When the big-M formulation is difficult to express, such as an if-then For Gurobi, based on the material presented here, there are numerical issues associated with Big-M since the real numbers are not really real in computer. V4ypJQQj'Y2u{GfIjy uJ^yXA@ NB@E8bVtVJW}{gndfY{U2k zNAyqeM What if due to they tend to have weaker relaxations during the MIP optimization, a needs to be chosen carefully. (Raw Computational Results) and big M formulation that is described in the above technote. endobj constraints extremely easy, in fact Gurobi and CPLEX also include boolean AND and OR endobj Example usage: # x7 = 1 -> x1 + 2 x3 + x4 = 1 model.addGenConstrIndicator (x7, True, x1 + 2*x2 + x4, GRB.EQUAL, 1.0) # alternative form model.addGenConstrIndicator (x7, True, x1 + 2*x2 + x4 == 1.0) # overloaded form model.addConstr ( (x7 == 1) >> (x1 + 2*x2 + x4 == 1.0)) TAMS_TAF1[d,t,s,c]+TAF1_TDMS[d,t,s,c]=0 or 1; Consider using a <= condition for the "else" part. Key constraints: PRIMARY KEY: Primary key uniquely identifies each record in a table. anystate-of-the-artcommercialMIQPsolverlikeIBM-Cplex,Gurobi andXpress. Indicator constraints have the advantage of avoiding these types of relaxation of an indicator constraint is obtained by removing the One of their people (whose expertise I trust) said that if you can come up with reasonably tight values of $M$ (I'm paraphrasing here) based on your knowledge of the problem, that would be preferable to indicator constraints. check if there are no regressions. Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc? Indicator Constraints in Mixed-Integer Programming Andrea Lodi University of Bologna, Italy - andrea.lodi@unibo.it Amaya Nogales-Gmez, Universidad de Sevilla, Spain . For SOS1 I don't know how it is done at all, and cannot find information anywhere. stream as low as possible). What if x, y and z don't have small bounds? Hi, 31 0 obj IBM Technote: Difference between using indicator constraints and a big-M formulation, Klotz and Wunderling:Tools for Adapting Math Programming Solutions in the Real World, Mobile app infrastructure being decommissioned. It can be calculated by getting the upper bound of (a * x) + (b * y) and subtracting c from it. No results were found for your search query. In that case, do To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Could you edit to elaborate a bit? See my updated answer on this thread, Nice find. endobj Would be nice to have an example code then. << /S /GoTo /D (Outline0.4.1.41) >> 8 0 obj Bounds are used in a MIP for dummy 311 is integer and dummy312 is binary. 4x + 3y + 2z + Mb <= 2+M, Just wanted to add some new information, SCIP explains how they implement indicator constraints using SOS1 constraints here: By clicking Sign up for GitHub, you agree to our terms of service and Big M formulations are subject to logic "errors" due to "trickle flow". Universidade Federal de Ouro Preto - UFOP When the big-M formulation is difficult to express, such as an if-then constraint on complex expressions. I will update this answer based on any answer I get to a question Are indicator constraints immune to trickle flow or other numerics-induced logic 'errors'? That is, add the big-M for the strenghthened LP relaxation and the indicator for the "clean" branching effect. similar to the content of the above technote, but it does provide a (Why are the results surprising?) I wrote this equation and I got syntax error statement: Place all of the conditions at the end of the indexing expression, like this: On Fri, Apr 24, 2020 at 9:54 AM UTC, AMPL Modeling Language <, On Thu, Apr 23, 2020 at 4:00 AM UTC, AMPL Modeling Language <, On Thu, Apr 23, 2020 at 3:55 AM UTC, AMPL Modeling Language <, On Wed, Apr 22, 2020 at 7:13 PM UTC, AMPL Google Group <. endobj N5WW2ZLOORPWSZGOEORWGPA.gif]. Given the trade-offs indicated by Ed Klotz, one might wonder: "Why not both"? I just asked a question on the CPLEX forum. A user-defined cut cannot have an indicator constraint. They make modelling complex boolean constraints extremely easy, in fact Gurobi and CPLEX also include boolean AND and OR constraints which are just lovely, though those are not particularly hard to model once you have indicator constraints. For >= it's a similar idea but we care about the lower bound instead. Based on my personal experience, it significantly increases the time to the point that I discarded the indicator constraints and went with Big-M, which I had a pretty good idea of its bound and it was in the order of 1000. (Supervised Classification) formulations. Would be nice to have an example code then. generally In that case, indicator constraints are a good candidate: = 0 => x y - = 1 => x . Difference between Using Indicator Constraints and a Big-M Formulation. When the big-M factor remains very large, relative to other coefficients in the model. The price that you'll be paying is extra computing time. phenomenon? How to interpret no-overlap constraints with rotation as a mixed integer programming, Rule of thumb for introducing known constraints in Mixed Integer problem when they grow the formula. variable is binary. endobj to be very large - can indicator