PuLP programming output

Question

I am working with a collaborator on a certain optimization project involving linear programming. We both use Coin-OR branch-and-cut solver to solve the problem. I construct the .LP file using Python-based PuLP package. I am not entirely sure how the collaborator creates their .LP file (definitely not using Python), but essentially, we have two different systems generating .LP files for the exact same problem - i.e. the objective function, variables, constraints are exactly the same.

I typically solve my problem within Python (myProblm.solve()), but I have also been generating a .LP file and calling a CBC solver from the command line to solve this file (problem). Next, I compare the output I get from my system (either Python or command-line), to that my collaborator obtains. [Please note that the output of the problem on my side is exactly the same whether solved in PuLP or on command-line.]

The values of the objective function match well between us, but the other details do not exactly match. For example, if we were to solve this Whiskas blending problem, the total cost of ingredients would be exactly same, but the ratios of ingredients differ. Any idea why that would be?

I manually compared our .LP files and noticed a few differences. For starters, the sequence of constraints and variables is different. In other words, if there are 5 constraints, my file lists them as C1,C2,C5,C4,C3, whereas the same constraints will be listed as C1,C2,C3,C4,C5. Also, my Python code rounds all numbers to 10's place, while his system rounds them to 1's place. Hence, the coefficients of some of the variables have slightly different values.

Do these differences play a role in the exact output of the solver?

Also, the next question by extension is: What should we do to get the exact same output when solving a linear programming optimization problem? Which factors influence the solution of LP problems? Do factors like the structure of an .LP file play a role? Will I get the exact same output if I run the same LP file with exact same conditions on different computers?

Answer 1

Because there are multiple solutions to an LP problem with the same optimal objective function, different solvers cant guarantee that they will return the same solution. This issue becomes even more complicated when MIP problems use branch and bound. Using Multi threading or multiprocessing makes it almost impossible.

In summary to get the same solution either generate the exact same LP files and solve with the same solvers. Or change you objective function so that there is only one optimal solution (perhaps prefer some ordering of ingredients, with a small change of the costs for the ingredients).