A2 - Modeling 1 - Gurobi
Modeling I
Anwendertage 2017 Frankfurt, Germany
Agenda for this session
? Small demos ? Useful knowledge
? Gurobi model components ? What makes a model difficult? ? Choosing an interface ? Programming pitfalls ? Model debugging
Copyright 2016, Gurobi Optimization, Inc.
Gurobi model components
? Decision variables
? Objective function
? minimize xTQx + cTx +
? Constraints
? Ax = b ? lxu ? some xh integral ? some xi lie within second order cones ? xTQjx + qjTx j ? some xk in SOS
(linear constraints) (bound constraints) (integrality constraints) (cone constraints) (quadratic constraints) (special ordered set constraints)
? Many of these are optional
Copyright 2016, Gurobi Optimization, Inc.
Example ? Mixed Integer Linear Program (MILP)
? Decision variables
? Objective function
? minimize xTQx + cTx +
? Constraints
? Ax = b ? lxu ? some xh integral ? some xi lie within second order cones ? xTQjx + qjTx j ? some xk in SOS
(linear constraints) (bound constraints) (integrality constraints) (cone constraints) (quadratic constraints) (special ordered set constraints)
? By far, most common model for Gurobi users
Copyright 2016, Gurobi Optimization, Inc.
MIP is versatile
? Giant leap from linear programming (LP) with respect to modeling power
? Modeling with MIP is more than LP with integer restrictions
? MIP versatility typically comes from binary decision variables
? bk = 0/1 ? Captures yes/no decisions
? Combine with linear constraints to capture complex relationships between decisions
? Ex: fixed charge for using a resource
minimize
... + 100 bk + ...
subject to
xk 10 bk
? Ex: pick one from among a set of options
b1 + b2 + b3 = 1
?...
Copyright 2016, Gurobi Optimization, Inc.
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