Downloads¶
The lecture notes in PDF, with the same numbering of definitions, theorems, examples and exercises as the website. Text and figures are released under CC BY 4.0.
Lecture notes 1 · Models, bounds and formulations¶
What an integer linear programming problem is (MIP, ILP, BIP), its solutions and outcomes; primal and dual bounds and the gap; the LP relaxation; ideal formulations, valid inequalities and cover inequalities. Worked examples and exercises with complete solutions.
Lecture notes 2 · Exact methods¶
The cutting plane algorithm with Gomory fractional cuts, LP-based branch-and-bound and branch-and-cut. Examples worked out step by step and exercises with complete solutions.
Lecture notes 3 · MIP solvers¶
What a MIP solver does (presolve, cuts, primal heuristics, tree strategies, tolerances) and how to read its log, with real examples.
Lecture notes 4 · MIP heuristics¶
Rounding, diving, feasibility pump, RINS, local branching, relax-and-fix and fix-and-optimize. Examples and exercises with complete solutions.
Exercises 1 · Models, bounds and formulations¶
What an integer linear programming problem is (MIP, ILP, BIP), its solutions and outcomes; primal and dual bounds and the gap; the LP relaxation; ideal formulations, valid inequalities and cover inequalities. Worked examples and exercises with complete solutions.
Exercises 2 · Exact methods¶
The cutting plane algorithm with Gomory fractional cuts, LP-based branch-and-bound and branch-and-cut. Examples worked out step by step and exercises with complete solutions.
Exercises 3 · MIP solvers¶
What a MIP solver does (presolve, cuts, primal heuristics, tree strategies, tolerances) and how to read its log, with real examples.
Exercises 4 · MIP heuristics¶
Rounding, diving, feasibility pump, RINS, local branching, relax-and-fix and fix-and-optimize. Examples and exercises with complete solutions.