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Integer Optimization

Integer Optimization. Basic Concepts. Integer Linear Program(ILP): A linear program except that some or all of the decision variables must have integer values. LP Relaxation: A LP model that is derived from an ILP by dropping the integer requirements for the variables.

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Integer Optimization

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  1. Integer Optimization

  2. Basic Concepts • Integer Linear Program(ILP): A linear program except that some or all of the decision variables must have integer values. • LP Relaxation: A LP model that is derived from an ILP by dropping the integer requirements for the variables. • In a Max model, the OV of the LP relaxation always provides an upper bound on the OV of ILP • In a Min model, the OV of the LP relaxation always provides a lower bound on the OV of ILP

  3. Why not just use rounded solution of LP? • Rounded solution may be infeasible. • Even if one or more of the neighboring integer points is feasible: • Such a point need not be optimal for the ILP. • Such a point need not even be near the optimal ILP solution.(see figure 6.4 on p.293 of the text)

  4. Types of Integer Program • All-Integer Linear Program: All of the decision variables are required to be integer. • Mixed Integer Linear Program(MILP): Some, but not all, of the decision variables in a LP are required to be integer. • Binary (0-1 )Integer Linear Program: The integer variables are only permitted to assume the values zero or one. It may be of either the all-integer or MILP type.

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