Advanced Linear Programming, McGraw-Hill, 1981. (Good one after you've read an introductory text.) - Schrijver, Theory of Linear and Integer Programming, Wiley. - Williams, H.P., Model Building in Mathematical Programming, Wiley 1985. (Little on algorithms, but excellent for learning what makes a good model.) Interior Point LP - Marsten, et al., "Interior point methods for linear programming", Interfaces, pp 105-116, July-August 1990. (Introductory article, written by authors of a good commercial code.) - Marsten, et al., article to appear in ORSA Journal on Computing, 1993. (The latest results; a tech report version may be available sooner.) - Wright, M., "Interior methods for constrained optimization", Acta Mathematica, Cambridge University Press, 1992. (Survey article.) There is also a bibliography (with over 1000 entries!?!) obtainable by mailing to "netlib@ornl.gov" and saying "send intbib.bib from bib". Nonlinear Programming (can someone help classify these more usefully?) - Bazaraa & Shetty, Nonlinear Programming, Theory & Applications. - Coleman & Li, Large Scale Numerical Optimization, SIAM Books. - Dennis & Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, 1983. - Fiacco & McCormick, Sequential Unconstrained Minimization Techniques, SIAM Books. (An old standby, given new life by the interior point LP methods.) - Fletcher, R., Practical Methods of Optimization, Wiley 1987. (Good reference for Quadratic Programming, among other things.) - Floudas & Pardalos, A collection of test problems for constrained optimization algorithms, Springer-Verlag, 1990. - Gill, Murray & Wright, Practical Optimization, Academic Press, 1981. (An instant NLP classic when it was published.) - Hock & Schittkowski, Test Examples for Nonlinear Programming Codes, Springer-Verlag, 1981. - Kahaner, Moler & Nash, Numerical Methods and Software, Prentice-Hall. - More, "Numerical Solution of Bound Constrained Problems", in Computational Techniques & Applications, CTAC-87, Noye & Fletcher, eds, North-Holland, 29-37, 1988. - More & Toraldo, Algorithms for Bound Constrained Quadratic Programming Problems, Numerische Mathematik 55, 377-400, 1989. - Schittkowski, Nonlinear Programming Codes, Springer-Verlag, 1980. - Torn & Zilinskas, Global Optimization, Springer-Verlag, 1989. Other publications - Forsythe, Malcolm & Moler, Computer Methods for Mathematical Computations, Prentice-Hall. -Hansen, Global Optimization Using Interval Analysis, Marcel Dekker, 1991(?). (I'd be interested if anyone has any opinions on this one.) - Kennington & Helgason, Algorithms for Network Programming, Wiley, 1980. (A special case of LP.) - Kirkpatrick, Gelatt & Vecchi, Optimization by Simulated Annealing, Science, 220 (4598) 671-680, 1983. - Press, Flannery, Teukolsky & Vetterling , Numerical Recipes, Cambridge, 1986. (Comment: use with care.) -------------------------------------------------------------------------- 8. "Just a quick question..." Q: What is a matrix generator? A: This is a code that creates input for an LP (or MIP, or NLP) code, using a more natural input than MPS format. There are no free ones. Big names in this area are GAMS (Scientific Press), LINGO (LINDO Systems), and AMPL (information is in netlib/opt on the Netlib server). These products have links to various solvers (commercial and otherwise). Q: How do I diagnose an infeasible LP model? A: A model is infeasible if the constraints are inconsistent, i.e., if no feasible solution can be constructed. It's often difficult to track this down. The cure may even be ambiguous: is it that some demand was set too high, or a supply set too low? A useful technique is Goal Programming, one variant of which is to include two explicit slack variables (positive and negative) with huge cost coefficients, in each constraint. The revised model is guaranteed to have a solution, and you can look at which rows have slacks that are included in the "optimal" solution. By the way, I recommend a Goal Programming philosophy even if you aren't having trouble with feasibility; "come on, you could probably violate this constraint for a price." Q: I want to know specifically which constraints contradict each other. A: This may not be a well posed problem. If by this you mean you want to find the minimal set of constraints that should be removed to restore feasibility, this can be modeled