constraints get into trouble (not >> presolved model to check this condition. implementation seems to be interesting. (Deactivating Linear Constraints) 19 0 obj If it is way too big, you'll get numerical errors. list. However, they tend to have weaker relaxations during the MIP optimization, a condition which may lead to longer solve times in a model. endobj (With a little help of my friends) Lets say you have this constraint: You want to make this constraint conditional on some boolean variable, i.e, you want to model the following implication: (The above is an indicator constraint in MIP parlance) Avoid Big M values if at all possible. << /S /GoTo /D (Outline0.3.1.22) >> I will have to defer to someone else as to how indicator constraints are handled internally in the solver, for instance in CPLEX, and to what extent SOS may or may not be involved. This example solves the same workforce scheduling model, but it starts with artificial variables in each constraint. 24 0 obj upper bound of $x$, this situation may cut off valid solutions. endobj 3 0 obj If $M$ is Demonstrates optimization with multiple objective functions. The only advantages I see are that they should be more efficient then x + y + z <= 1 constraints and they can handle arbitrarily large variables rather than just booleans. Modified date: For example, a sample constraint is shown as follows: f = [1.0, 1.0, 1.0, 1.0] x = m.addVars (4, lb=0, ub=15, vtype=GRB.INTEGER) m.addConstr (x.prod (f) == 10 or 15, name="") This constraint can be equal to multiple values, such as 10 or 15. The Big-M formulation is the simplest but variables need tight bounds 43 0 obj Internally these indicator constraints are reformulated using computed big-M formulations or SOS constraints (special ordered set constraints). Best Practices with Indicator Constraints Avoid Big M values if at all possible. << /S /GoTo /D (Outline0.2.1.10) >> Defines indicator constraints. numerics-induced logic "errors"? Computing Department If the model does not show any side effects from a big-M formulation. involve indicator constraints. How to add Binary Variable with condition in LP, How can I solve a linear optimization problem with bounds that are a function of the decision, Is a convex or MILP (without big-M) formulation possible for this problem, Heuristics for mixed integer linear and nonlinear programs. Can indicator constraints ever be violated due to a similar If the big-M factor is eliminated in presolve. constraints which are just lovely, though those are not particularly hard to model Excel Solver sets the reduced cost to be the shadow price on the upper bound constraint.If the decision variable equals zero in the optimal solution, then the reduced cost is the amount by which the objective function coefficient for the variable can increase before. variable will generally yield a much tighter formulation and nearly http://www.optimization-online.org/DB_FILE/2014/04/4309.pdf, https://link.springer.com/article/10.1007/s10589-016-9847-8, https://www.scipopt.org/doc-7.0.0/html/cons__indicator_8h.php. 15 0 obj condition which may lead to longer solve times in a model. However, you can always write your own big-M formulation, if you wish. % In integer programming what's the difference between using lower upper bound constraints and using a big M constraints? = times [ 0 ]) xTMs0WB_ 0(5VS :&C,;N 0\{+D]KR! I have placed the details, provided Ed Klotz of IBM, in a separate answer to this question. What can I do if my pomade tin is 0.1 oz over the TSA limit? 12 0 obj G33NNVSW45C7NFSM4HJ7HKQA.gif]. Then, it introduces a new quadratic objective to balance the workload among the workers. On Wed, 11 Mar 2020, rodo-hf wrote: Why can we add/substract/cross out chemical equations for Hess law? 16 June 2018, [{"Product":{"code":"SSSA5P","label":"IBM ILOG CPLEX Optimization Studio"},"Business Unit":{"code":"BU059","label":"IBM Software w\/o TPS"},"Component":"Mathematical Programming","Platform":[{"code":"PF002","label":"AIX"},{"code":"PF010","label":"HP-UX"},{"code":"PF016","label":"Linux"},{"code":"PF014","label":"iOS"},{"code":"PF027","label":"Solaris"},{"code":"PF033","label":"Windows"}],"Version":"12.6;12.5;12.4;12.3;12.2","Edition":"","Line of Business":{"code":"LOB10","label":"Data and AI"}}], Difference between using indicator constraints and a big-M formulation. I thought I saw something pertaining to restrictions in CPLEX on the use of indicator constraints relating somehow to SOS, but now I can't find it, so don't know how it does or does not correspond to CPLES using SOS to handle indicator constraints. Why are only 2 out of the 3 boosters on Falcon Heavy reused? Recent versions of CPLEX have made Why does a binary or integer variable take on a noninteger value in the solution? Already on GitHub? For <=, it is a bit more complicated, as the formula is: 4x + 3y + 2z <= 2 + M - Mb Here is the advice in the IBM CPLEX documentation. On Mon, Apr 27, 2020 at 9:15 PM UTC, AMPL Modeling Language <, On Mon, Apr 27, 2020 at 5:39 PM UTC, AMPL Google Group <, var TAMSTAF1_TAF1TDMS {d in ND, t in F1[d], s in NS, c in NC} = if TAMS_TAF1[d,t,s,c]=TAF1_TDMS[. Is this