I want to add indicator constraints (e.g. if z=0, then x=0 with x>=0 and z being a binary variable) to my problem written in PuLP. Obviously, I could make use of the big-M method as suggested here and here.
However, I cannot use the big-M workaround since my term is unbounded within the MILP. I found this post from 2016 stating that PuLP cannot handle indicator constraints.
Does anyone know if that is still the case or any other solution?
Thanks in advance.
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 working on a complex model in pyomo. Unfortunately, i have to change the formula of the objective function, based on how is the previous value.
In particular my objective function is composed of two terms ,call them A and B, that have different order of magnitude (A is usually 2 or 3 order of magnitude higher than B, but this may vary)
In order to guarantee that A and B have the same weight of the formula, i need to write my objective function as below:
objective= A + B*K`
Where K is the value which bring the second term at the same scale/magnitude of A
example:
A=4e10
B=2e3
K=1e(10-3)=1e7
The problem is that, in order to know K, i must know the values of A and B, but pyomo doesn't give value, it just pass an expression to the solver.
I have read that thanks to a smart use of binary variables is possible to overcome this issue, anyone could suggest a useful methodology?
Kind regards
It seems like you are dealing with a multi-objective optimization problem. Since the values of variables involved in A and B are not known before solving the model, you can't define the value of K based on A and B.
There are different ways to solve multi-objective optimization problems which you can consider for your specific problem (e.g., ε-constraints method). In these problems, usually you are not interested in finding a single solution, but finding a set of Pareto optimal solutions which are not dominated by any other solution in the feasible region.
When I tried to use piecewise linear (PWL) function in Python, after I set the problem type to cplex.Cplex.problem_type.LP, the PWL cpnstraint (or function) disappear when I write out the model to the file. However if I specified the problem type is cplex.Cplex.problem_type.MILP, it said that no solution, although there exist solution in LP. So I want to ask if someone face this problem before and how to solve it
The behavior you describe is expected. PWL constraints are considered MILP modeling objects. When you change the problem type to an LP, the MILP modeling objects are removed. Given that the LP is feasible, it sounds like your PWL constraint has introduced a conflict or there is something wrong with the definition of the PWL.
What exactly is the solution status code that you are getting when solving the MILP? That is, what is the value of Cplex.solution.get_status()? What does the engine log contain? These will likely give you some useful information.
In case you haven't found it, the CPLEX User's Manual contains a section on piecewise linear constraints here. See also the transport.py example that is included when you install CPLEX.
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 trying to solve a system of partial differential equations of the general form
F(f(x,y), f'(x,y), f''(x,y), g(x,y), g'(x,y), g''(x,y)) = 0
where the derivatives may be taken with respect to both x and y and f(x,y) and g(x,y) are subject to some constraint
G(f(x,y),g(x,y)) = 0
I wonder if there exists any (preferably Python based) solver (not a method, as I know the methods) that can deal with a problem of this kind? Would appreciate any help and apologise if my question seems to general.
Such a problem will require initial conditions and boundary conditions to be satisfied to obtain an unique solution. Also you will need to provide a domain (geometry) to the solver. I think you must look at finite element solvers in python.
Just a quick Google search provided few finite element solvers in python, however I have not tested any. So I guess that would be a good starting point.
If you are looking for a finite element solver, Fenics has python bindings.