as an Integer LP (which means, it's potentially a hard problem). Start with a Goal Programming approach as outlined above, and introduce some 0-1 variables to turn the slacks off or on. Then minimize on the sum of these 0-1 variables. Q: I just want to know whether or not there *exists* a feasible solution. A: Finding out if a model has a feasible solution is essentially as hard as finding the optimal solution (within a factor of 2 on average, in terms of effort in the Simplex Method). There are no shortcuts in general, unless you know something useful about your model's structure. Q: I have an LP, except it's got several objective functions. Help! A: This is indeed a difficult class of model. Fundamental to it is that there may be no unique solution. Approaches that have worked are Goal Programming (treat the objectives as constraints with costed slacks), Pareto preference analysis, and forming a composite objective from the real ones. There is a section on this whole topic in Reference [1]. My general advice is to attempt to cast your model in terms of dollars and cents wherever possible; sometimes the multiple objectives disappear! 8v) Q: I have an LP that has large almost-independent matrix blocks that are linked by a few constraints. Can I take advantage of this? A: In theory, yes. See section 6.2 in Reference [1] for a discussion of Dantzig-Wolfe decomposition. However, I am unaware of any commercial codes that will help you do this, so you'll have to create your own framework and then call your chosen LP solver to solve the subproblems. The folklore is that generally such schemes take such a long time to converge that they're slower than just solving the model as a whole. My advice, unless your model is so huge that a good solver can't handle it, is to not bother decomposing it. (It's probably more cost effective to upgrade your solver, if that's why you can't solve it, than to invest your time.) Q: I need to find all integer points in a polytope. A: There is no known way of doing this efficiently. A related question is how to find all the vertices of an LP, with the same pessimistic answer. The book by Schrijver is said to discuss this. Q: Are there any parallel LP codes? A: IBM has announced a parallel Branch and Bound capability in their package OSL, for use on clusters of workstations. "This is real, live commercial software, not a freebie. Contact forrest@watson.ibm.com". Jeffrey Horn (horn@cs.wisc.edu) recently compiled a bibliography of papers relating to research on parallel B&B. I'm not aware of any implementations (beyond the "toy" level) of simplex or interior-point solvers on parallel machines. Q: From a roll of cloth of given width and unlimited length, cut out ... A: You are referring to the Cutting Stock (or Trim Loss) problem. It is in most LP textbooks, or Reference [1]. I think it's an interesting problem, because the model formulation hinges on how you generate the variables of the eventual LP; you can't really just write down the equations. This trick of so-called Column Generation is used in diverse other problems such as airline crew scheduling. A related idea, Constraint Generation, is used to solve the Traveling Salesman Problem. Q: I am trying to solve a Traveling Salesman Problem ... A: I knew you'd ask that. Look at the bibliography in the Integer Programming section of Reference [1], particularly the ones with the names Groetschel and/or Padberg in them. TSP is a famously hard problem that has attracted many of the best minds in the field. I don't believe there are any commercial products to solve this problem. Q: I heard about this new Russian algorithm for Traveling Salesman Problems. A: You are speaking of Khachian's method for LP, published in 1979. It was the first LP algorithm to have a polynomial bound on the amount of work. Though important theoretically, it has had no impact in practice, because the polynomial bounds are huge. It works by surrounding the solution space with a sequence of shrinking ellipsoids. There continues to be research done on this method, for NLP. The connection to TSP is false, brought about by an erroneous New York Times article back then. Q: I need to do post-optimal analysis. A: Many commercial LP codes have features to do this. Also called Ranging or Sensitivity Analysis, it gives you information about how much the