# Gurobi is unable to give an optimal solution even when it exists

I am trying to solve Logarithmic Fuzzy Preference Programming (LFPP) for criteria weight evaluation, based on fuzzy comparisons between criteria, and I am solving it with Gurobi in Python 2.7. It is a basic operational research thing. The model that solves this kind of problems is very simple ($$n$$ is the number of the criteria): The problem is that Gurobi isn't able to solve this accurately. I have some proven solutions for a specific configuration, but my program does not yield the adequate solution. Here is the literature example that i am trying to solve: The $$x_i$$ values from my models' output are very large (for example 420699.256539 instead of 0.6). Does anyone has an advice how to approach this? I have solved many complex and more complicated MILP, MIQP and MP problems so far, but never had an issue like this.

• To check if a) the textbook solution is feasible/correct and b) your model is correctly implemented, I suggest you add the given values as constraints, and see if you get the optimal objective value. – Kuifje May 19 '20 at 14:17
• Also, $x$ variables are not in the objective function ? In this case it is very well possible that the solution you have found is another optimal solution. – Kuifje May 19 '20 at 14:52
• @Kuifje I had that in mind and tried with adding the sum of x variables to the objective function. The results are close to the ones that i aim to, but differ after the first decimal. – Milovan May 19 '20 at 14:56
• @Milovan, welcome to OR.SE. As you have a non-linear term in the objective function I assume that you did appropriate linearization and then solve the model using Gurobi (because Gurobi is an LP/MIP/QP solver). I tried your second problem by using GAMS and the results are a bit different from what the mentioned (e.g. $x_1 = 0.608$). Would you sure the second problem you mentioned is correct? I agree with Kuifje to check the optimal solution. – A.Omidi May 19 '20 at 19:19
• @A.Omidi Thanks for the help. I've never assumed that Gurobi could not handle nonlinear problems like this. I've used Excel Pro Solver, and managed to get a solution that is more reasonable. Gonna give a check to the GAMS solver as well. – Milovan May 20 '20 at 11:07