Applied Mixed Integer Programming: Beyond 'The Optimum'

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Practical claim: mixed integer programming lets engineers express complex product rules quickly and change them incrementally — a multi‑dimensional bin‑packing with balancing and minimal reconfiguration implements in a few lines and solves well. Solver reality: decades of engineering give huge speedups (1.5 million solver speedup in 30 years plus hardware, ≈1 trillion overall), and real instances like 200k variables 50k constraints half‑million nonzeros see most gains from preprocessing, root relaxation and primal heuristics before expensive tree search.

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1. 0:00Start
2. 1:13Outline
3. 2:33Declarative programming
4. 2:56Mixed integer programming
5. 10:50Less accurate data More accurate data
6. 15:55MIP: branch-and-bound + simplex
7. 17:17Preprocessing: Clean-up
8. 18:03Preprocessing: Bound propagation
9. 18:50Preprocessing: Probing
10. 19:27Preprocessing: Cuts
11. 22:31Relaxation: Revised Simplex
12. 22:58Relaxation: Incrementality
13. 23:37Primal heuristics: Pivot and Shift
14. 24:44Primal heuristics: Shift and Propagate
15. 25:20Primal heuristics: Feasibility Pump
16. 26:20Primal heuristics: Objective Feasibility Pump
17. 26:39Search tree: Pruning
18. 28:04Search tree: Branching
19. 29:43Search tree: Conflict propagation
20. 30:17Search tree: Neighborhoods
21. 31:01Search tree: Parallelism
22. 32:28Other models?
23. 33:26Optimum?
24. 34:07Summary