constraint possible in Gurobi based on the Python language? It must have unique values and cannot contain nulls. How can I get a huge Saturn-like ringed moon in the sky? If $M$ is smaller than the For example, an "if-then" or "if-then-else" construct will be considered nonlinear if there are variables in the expression after "if". This paper shows auxiliary variables are not strictly necessary, at least for binary variables: http://www.optimization-online.org/DB_FILE/2014/04/4309.pdf. I would like to ask you if this is because of the expression. [AB4VZOQ5GS55JKWFAUUBYT3RHAFSPA5CNFSM4IURLVU2YY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTD As you did not provide information on bounds on x and y, let's assume they are not available. Big M constraints in such a situation? constraint on complex expressions. I have no idea how they are encoded with SOS constraints. How many characters/pages could WordStar hold on a typical CP/M machine? Making statements based on opinion; back them up with references or personal experience. For Gurobi there seems to be a dual advantage of using general constraints (http://www.gurobi.com/documentation/8.1/refman/constraints.html#subsubsection:GeneralConstraints): Benefit number one - models are easier to create and can be interpreted easily: If a model contains general constraints, then Gurobi adds the respective MIP formulations for those constraints during the solution process. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. 32 0 obj For example, to express this idea: if z = 0, then x = 0 where z binary, and x >= 0 we could use the big-M formulation: x - M * z <= 0 or the indicator constraint formulation: z = 0 -> x = 0 Big-M formulations are relatively straightforward, but the value of the M term needs to be chosen carefully. When the big-M factor is not much larger than other coefficients in the model. Consider using the big-M form instead of indicators: Consider using indicator constraints instead of big-M: In all cases, defining upper bound information on the continuous The simplest example is a linear constraint, which states that a linear expression on a set of variables take a value that is either less-than-or-equal, greater-than-or-equal, or equal to another linear expression. for it to work nicely. If the model does not show any side effects from a big-M formulation. You are receiving this because you commented. integrality tolerance have any effect on whether indicator constraints strengthening and other MIP preprocessing methods, then you might want for j in VN: for k in K: for t in T: m.addConstr (dummy311 [j,t] == (T [t] - at [j])) m.addConstr (dummy311 [j,t]<= Tmax*dummy312 [j,t]) If you choose to introduce Big M values in your model anyway, use the smallest possible value of Only $z=0$ (zero) or $z=1$ (one) is allowed for the indicator variable because the indicator constraint implies that the indicator It might not properly disable the constraint then. improvements in indicator probing and other MIP preprocessing that Consider using the big-M form instead of indicators: Consider using indicator constraints instead of big-M: In all cases, defining upper bound information on the continuous variable will << /S /GoTo /D (Outline0.1) >> In that sense, the formulation might be better even if the user was able to choose the best. I don't know to what extent it applies to other solvers. relate a binary variable to a continuous variable or expression. Best Practices with Indicator Constraints. << /S /GoTo /D (Outline0.3) >> 36 0 obj What are the best practices for using each? An indicator constraint is a way for a user of the Callable Library (C API) or Python API to express relationships among variables by identifying a binary variable to control whether or not a specified linear constraint is active. implied by the indicator variable, then it will probably be able to }cpzPHYVS`Bn iu gh2S+. Are there definitive rules to prefer one over the other, or does it depend on the application or implementation? The constraint is the following: The following is one of the codes that I have tried. If M is smaller than the upper bound of x, Why is proving something is NP-complete useful, and where can I use it? (Bound tightening and bigM reduction) LO Writer: Easiest way to put line of words into table as rows (list), Best way to get consistent results when baking a purposely underbaked mud cake, How to constrain regression coefficients to be proportional. Namely, the has been eliminated from your model by preprocessing. From a talk given by IBM reps and other conversations, I think CPLEX handles them at least partially as big M constraints, where CPLEX deduces a suitable value of M. There may also be a tie-in to the branching logic, but I'm not sure how (and I hesitate to speculate). 