coefficients in the problem could change without affecting the nature of the solution. Most LP textbooks, such as Reference [1], describe this. -------------------------------------------------------------------------- 9. "Who maintains this FAQ list?" A: John W. Gregory LP Specialist (it says that on my business card, it must be true!) Applications Department Cray Research, Inc. Eagan, MN 55121 USA jwg@cray.com 612-683-3673 I suppose I should say something here to the effect that "the material in this document does not reflect any official position taken by Cray Research, Inc." Also, "use at your own risk", "no endorsement of products mentioned", etc., etc. I probably should have scattered more "IMHO"s around in the text, but that acronym seems weaselly and once you start it's hard to know where to stop. I should have put in a few more smilies here and there too, to assist the humor impaired - be on your toes. 8v) I've tried to keep my own biases (primarily, toward the high end of computing) from dominating what I write here, and other viewpoints that I've missed are welcome. Suggestions, corrections, topics you'd like to see covered, and additional material (particularly on NLP) are solicited. Comments to the effect "who died and made *you* optimal?" will likely result in you getting stuck with maintaining the FAQL instead of me. 8v) I regret that when I started this list I didn't keep careful track of all the contributors whose knowledge I tapped. In several instances, the information herein comes from postings on the net, which I assumed to be fair use and in the public domain. It being too late now to make individual acknowledgements, I offer a blanket THANKS to all who have posted on these topics to the net. This FAQL is also being posted to news.answers, which is archived in the periodic posting archive on pit-manager.mit.edu [18.172.1.27], in the anonymous ftp directory /pub/usenet/news.answers. Copies of this FAQL may be made freely, as long as it is distributed at no charge and with this disclaimer included. -------------------------------------------------------------------------- END lp_faq Xref: bloom-picayune.mit.edu alt.locksmithing:2310 news.answers:4507 Path: bloom-picayune.mit.edu!enterpoop.mit.edu!biosci!uwm.edu!linac!pacific.mps.ohio-state.edu!zaphod.mps.ohio-state.edu!cs.utexas.edu!sun-barr!olivea!uunet!world!spike From: spike@world.std.com (Joe Ilacqua) Newsgroups: alt.locksmithing,news.answers Subject: alt.locksmithing answers to Frequently Asked Questions (FAQ) Summary: This post gives answers to many of the common questions asked. It is strongly recommended that it be read before posting to this group. Message-ID: <locksmith-faq_723942608@world.std.com> Date: 9 Dec 92 23:10:11 GMT Expires: Fri, 22 Jan 1993 23:10:08 GMT Reply-To: alt-locksmithing-faq@world.std.com Followup-To: alt.locksmithing Organization: Software Tool & Die Lines: 494 Approved: news-answers-request@MIT.Edu Supersedes: <locksmith-faq_719681553@world.std.com> Archive-name: locksmith-faq Last-modified: 92/10/20 Version: 1.0 [This was written and posted a few times early this summer. We have final gotten ready for news.answers and it will now be a monthly posting ->Spike] This FAQ does not attempt to teach you locksmithing, just to answer simple questions, give you some hints on getting started, and point you to sources of information. Also included is a glossary of common terms. The Appendix covers many supply places, books and tapes. Questions Answered: 1. Where can I get a lock pick set? 2. How can I make my own picks and tension wrenches? 3. Is it legal to carry lock picks? 4. Where can I get the "MIT Guide to Picking Locks"? 5. What books can I get on locksmithing? 6. What are "pick guns" or "automatic pickers" and do they work? 7. How do I open a Kryptonite lock? 8. How can I get keys stamped "DO NOT DUPLICATE" duplicated? 9. Do Skeleton Keys Exist? 10. Should I bother with high security ("pick proof") locks for my home? 11. What should I do after I read a book? 12. How do I continue learning about locksmithing? 13. How do Simplex pushbutton locks work? 14. What is the "shear line". Glossary Appendix of sources, books, videotapes. Credit & Thanks 1. Where can I get a lock pick set? Try a locksmith supply house. Look under "Locksmiths' Equipment & Supplies" in the Yellow Pages. Your State or the company may have requirements, such as having to prove you are a locksmith or showing a drivers license; call and find out. Also look for mail order houses in the Appendix. 