numerically difficult or exhibit trickle flow. << /S /GoTo /D (Outline0.1.1.2) >> Example usage: /* x7 = 1 -> x1 + 2 x3 + x4 = 1 */ int ind [] = {1, 3, 4}; double val [] = {1.0, 2.0, 1.0}; error = GRBaddgenconstrIndicator (model, NULL, 7, 1, 3, ind, val, GRB_EQUAL, 1.0); Next: GRBaddgenconstrPWL Up: Model Creation and Modification Previous: GRBaddgenconstrNorm Spanish - How to write lm instead of lim? condition which may lead to longer solve times in a model. 24 0 obj Here some details in addition to the IBM Technote: Difference between using indicator constraints and a big-M formulation . Given the trade-offs indicated by Ed Klotz, one might wonder: "Why not both"? It must have unique values and cannot contain nulls. 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)) trickle flow. On Wed, 11 Mar 2020, rodo-hf wrote: It is still in the TODO list. for example model.addConstr ( (a==1)>> (b==1)) what does it exactly mean? Convex Hull needs less tight bounds and has better numerical properties but is more complicated and needs more additional variables and constraints. Are there any plans to expose the indicator constraint features of Gurobi? I'd be very interested in explanations of how they are handled in branch-and-bound, as well as any studies reporting empirical evidence. Big M formulations are subject to logic "errors" due to "trickle flow". 4x + 3y + 2z + Mb <= 2+M, Just wanted to add some new information, SCIP explains how they implement indicator constraints using SOS1 constraints here: The paper "A Note on Linear On/Off Constraints" shows the case for bounded variables, which seems to be easy to implement. Following up from my boolean modelling issue, one of the nicest features of Gurobi, CPLEX and SCIP are indicator constraints. Following up from my boolean modelling issue, one of the nicest features of Gurobi, CPLEX and SCIP are indicator constraints. With the above formulation, we can use variable b to formulate the indicator constraints b = 1 z = w 1 b = 0 z = w 2. Because I am having such a problem at the moment. Unfortunately I'm still struggling to understand this one, so I'll have to leave it for now. << /S /GoTo /D (Outline0.2.2.15) >> How can I get a huge Saturn-like ringed moon in the sky? 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. properties but is more complicated and needs more additional variables and For each variable in the constraint, if the weight is positive, multiply it by the variables lower bound. If neither CPLEX 10.0 nor 10.1 can efficiently solve the model formulated 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). Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc? Does the setting of endobj 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. The Big-M formulation is the simplest but variables need tight bounds for it to work nicely. (Why are the results surprising?) As you did not provide information on bounds on x and y, let's assume they are not available. Stack Overflow for Teams is moving to its own domain! Both of these constructions typically use a binary variable to dummy 311 is integer and dummy312 is binary. CPLEX and SCIP are indicator constraints. MathJax reference. endobj 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. privacy statement. subject to Contrainte_3 {d in ND, i in NS, j in NS: i <> j, c in NC, m in NC: m<>c}: sum {t in F1[d]}( X_F1[d,t,i,j]+TRUCK_CUST[d,t,i,c]+TRUCK_CUST[d,t,j,m]) <= home/research page: On Sat, 7 Sep 2019, Csar Santos wrote: In gurobipy this is written as model.addConstr ( (x == 1) >> (y + z <= 5)) where x is a binary variable, y and z are integer variables. Sign in Best Practices with Indicator Constraints. 31 0 obj Would be nice to have an example code then. above? The goal is to have the constraint "always succeed" when I is false (essentially turning it off). Why does Q1 turn on and Q2 turn off when I apply 5 V? Indicator constraints can be implemented using Big-M, Convex Hull, or SOS 40 0 obj 35 0 obj constraint on complex expressions. 12 0 obj Indicator constraint is nothing but depending on a binary variable a constraint does or does not hold. IBM Technote: Why does a binary or integer variable take on a noninteger value in the solution?, depending (Introduction) Sum all of that, and you have the minimal M for that one constraint. "On handling indicator constraints in mixed integer programming" (Bound tightening by enumeration) issue associated with big M formulations. variable is binary. There you go, that's big M. If you want to model it in python-mip, we need to move that b back but that's no problem: If b is true and x, y and z have small bounds, this constraint will always work. g&g? for it to work nicely. 28 0 obj How are indicator constraints implemented? The following model has been developed to deter-mine how much of each type should be produced to maximize profit subject to a . () model. always helps with performance. Thisisquitecounter-intuitivebecause,ingeneral,convexMIQPs former wsls reporters But there still is a trade not introduce indicator constraints for that Big M. If valid upper bounds on continuous variables are available, use them. indicator constraints first appeared around CPLEX 10.0. If $M$ is smaller than the Years ago, I attended an IBM workshop at an INFORMS conference. 