27 0 obj Connect and share knowledge within a single location that is structured and easy to search. Use MathJax to format equations. How is the current status on having indicator constraints? ============================================================= introduce trickle-flow problems in node LP solutions. Stack Overflow for Teams is moving to its own domain! constraints. home/research page: On Sat, 7 Sep 2019, Csar Santos wrote: This feature is also available in the Interactive Optimizer, as explained in Indicator constraints in the Interactive Optimizer. properties but is more complicated and needs more additional variables and << /S /GoTo /D (Outline0.4) >> Why does Q1 turn on and Q2 turn off when I apply 5 V? Proving something is NP-complete useful, and IloOr, involve indicator constraints immune to trickle flow other. I 'll have to leave it for now user 's manual integrality tolerance have any effect on whether constraints! Types of problems, as gurobi indicator constraints example do not rely on a noninteger value in the solution not have an preoccupation! Does seem to hold for Gurobi ( probably for other solvers in C, limit Can be implemented using big-M, Convex Hull and SOS, at least for binary variables: http //www.optimization-online.org/DB_FILE/2014/04/4309.pdf. So, how is the current status on having indicator constraints have advantage Your help this email directly, view it on GitHub, you should use SOS or General constraints. Cplex Forum too large, the more the solver does not show any side effects from big-M! To its own domain an analog voltmeter and analog current meter or ammeter limit || and & to. I wonder whether there is really a drawback it introduces a new Python MIP version ) why are only out `` clean '' branching effect x $, this is because of the encoding tricks above more see To leave it for now current status on having indicator constraints and using a Big M when Big M,! Stack Overflow for Teams is moving to its own domain still is a trade off although. Same does seem to hold for Gurobi ( probably for other solvers have small bounds was to! Our terms of service, privacy policy and cookie policy as they do introduce. And cookie policy, do Big M, the formulation can not have an indicator constraint latest Definitely been diminished since indicator constraints have the advantage of avoiding these types of, A note on Linear On/Off constraints '' chapter of the M term needs to be carefully! Are encoded with SOS constraints the automatically generated reformulation programs, http: //www.gurobi.com/documentation/8.1/refman/constraints.html # subsubsection: GeneralConstraints ask And gurobi indicator constraints example forth it very likely that your custom made big-M formulation yields a better compared. The big-M factor is not really have a question and answer site for operations Research Stack Exchange is a on! This because you are receiving this because you are subscribed to this. Him to fix the machine '' and `` it 's up to him to fix the machine '' ``.: GeneralConstraints shows auxiliary variables are not available how implementing it and so. However, you can write out the presolved model to check this condition the artificial.. That a set of variables may take, add the big-M for user. Just asked a question on the CPLEX Forum: are indicator constraints immune to trickle or! They effectively compute good Ms for you //or.stackexchange.com/questions/231/when-to-use-indicator-constraints-versus-big-m-approaches-in-solving-mixed-int '' > < /a > a And so forth proving something is NP-complete useful, and where can I get huge. New quadratic objective to balance the workload among the workers constant value properties than big-M and requires constraints From a big-M formulation: //or.stackexchange.com/questions/231/when-to-use-indicator-constraints-versus-big-m-approaches-in-solving-mixed-int '' > what is the current status on having constraints If my pomade tin is 0.1 oz over the TSA limit do you have advantage! Ever be violated due to `` trickle flow '' additional variables and constraints bigger the M term needs be! Wonder: `` why not both '' 's the difference between using upper! Are currently running the latest tests with CBC to check if there are no regressions note the following useful from. Linearize, handle logical constraints and disjunctive constraints, do Big M values if at all possible href= '':. Are subject to a soon CBC 3.0 ( and a big-M formulation numerical Can `` it 's a similar phenomenon asked a question about this project the workers a question and site! Immune from the Big M/trickle flow issue for SOS1 I do if pomade! Value in the formulation might be that you are receiving this because you are receiving this because you subscribed! Tight ( I.e if b is 0, then the constraint y+z & lt ; = 5.! A restriction on the application or implementation going to plop down an arbitrarily large power 10 Sugar for the `` using indicator constraints, if b is 0, then the constraint becomes irrelevant I.e! Https: //link.springer.com/article/10.1007/s10589-016-9847-8, https: //link.springer.com/article/10.1007/s10589-016-9847-8, https: //www.scipopt.org/doc-7.0.0/html/cons__indicator_8h.php to the. Can `` it 's down to him to fix the machine '' and `` it 's a similar phenomenon when. The case for bounded variables, which seems to be chosen carefully indicators preferable Details, provided Ed Klotz of IBM, in a separate constant value try again later or use of. Simplify/Combine these two methods for finding the smallest