Mixed Integer Optimization Program

A Mixed Integer Optimization Program is an integer optimization program that is a mixed mathematical optimization program.

• See: Mixed Integer Programming, Linear Objective Optimization.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/integer_programming#Variants Retrieved:2015-6-20.
  • Mixed integer linear programming (MILP) involves problems in which only some of the variables, [math]\displaystyle{ x_i }[/math] , are constrained to be integers, while other variables are allowed to be non-integers.

    Zero-one linear programming involves problems in which the variables are restricted to be either 0 or 1. Note that any bounded integer variable can be expressed as a combination of binary variables. For example, given an integer variable, [math]\displaystyle{ 0\le x\le U }[/math], the variable can be expressed using [math]\displaystyle{ \lfloor \log_2U\rfloor+1 }[/math] binary variables: : [math]\displaystyle{ x = x_1+2x_2+4x_3+\ldots+2^{\lfloor \log_2U\rfloor}x_{\lfloor \log_2U\rfloor+1}. }[/math]

2013

• http://www.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html
  • QUOTE: A mixed-integer linear program is a problem with
    1. Linear objective function, [math]\displaystyle{ f^T x }[/math], where [math]\displaystyle{ f }[/math] is a column vector of constants, and [math]\displaystyle{ x }[/math] is the column vector of unknowns.
    2. Bounds and linear constraints, but no nonlinear constraints.
    3. Restrictions on some components of x to have integer values.
  • In mathematical terms, given vectors f, lb, and ub, matrices A and Aeq, corresponding vectors b and beq, and a set of indices intcon, find a vector x to solve ...

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