Faster Integer Solver in What'sBest! and LINGO

The integer solver used in What'sBest! 3.0 and LINGO 3.1 utilizes several new enhancements. Modelers intimately familiar with the art of solving integer models might appreciate the description of the enhancements listed below. Those interested in the results of the enhancements should check out the time comparisons of selected models from the MIPLIB Mixed Integer Programming Library (bottom right). Compare these times to your current solver.

Cut Generation

On integer models with 0/1 knapsack constraints with Generalized Upper Bound (GUB) constraints, also known as Special Ordered Set (SOS) constraints, lifted cover inequalites are added. Primarily on mixed 0/1 models, lifted flow cover inequalities are added.

Preprocessing

Before the branch and bound procedure begins, the integer solver tightens variable bounds, reduces coefficients, fixes variables and deletes redundant constraints based upon feasibility and optimality conditions and GUB constraints.

Reduced Cost Variable Fixing

At each node of the branch and bound tree, variables are fixed or tightened based upon reduced costs and feasibility condition.

Heuristics

Using the current LP solution and feasibility condition at each node, heuristics are used to quickly find a good IP solution. If an IP solution is found that is better than the incumbent, then it is used to fix or tighten global and local variable bounds.

Branching Strategies

Improved branching rules based upon penalties have been implemented.

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