2. How can I make my own picks and tension wrenches? You can file or grind picks out of spring steel. It is best to use spring steel - sources include hacksaw blades, piano (music) wire, clock springs, streetsweeper bristles (which can be found along the street after the sweeper has passed), etc. In a pinch safety pin steel, or even a bobby pin (much worse) can be used. When grinding, keep the steel from getting so hot as to anneal (soften) it. You may have to re-harden/re-temper it. (See a book on knife making, gunsmithing, or machine shop practice for a discussion on heat treating steel.) Some people prefer a rigid tension wrench and just bend a small screwdriver for this, but many prefer a slightly flexible wrench and use spring steel. The "MIT Guide to Picking Locks" and the "Eddie The Wire" books (see below) cover making these tools. There are many places you can buy picks and tension wrenches. See the appendix. 3. Is it legal to carry lock picks? This depends on where you are. In the U.S. the common case seems to be that it is legal to carry potential "burglar tools" such as keys, picks, crowbars, jacks, bricks, etc., but use of such tools to commit a crime is a crime in itself. Call your local library, district attorney, or police department to be sure. Places where it *is* illegal to carry lock picks: The District of Columbia. 4. Where can I get the "MIT Guide to Picking Locks"? You can't. The guide must exist in an online form, but no one seems to have it. Rumor has it that (one of) the author(s) is aware of this group and is unwilling to post the guide. The guide is copyrighted, so scanning it in and posting would, in addition to violating the author's wishes, be illegal. 5. What books can I get on locksmithing? An excellent encyclopedic reference (based on reading the 1st edition - but people have said that the 2nd and 3rd editions carry on the coverage) The Complete Book of Locks & Locksmithing, 3rd Ed. C.A. Roper and Bill Phillips TAB Books ISBN 0-8306-3522-X (Paper) 0-8306-?522-1 (Hard) $18.95 (Paper) $26.95 (Hard) also many people think highly of: Eddie The Wire: How to Make Your Own Professional Lock Tools "Eddie The Wire" Loompanics Unlimited ISBN 0-685-39143-4 4 Volumes $20 Your local book store should be able to order these for you. You can find other titles under "Locksmithing" in the Books In Print Subject Index, which any decent bookstore should have. Also see the Appendix. 6. What are "pick guns" or "automatic pickers" and do they work? A "pick gun" is a manual or powered device that uses a vibrating pin to try to bounce the pin tumblers so there are spaces at the shear line so the the plug can rotate. They are not a panacea, aren't always effective, and the net seems to feel that these are no substitute for a little skill with a pick and learning how locks work. 7. How do I open a Kryptonite lock? Easiest: If you registered your lock, call or write Kryptonite for a new key. Or call a local locksmith, they should be able to pick and re-key the lock for you. Easy: Get a car jack and jack it apart. Careful, otherwise it is very possible that you'll damage the bike. Easy: Use a cut-off wheel in a Dremel tool to cut the lock at the hole in the shackle (where there is the least to cut.) Harder: If it doesn't have the newer brass jacket, peel back the plastic coating on the key end, drill out the pin that holds in the cylinder, remove the cylinder, open. Hardest: Chill the metal of the "U" with liquid Nitrogen or Freon, smash with hammer. While this is a "well known" method, it may be an urban legend. 8. How can I get keys stamped "DO NOT DUPLICATE" duplicated? Some locksmiths will take the Nike approach and "Just Do It". Some will even stamp "DO NOT DUPLICATE" on the copy for you. If that doesn't work, label the key by sticking some tape on the "DO NOT DUPLICATE" stamp and try again. 9. Do Skeleton Keys Exists? "Skeleton Keys" are keys ground to avoid the wards in warded locks. There is no analog with modern pin tumbler locks. Master keys may open a large set of locks, but this is designed in when the locks are installed. 10. Should I bother with high security ("pick proof") locks for my home?