I am tried to solve a MILP problem using python pulp and The solution is infeasible. So, I want to find where infeasibility is coming and want to relax it or remove it to find feasible solution. it is difficult to check manually in the LP file bcz large number of constraints are present. So How I can handle this issue?
I went through some articles they mentioned that check manually in the LP file but it is very difficult to do manually for a huge number of variables/constraints.
It is giving just infeasibility
In general, this is not so easy. Some pointers:
If you can construct a feasible but not necessarily optimal solution for your problem, plug this in and you will find the culprits very easily.
Some advanced solvers have tools that can help (IIS, Conflict refiner). They may or may not point to the real problem.
Note that the model can be LP infeasible or just integer infeasible.
In some cases it is possible just to relax a suspect block of constraints and see what happens.
A more structural approach I often use is to formulate an elastic model: allow constraints to be violated but at a cost. This often makes some economic sense: hire temp workers, rent extra capacity, buy from 3rd parties etc.
I use some rule of thumbs to check infeasibility.
Always start with a small data set that you can inspect more manually.
After relax all integer variables. If this relaxation is infeasible, your problem is linear infeasible. You might have constraints saying stuff like x > 3 and x < 2;
If the linear relaxation is feasible, then deactivate each constraint once. Frequently you find some obvious constraints being infeasible, such as sum(i,x_i) = 1. But if you deactivate one by one, you may find that another more complex constraint set is causing infeasibility, and there you might investigate better.
Related
I need to run a model, where I optimise a diet within a set of constraints and call all integer solutions in the end. I have found a diet example matching almost what I need here: hakank.org. However, in my case, my variables take continuous values, so in the examples this would be all the nutritional values and the cost, while only x take integer. However, it seems like I can only define either 'intvar' or 'boolvar' when defining by variables with this model. Is there a way to overcome this? Other would there be other more suitable models with examples that I can read online?
I'm new to constraint programming, so any help would be appreaciated!
Thanks.
Most Constraint Programming tools and solvers only work with integers. That is where their strength is. If you have a mixture of continuous and discrete variables, it is a good idea to have a look at Mixed Integer Programming. MIP tools and solvers are widely available.
The diet model is a classic example of an LP (Linear Programming) Model. When adding integer restrictions, you end up with a MIP model.
To answer your question: CPMpy does not support float variables (and I'm not sure that it's in the pipeline for future extensions).
Another take - than using MIP solvers as Erwin suggest - would be to write a MiniZinc (https://www.minizinc.org/) model of the problem and use some of its solvers. See my MiniZinc version of the diet problem: http://hakank.org/minizinc/diet1.mzn. And see the MiniZinc version of Stigler's Diet problem though it's float vars only: http://hakank.org/minizinc/stigler.mzn.
There are some MiniZinc CP solvers that also supports float variables, e.g. Gecode, JaCoP, and OptimathSAT. However, depending on the exact constraints - such as the relation with the float vars and the integer vars - they might struggle to find solutions fast. In contrast to some MIP solvers, generating all solutions is one of the general features of CP solvers.
Perhaps all these diverse suggestions more confuse than help you. Sorry about that. It might help if you give some more details about your problem.
I am trying to use GLPK for solving an LP problem. My problem is the routing problem in a computer network. Given network topology and each link capacity and the traffic demand matrix for each source-destination pair in the network, I want to minimize maximum link utilization in the network. This is an LP problem and I know how to use GLPK to get the optimum solution.
My problem is that I want to get the sub-optimal solutions also. Is there any way that I can get say top 10 suboptimal solutions by GLPK?
Best
For a pure LP (with only continuous variables), the concept of finding "next best" solutions is very difficult (just move an epsilon away, and you have another solution). We can define this differently: find "next best" corner points (a.k.a. bases). This is not so easy to do, but there is a somewhat complex way by encoding bases using binary variables (link).
If the problem is actually a MIP (with binary variables) it is easier to find "next best" solutions. Some advanced solvers have built-in facilities for this (called: solution pool). Note: glpk does not have this option. Alternatively, we can also do this by adding a cut that forbids the best-found solution and then resolve (link). In this case we exploited some structure. A general cut for 0-1 variables is derived here. This can also be done for general integer variables, but then things get a bit messy.