19 0 obj endobj << /S /GoTo /D (Outline0.5.1.44) >> endobj 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. When the big-M factor remains very large, relative to other coefficients To solve these issues, you should use SOS or General Implication constraints, however. In the "else" part of your constraint, you have, On Mon, Apr 27, 2020 at 8:53 AM UTC, AMPL Modeling Language <. I would also like to ask you if it is because of variable above, how can I write it so that gurobi can accept it. formulations. << /S /GoTo /D (Outline0.4) >> Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc? (Raw Computational Results) Demonstrates optimization with multiple objective functions. What is the difference between using indicator constraints and a big-M formulation? Full support for indicator constraints, if it happens, should be at the CBC level and not Python-MIP. 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. Thanks a lot. /Length 733 To the best of my knowledge the indicator constraints are just syntactic sugar for the user. ibm.com/developerworks/community/forums/html/. I am trying to have a conditional constraint for when x [t-1] = 0. ). We are now working to improve the cbc binaries, but this will be my next task ! endobj Hi, I assume that if you're just going to plop down an arbitrarily large power of 10, indicators are preferable. If the model does not show any side effects from a big-M formulation. 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. However, you can always write your own big-M formulation, if you wish. If you choose to introduce Big M values in your model anyway, use the smallest possible value of tighten the formulation for you, and you don't need to worry about the For Gurobi, define a binary variable and a separate constraint: On Tue, Apr 21, 2020 at 8:38 PM UTC, AMPL Modeling Language <, On Tue, Apr 21, 2020 at 4:28 PM UTC, AMPL Google Group <. Use MathJax to format equations. 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 Use smallest possible value of big-M that doesnt violate intent of model, Bound strengthening in CPLEX presolve often does this automatically, Set simplex tolerances to minimum values, 1e-9, Ask for more accuracy on an ill-conditioned system. fixing and so forth. I have no idea how they are encoded with SOS constraints. (Deactivating Linear Constraints) By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. 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. 52 0 obj Key constraints: PRIMARY KEY: Primary key uniquely identifies each record in a table. [AB4VZOWH3QSGUZE6YGSA4PLQIQNS3A5CNFSM4IURLVU2YY3PNVWWK3TUL52HS4DFUVEXG43VMWVG too large, the model may become numerically difficult or exhibit (A class of surprising problems) After that I can go back to my TODO 56 0 obj I'm not sure about the definition of an indicator constraint. Modified date: Hi, = times [ 0 ]) For more information about indicator constraints, see the "Using Could someone please provide a little sample code for Big-M? The same does seem to hold for gurobi (probably for other solvers as well). However, they tend to have weaker relaxations during the MIP optimization, a condition which may lead to longer solve times in a model. For example, for a linear program in canonical form: max c t x Ax = b x 0 The interface takes the matrix A and vectors b and c, and returns the optimal solution. Defines indicator constraints. It might be that you are better at computing the value of the big-M using additional knowledge that the solver does not have. << /S /GoTo /D (Outline0.6) >> endobj 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. The statements I wrote in the variables description are the followings: var TA_F1 {d in ND, t in F1[d], i in (ND union NS) } >= 0 ; var TA_MRS_SAT {d in ND, t in F1[d], s in NS, c in NC} >= 0 ; var TAMS_TAF1 {d in ND, t in F1[d], s in NS, c in NC} = if TA_MRS_SAT[d,t,s,c] <= TA_F1[d,t,s] then 1 else 0; They contain the "if-then-else" expression as you have mentioned before, perhaps it because of this I have the notice of ", To satisfy Gurobi, write these variable definitions as "indicator constraints" instead. Yes, I recently noticed after watching a workshop that the implementation is simple indeed. 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. 11 0 obj You signed in with another tab or window. Only z = 0 (zero) or z = 1 (one) is allowed for the indicator variable because the indicator constraint implies that the indicator variable is binary. The following is a simple example of a valid linear constraint: c0: 2.5 x + 2.3 y + 5.3 z <= 8.1 The following is a valid quadratic constraint: qc0: 3.1 x + 4.5 y + 10 z + [ x ^ 2 + 2 x * y + 3 y ^ 2 ] <= 10 The constraint section may also contain another constraint type: the so-called indicator constraint. few more details. constraints which are just lovely, though those are not particularly hard to model # Indicator constraints z = [] # Initialization of an input for nonlinear-type formulation t = -1 for i in range ( 10 ): m.addConstr ( (b [i] == 1) >> (t == i)) z.append (t) # Objective function obj = gp.quicksum (x [i] + y [i] for i in range ( 10 )) m.setObjective (obj + tmp_f (z), GRB.MAXIMIZE) m.optimize () 0 turn on or turn off the enforcement of a constraint, or to By clicking Sign up for GitHub, you agree to our terms of service and for example 1 or 2. in the blow is a semi code of my implementation: m = Model("mip1") << /S /GoTo /D [61 0 R /Fit ] >> email: haroldo@ufop.edu.br When the big-M formulation is difficult to express, such as an if-then constraint on complex expressions. If so, how should I write the code? For example, you have. No results were found for your search query. << /S /GoTo /D (Outline0.2.1.10) >> to your account. There are two issues though: This is why Gurobi and CPLEX have indicator constraints, they effectively compute good Ms for you. would they be replicated in Python-MIP for CBC by using one of the encoding tricks 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) 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. with indicator constraints. similar to the content of the above technote, but it does provide a Do you have any 15 0 obj 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 I wonder whether there is really a computational disadvantage with big-M if M is tight (I.e. What exactly makes a black hole STAY a black hole? constraints. << /S /GoTo /D (Outline0.5) >> Is this constraint possible in Gurobi based on the Python language? If I figure it out I will inform you. I read the article on indicator constraint but it was not lear to me 0 Please sign in endobj Note the following useful tips from slide 20 of Klotz and Wunderling:Tools for Adapting Math Programming Solutions in the Real World. When the big-M factor is not much larger than other coefficients in the model. 100000, which can still potentially have trickle flow issues, this can This would be a nice feature. I would definitely stick with the simple implementation. I write to you again because I have an another preoccupation. yield a much tighter formulation and nearly always helps with performance. endobj upper bound of $x$, this situation may cut off valid solutions. Difference between Using Indicator Constraints and a Big-M Formulation. presolved model to check this condition. variable will generally yield a much tighter formulation and nearly this is not really a drawback. 59 0 obj Bounds are used in a MIP for Until CBC decides this is an important thing to do, here's what can be done: If the constraint is >=: I just know it has better numerical properties than Big-M and requires more constraints and auxiliary variables. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. What are the best practices for using each? It can be calculated by getting the upper bound of (a * x) + (b * y) and subtracting c from it. Making statements based on opinion; back them up with references or personal experience. You might have some logical expression in your constraints, which Gurobi would reject as "nonlinear" since it is not a linear expression. https://www.scipopt.org/doc-7.0.0/html/cons__indicator_8h.php. 32 0 obj For >= it's a similar idea but we care about the lower bound instead. Here is the advice in the IBM CPLEX documentation. integrality tolerance have any effect on whether indicator constraints For example, an "if-then" or "if-then-else" construct will be considered nonlinear if there are variables in the expression after "if". 23 0 obj In C, why limit || and && to evaluate to booleans? Hi, endobj 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]) Indicator constraints have the advantage of avoiding these types of endobj If $M$ is Why are only 2 out of the 3 boosters on Falcon Heavy reused? A constraint in Gurobi captures a restriction on the values that a set of variables may take. the indicator variable have implicit modest bounds that involve a very large bounds on involved variables, M in a Big M constraint would have endobj In that sense, the formulation might be better even if the user was able to choose the best. How do you encode an implication like the above in MIP? 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. Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. For the most general case it seems that a way more complicated approach is needed: endobj problems, as they do not rely on a separate constant value. generally 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 <. phenomenon? 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. complex combination of constraints that elude CPLEX's bound 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. This is the simplest possible way to get half-decent Ms. You really want to do some pre-solving where you minimize the Ms though, as Gurobi and CPLEX do, since that will give much better results by taking all constraints into account simultaneously (such that you have tighter bounds on every variable). has been eliminated from your model by preprocessing. ============================================================= Well occasionally send you account related emails. Unfortunately, indicator constraints are not supported by the Gurobi MATLAB and R interfaces. What if due to Where M is some "very large number", a big M so to say, e.g. These interfaces use a matrix representation. << /S /GoTo /D (Outline0.3) >> how to fix ticketmaster pardon the interruption bot knex create table if not exists If For this reason, Gurobi might be able to produce a smaller or tighter representation of the general constraint than you would get from the most general formulation. But for modest values of big M of say Does it make sense to say that if someone was hired for an academic position, that means they were the "best"? Already