MIP Models and BB Strategies in Brachytherapy Treatment Optimization
Journal of Global Optimization
Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition
INFORMS Journal on Computing
Octane: A New Heuristic for Pure 0-1 Programs
Operations Research
Mathematical Programming: Series A and B
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Active-constraint variable ordering for faster feasibility of mixed integer linear programs
Mathematical Programming: Series A and B
Counting solutions of knapsack constraints
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Operations Research Letters
On counting lattice points and Chvátal-Gomory cutting planes
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Three Ideas for the Quadratic Assignment Problem
Operations Research
Achieving MILP feasibility quickly using general disjunctions
Computers and Operations Research
INFORMS Journal on Computing
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Branching in mixed-integer (or integer) linear programming requires choosing both the branching variable and the branching direction. This paper develops a number of new methods for making those two decisions either independently or together with the goal of reaching the first integer-feasible solution quickly. These new methods are based on estimating the probability of satisfying a constraint at the child node given a variable/direction pair. The surprising result is that the first integer-feasible solution is usually found much more quickly when the variable/direction pair with the smallest probability of satisfying the constraint is chosen. This is because this selection forces change in many candidate variables simultaneously, leading to an integer-feasible solution sooner. Extensive empirical results are given.