Computational Progress in Linear and Mixed Integer Programming

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Solvability of MIPs – Gurobi (6.5) 3550 MIPs, 30000 second time limit, run with defaults 100% 90% 80% 8% 14% 70% 60% 50% 40% 30% 75% 97% (107 MIPs found no solution) • 54 blocked by LP, ~1.5% • 16 tunable • 37 remain, ~1% 20% 10% 0% Integer Solution with > 10% Gap v v Integer Solution with < 10% Gap Solved to provable optimality
Suppose you were given the following choices: ▸ Option 1: Solve a MIP with today’s solution technology on a machine from 1991 ▸ Option 2: Solve a MIP with 1991 solution technology on a machine from today Which option should you choose? ▸ Answer: Option 1 would be faster by a factor of approximately ~300. © 2015 Gurobi Optimization 39
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 and 22: Solving MIPs © 2015 Gurobi Optimiz
Page 23 and 24: A Bumpy Solution Landscape © 2015
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: MIP Solvability © 2015 Gurobi Opti

Computational Progress in Linear and Mixed Integer Programming

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