I am trying to solve a MIP problem in GAMS by using CPLEX Solver.
The nature of the problem is large which involves large number of constraints, variables and equation.
The model is successfully completed, however, it is not displaying any output result due to infeasible problem in some equations.
this is what I want from my model,
MODEL Stochastic /all/;
OPTION optcr=0;
OPTION mip=CPLEX;
SOLVE Stochastic using mip maximizing z1;
And this is what I got.
MIP status(119): integer infeasible or unbounded
Cplex Time: 0.00sec (det. 2.73 ticks)
Problem is integer infeasible.
No solution returned
I checked through the .lst file to know which equations are causing infeasibility and I found out many of them including infeasibility in my objective function.
I am not sure how can I remove infeasibility from my problem?
I would like to ask for suggestions and recommendations.
I have been to some online posts about the problem such as (https://www.researchgate.net/post/I-am-using-GAMS-in-MINLP-and-it-results-in-an-infeasible-solution-any-help), but it didn't helped though.
Note: I am using GAMS IDE version 24.
There is no general, easy solution for this problem. But since you use Cplex as your solver, you could try its IIS option (see https://www.gams.com/latest/docs/S_CPLEX.html#CPLEXiis) which can help to identify groups of conflicting constraints. That could give you at least a handle for a more detailed analysis of your problem.
Related
I am using GAMS to solve a nonlinear programming problem. The problem size is about 500K rows, 500k columns, and 1M non-zeros. I found that it took long time to generate the model, sometimes even longer than solving the model. Are there any ways to speed up the generating process inside GAMS? Alternatively, if I switch to other platforms, are there any good choices to resolve this issue? Thanks.
As far as i know Gurobi resumes optimizing where it left after calling Model.Terminate() and then calling Model.Optimize() again. So I can terminate and get the best solution so far and then proceed.Now I want to do the same, but since I want to use parts of the suboptimal solution I need to set some variables to fixed values before I call Model.Optimize() again and optimize the rest of the model. How can i do this so that gurobi does not start all over again?
First, it sounds like you're describing a mixed-integer program (MIP); model modification is different for continuous optimization (linear programming, quadratic programming).
When you modify a MIP model, the tree information is no longer helpful. Instead, you must resolve the continuous (LP) relaxation and create a new branch-and-cut tree. However, the prior solution may still be used as a MIP start, which can reduce the solve time for the second model.
However, your method may be redundant with the RINS algorithm, which is an automatic feature of Gurobi MIP. You can control the behavior of RINS via the parameters RINS, SubMIPNodes and Heuristics.
I know that column generation gives an optimal solution and it can be used with other heuristics. But does that make it an exact algorithm? Thanks in advance.
Traditional CG operates on the relaxed problem. Although it finds the optimal LP solution, this may not translate directly into an optimal MIP solution. For some problems (e.g. 1d cutting stock) there is evidence this gap is small, and we just apply the set of columns found for the relaxed problem to a final MIP knowing this is a good solution but necessarily optimal. So it is a heuristic.
With some effort you can use column generation inside a branch-and-bound algorithm (this is called branch-and-price). This gives proven optimal solutions.
An exact algorithm means that the algorithm can solve the optimization problem globally i.e it has given the global optima.
Column generation technique is conventionally applied to relaxed LP problem and tries to optimize the relaxed LP problem by constantly improving the current solution with the help of dual multipliers. It gives an exact LP solution for the relaxed LP problem. But sometimes in real-world problems, the exact solution of the relaxed Lp problem is not feasible to use, it needs to be translated to an integer solution in order to use it. Now if the problem scale is small, then there are many exact MIP algorithms (such as Branch and Bound) which can solve it exactly and give an integer solution. But if the problem is large-scale, even the exact MIP algorithms can take longer runtimes, hence, we use some special/intelligent heuristics to lower the difficulty of the MIP problem.
Summary: Column generation is an exact technique for solving the relaxed LP problem, not the original IP problem.
First, strictly speaking, all algorithms are heuristic, including Simplex Method.
Second, I think Column generation is a heuristic algorithm, because it solves the LP relaxation of the master problem. It does not guarantee IP optimal. Actually CG does not always converge very well.
I am using GAMS for solving a MILP problem which includes binary variables. However there is a problem in the solution. Surprisingly, I have seen that one of the binary variables in the solution has a found value of "-1" another one "2". That is not acceptable. I do not know what happened. GAMS gives me the message primal infeasible.
I have a large MIP problem, and I use GLPSOL in GLPK to solve it. However, solving the LP relaxation problem takes many iterations, and each iteration the obj and infeas value are all the same. I think it has found the optimal solution, but it won't stop and has continued to run for many hours. Will this happen for every large-scale MIP/LP problem? How can I deal with such cases? Can anyone give me any suggestions about this? Thanks!
The problem of solving MIPs is NP-complete in general, which means that there are instances which can't be solved efficiently. But often our problems have enough structure, so that heuristics can help to solve these models. This allowed huge gains in solving-capabilities in the last decades (overview).
For understanding the basic-approach and understanding what exactly is the problem in your case (no progress in upper-bound, no progress in lower-bound, ...), read Practical Guidelines for Solving Difficult Mixed Integer Linear
Programs.
Keep in mind, that there are huge gaps between commercial solvers like Gurobi / Cplex and non-commercial ones in general (especially in MIP-solving). There is a huge amount of benchmarks here.
There are also a lot of parameters to tune. Gurobi for example has different parameter-templates: one targets fast findings of feasible solution; one targets to proof the bounds.
My personal opinion: compared to cbc (open-source) & scip (open-source but non-free for commercial usage), glpk is quite bad.