I've a MIP to solve with Pyomo and I want to set an initial solution for cplex.
So googling I find that I can set some variable of instance to some value and then execute this:
solver.solve(instance,warmstart=True,tee=True)
But when I run cplex it seem that it doesn't use the warm start, because for example i pass a solution with value 16, but in 5 seconds it return a solution with value 60.
So I don't know there is some error or other stuff that doesn't work.
P.S.
I don't know if is a problem but my warm start solution set only some variale to a value, but not all. Could be a problem?
Make sure that the solution you give to CPLEX is feasible. Otherwise, CPLEX will reject it and start from scratch.
If your solution is feasible, it is possible that CPLEX simply found a better solution than yours, since, after all, it is CPLEX's job, and in my own experience, CPLEX is very good at it. Is this a maximization problem? If so, in your example, CPLEX found a better solution (objective=60) than yours (objective=16), which is the expected behavior.
Sadly, CPLEX is often greedy in term of verbose, so it is hard to know from the solver log if warmstart was used or not (unlike its competitor GUROBI where it is clearly written in the log). However, it seems like you started the warmstart correctly, using the warmstart=True parameter.
If, however, your problem isn't a maximization problem, it is possible that CPLEX will not make a differenciation between the variables that you gave a value and the variable that still holds a solution from last solve. Plus, giving values to only a fraction of your variables might make the problem infeasible, considering that all values not manually specified are the values previously found by CPLEX. ex: contraint x<=2y. The solver found x=2, y=1 as a feasible solution. You define x:=3, then your constraint is not respected (y is still =1 for CPLEX, so the constraint x<=2y is 3<=2, which is false). CPLEX will see it as infeasible and will reject your solution.
One alternative that I can give you, if you absolutely want to use your own values in the final solution, is instead of defining values for your variables, create a constraint that explicitly defines your variable value. This constraint can afterward be "deactivated" if needed. But be careful, as this does not necessarily yield the optimal solution, but the "optimal solution when some variables have the specific value".
I am solving a minimization linear program using COIN-OR's CLP solver with PULP in Python.
The variables that are included in the problem are a subset of the total number of possible variables and sometimes my pricing heuristic will pick a subset of variables that result in an infeasible solution. After which I use shadow prices to price new variables in.
My question is, if the problem is infeasible, I still get values from calling prob.constraints[c].pi, but those values don't always seem to be "valid" or "good" per se.
Now, a solver like Gurobi won't even let me call the shadow prices after an infeasible solve.
Actually Stu, this might work! - the "dummy var" in my case could be the source/sink node, which I can loosen the flow constraints on, allowing infinite flow in/out but with a large cost. This makes the solution feasible with a very bad high optimal cost; then the pricing of the new variables should work and show me which variables to add to the problem on the next iteration. I'll give it a try and report back. My only concern is that the bigM cost coefficient on the source/sink node may skew the pricing of the variables making all of them look relatively attractive. This would be counter productive bc adding most of the variables back into the problem will defeat the purpose of my column generation in the first place. I'll test it...
I am using Pyomo to model my optimization problem (MILP) and solve it using Gurobi.
What would be the best, fastest or easiest way to find a heuristic solution using the Pyomo model, knowing that I do not care about the Gap bounds.
Note: I know that Gurobi has a heuristic solver but it doesn't tell what heuristic algorithm they are using!
Finding a heuristic solution to some MILP problem is complexity-wise as hard as optimizing it!
There is no best, fastest, easiest way in general. You always want to exploit some problem-characteristics.
As start, just use any MIP-solver and tune the params to reflect your needs. If you want just any heuristic solution, tune the solver for feasibility, probably meaning a higher frequency of heuristic-steps and early-stop with the first feasible solution.
Yes, you won't know what's Gurobi using internally. But knowing all of the code would not help much either. It's surely not something which you can find on wikipedia then (except for classic stuff like the feasibility pump or Relaxation induced neighborhood search).
If you want to know more about these methods, check out papers on MIP-heuristics in general! You will see, that most Heuristics are tightly coupled with the MIP-nature of the problem (although i expect some SAT-solver-usage internally too in commercial ones).