on GitHub? >> Various optimization modeling languages and solvers allow for both indicator constraints (see for example here, here and here) and traditional binary variable and big-M approaches can be used to model whether a linear constraint such as $a'x \le b$ should be active in solving (mixed)-integer programs. With Concert and CPLEX 10, the default formulation of linearized operators, How can I increase the full scale of an analog voltmeter and analog current meter or ammeter? endobj 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. In that case, indicator constraints are a good candidate: = 0 => x y - = 1 => x . Avoid Big M values if at all possible. implied by the indicator variable, then it will probably be able to 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. this situation may cut off valid solutions. In integer programming what's the difference between using lower upper bound constraints and using a big M constraints? There isn't really much to code, big-M is just an encoding trick. (Bound Reduction in nonconvex MINLPs) [AB4VZOQ5GS55JKWFAUUBYT3RHAFSPA5CNFSM4IURLVU2YY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTD @prubin Can you give us some insight as to how indicator constraints are handled( nternally by (or formulated for) solvers, for example CPLEX, or any others you are familiar with? Hi, The best answers are voted up and rise to the top, Not the answer you're looking for? just slow solution, but wrong solution) if they are used in lieu of (Supervised Classification) %PDF-1.4 potential weakness. Do not introduce indicator constraints if Big M is eliminated by preprocessing. Big-M formulations are relatively straightforward, but the value of the M term endobj How do I simplify/combine these two methods for finding the smallest and largest int in an array? << /pgfprgb [/Pattern /DeviceRGB] >> 66 0 obj << Your help is very precious for me. You can write out the presolved model to check this condition. endobj Only $z=0$ (zero) or $z=1$ (one) is allowed for the indicator variable because the indicator constraint implies that the indicator endobj python MIP version). result in a weaker formulation. V4ypJQQj'Y2u{GfIjy uJ^yXA@ NB@E8bVtVJW}{gndfY{U2k zNAyqeM https://link.springer.com/article/10.1007/s10589-016-9847-8. 55 0 obj (Interpreting the numbers) once you have indicator constraints. I would like to ask you if this is because of the expression. How is the current status on having indicator constraints? involve indicator constraints. Question by me at the IBM CPLEX Forum: Are indicator constraints immune to trickle flow or other numerics-induced logic "errors"? When the big-M factor remains very large, relative to other coefficients in the model. they tend to have weaker relaxations during the MIP optimization, a improvements in indicator probing and other MIP preprocessing that typically reduce the burden on the user to decide between an indicator I'm not sure how much I trust the advice to use indicators in preference to big-M if M cannot be "reduced" (from what to what?). However, for a simple logical condition like the one that defines your variable e_ih^m, there is often a reformulation that Gurobi does accept. (With a little help of my friends) Big-M formulations are relatively straightforward, but the value of Haroldo.GambiniSantos@cs.kuleuven.be stream Bounds strengthen LP relaxations. They make modelling complex boolean In the below relate a binary variable to a continuous variable or expression. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 16 0 obj Then it very likely that your custom made big-M formulation yields a better bound compared to the automatically generated reformulation. indicator constraints are indeed completely immune to the trickle flow @MarkL.Stone I'm not familiar with other solvers, and I'm not privy to the (proprietary) inner workings of CPLEX. Would be nice to have an example code then. Hi @drlagos ! Can indicator constraints ever be violated due to a similar In that case, do 48 0 obj check if there are no regressions. Indicator constraints have the advantage of avoiding these types of problems, as they do not rely on a separate constant value. If the big-M factor is eliminated in presolve. illumina senior director salary x icarsoft communication error. To satisfy Gurobi, write these variable definitions as "indicator constraints" instead. Internally these indicator constraints are reformulated using computed big-M formulations or SOS constraints (special ordered set constraints). Python code modeling a conditional statement in Gurobi might look similar to the following: import gurobipy as gp from gurobipy import GRB # Create a new model m = gp.Model ( "test") # Create variables << /S /GoTo /D (Outline0.1) >> Best Practices with Indicator Constraints Avoid Big M values if at all possible. Operations Research Stack Exchange is a question and answer site for operations research and analytics professionals, educators, and students. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. constraints. We do not plan to implement Gurobi only When the big-M factor is not much larger than other coefficients in the constraints extremely easy, in fact Gurobi and CPLEX also include boolean AND and OR 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'?
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