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Faster Integer Solver in What'sBest! and LINGO
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.
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.
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.
Improved branching rules based upon penalties have been implemented.