# Tag Info

### For an ILP relaxed to LP is the LP solution objective always less than the ILP solution?

If the integer linear programming is a minimization problem then whose linear relaxation is a lower bound for the original MILP model, and for the maximization problem it is an upper bound. In the ...
Accepted

### if else condition with multiple criteria in MIP

Let $\epsilon$ be a small constant positive tolerance, and let $M$ be a constant upper bound on $x_1$. Now impose linear constraints $$\epsilon s_1 \le x_1 \le M s_1.$$

### How to properly tackle a big model using weak constraints

How lazy constraints are handled may depend on the solver, but CPLEX turns off dual reductions in the presence of lazy constraints, which could negatively impact performance. So I would probably limit ...
Accepted

1 vote

### How to select intermediate nodes in a network?

Option 1: Run Dijkstra's algorithm first. Then you will have a grid of positive numbers that you can use for additional constraints. E.g. require a positive number to know that a path is available ...
1 vote

### Coefficient Scaling for MIP

In my opinion, these two formulations are exactly the same. However, coefficience scalling would lead the float number coefficience in the first constraints, and then that would not be the benefit for ...
1 vote

### Cplex seems to terminate early as optimal when starting solution polishing

First of all, I think you have to display the final MIP gap in your terminal, maybe that actually MIP gap is zero. If not, in my opinion, you have to check several experiments. Using MIP solver solve ...
1 vote

### Does OptaPlanner give equally good results when comparing with commercially available MIP solvers?

It depends on the use case. The right tool for the job. Generally speaking, in my experience, for Vehicle Routing Problems and many other use cases, when scaling out, a good metaheuristics solver (...

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