Computational Progress in Linear and Mixed Integer Programming

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Solve LP relaxation: v=3.5 (fractional) x 2 MIP solution framework: LP based Branch-and-Bound v 3 x 3 Root v 4 z 0 z 1 Upper Bound G A P Integer y 0 y 1 Lower Bound z 0 z 1 Infeas Integer Remarks: (1) GAP = 0 Proof of optimality (2) In practice: Often good enough to have good Solution © 2010 Gurobi Optimization 22
A Bumpy Solution Landscape © 2015 Gurobi Optimization 23
Page 1 and 2: Computational Progress in Linear an
Page 3 and 4: The Early History ▸ 1947 - George
Page 5 and 6: The Decade of the 80’s ▸ Mid 80
Page 7 and 8: Linear Programming © 2015 Gurobi O
Page 9 and 10: Example: A Production Planning Mode
Page 15 and 16: Progress in LP: 1988—2015 Algorit
Page 17 and 18: LP Today ▸ However, a word of war
Page 19 and 20: A Definition A mixed-integer progra
Page 21: Solving MIPs © 2015 Gurobi Optimiz
Page 25 and 26: Example 2: MIP really is HARD A cus
Page 27 and 28: Example 3: A typical situation toda
Page 29 and 30: Computational History: 1950 -1998
Page 31 and 32: MIP Speedups © 2015 Gurobi Optimiz
Page 33 and 34: CPLEX Version Performance Improveme
Page 35 and 36: 1000000000 Gurobi MIP Library (3550
Page 37 and 38: MIP Solvability © 2015 Gurobi Opti
Page 39 and 40: Suppose you were given the followin

Computational Progress in Linear and Mixed Integer Programming

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