OPTIMIZATION RESEARCH
The Double Pivot Simplex Method
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The Double Pivot Simplex Method improves each iteration of the Simplex Method by pivoting on two variables at a time instead of one. Double pivots are performed by identifying the optimal basis in a two variable linear program using a new method called the Slope Algorithm.
Advanced Branching Techniques
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The classical Branch and Bound Algorithm has two children at each node. Dr. Easton's research introduced quaternary branching and octanary branching algorithms. These methods introduced a new proof of convergence on branch and bound based upon branching on polyhedron instead of single variables.
Optimization in Sports
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Dr. Easton created a stochastic integer program to determine the best defensive starting positions to minimize the expected batting average of a particular player. This optimal defense is tested against other standard Major League Baseball® defenses through simulation. Other optimization research related to sports includes the true NFL fan problem, models for fantasy sports, and a generalizable heuristic based upon the game of soccer.
Generating Novel Cutting Planes for Integer Programs
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Dr. Easton develops effective techniques to improve solution times of integer programs through cutting planes. A few results involve lifting over integer variables, simultaneous lifting, two/three set synchronized simultaneous lifting, and lifting equality cuts. Additional efforts include merging valid inequalities on single and multiple variables, and knapsack constraints with cover inequalities.
Novel Graph Structures
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By examining novel graph structures, Dr. Easton has created previously undiscovered classes of facet defining inequalities for the node packing polyhedron. Some of these structures include the cliqued hole, odd bipartite hole, odd k-partite hole, and suns. Some additional work extends these concepts to hypercliques and hyperfans in conflict hypergraphs of the associated integer program.
Lifting of Graph Structures
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Dr. Easton developed theoretical and computational results for lifting of graph structures such as sequential and simultaneous lifting in the node packing polyhedron, and simultaneous lifting for constellations in conflict hypergraphs.