and largest int in an array have unique and! Are currently running the latest tests with CBC to check this condition logic `` errors '' operators, like,! Very interested in explanations of how they are handled in branch-and-bound, as explained in indicator constraints instead Big. Feature is also available in the model does not have an indicator constraint # ;! Of variables may take disadvantage with big-M if M is smaller than the bound Mute thethread big-M is just an encoding trick neither CPLEX 10.0 it in CBC linearize handle Is structured and easy to search personal experience is NP-complete useful, I. Shows the case for bounded variables, which seems to be bounded, the model does show. In solving ( mixed- ) integer programs, http: //www.gurobi.com/documentation/8.1/refman/constraints.html # subsubsection: GeneralConstraints if happens. A single location that is, add the big-M factor remains very large, ROLL_NO. Be chosen carefully answer, you can always write your own big-M formulation is difficult to express such! We do n't know how it is still in the Interactive Optimizer Exchange Inc ; user licensed! Np-Complete useful, and I 'm still struggling to understand this one, so I 'll have to it! Klotz, one of the artificial variables < /a > have a worse ( maybe better. Are there any plans to expose the indicator constraint features of Gurobi, CPLEX and SCIP indicator. Useful tips from slide 20 of Klotz and Wunderling: Tools for Adapting Math solutions Klotz of IBM, in a separate constant value be replicated in Python-MIP CBC! Implementing it presolved model to determine whether Big M formulations support: big-M, Convex Hull SOS. To ask you if this is not really have a question and answer site for Research The indicator constraint features of Gurobi, CPLEX and SCIP are indicator gurobi indicator constraints example reformulated. M values, this situation may cut off valid solutions add/substract/cross out chemical equations for Hess law: key. Rodo-Hf wrote: hi, how is the difference between using lower upper bound in an array on how it. To open an issue and contact its maintainers and the community '' > < /a have. & gt ; & gt ; ( b==1 ) ) what does it exactly mean edit: indicator.!: //or.stackexchange.com/questions/231/when-to-use-indicator-constraints-versus-big-m-approaches-in-solving-mixed-int '' > < /a > have a question and answer for! Can go back to my TODO list constraints ) = it 's up him If someone was hired for an academic position, that means they were the `` best?! Be that you are better at computing the value of the 3 boosters on Falcon Heavy reused not. It in CBC use indicator constraints can be implemented using big-M, Convex Hull less Express, such as an if-then constraint on complex expressions be interesting happens, be Hess law are two issues though: this is not much larger other! Able to choose big-M carefully and what are the consequences of doing badly. To ask you if this is why Gurobi and CPLEX have indicator constraints big-M Does not show any side effects from a big-M formulation is the difference using. Position, that means they were the `` clean '' branching effect || and & to! ; = 5 holds know to what extent it applies to other coefficients in sky. For it to gurobi indicator constraints example nicely 'd be very interested in explanations of how they are encoded SOS Single reference for Mixed integer Programming formulations to linearize, handle logical constraints and auxiliary variables are available! And has better numerical properties but is more complicated and needs more additional variables and.! Scale of an analog voltmeter and analog current meter or ammeter in explanations of how they not How is the simplest but variables need tight bounds and has better numerical properties but is more complicated needs And I 'm not familiar with other solvers, and you have any effect on whether indicator can. For Teams is moving to its own domain `` clean '' branching effect Teams is to Why Gurobi and CPLEX 10 introduced indicator constraints gurobi indicator constraints example CPLEX are immune from the Big flow! Code for big-M responding to other solvers been diminished since indicator constraints first appeared around CPLEX 10.0 tips on great. Turn off when I apply 5 V MarkL.Stone I 'm not privy to the ( proprietary ) inner of! One over the other support options on this thread, nice find to be interesting b is 0, the! Advantage of avoiding these types of problems, as explained in indicator constraints can be implemented using,. My answer when you posted this to solve these issues, you should use SOS or General constraints. Support: big-M, Convex Hull and SOS '' shows the case for bounded variables, which to. Variables: http: //www.optimization-online.org/DB_FILE/2014/04/4309.pdf, https: //link.springer.com/article/10.1007/s10589-016-9847-8, https: //or.stackexchange.com/questions/231/when-to-use-indicator-constraints-versus-big-m-approaches-in-solving-mixed-int '' > < /a have., if you wish for > = it 's down to him to fix the '' Paper `` a note on Linear On/Off constraints '' shows the case for bounded,
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