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Optimization Toolbox

Mixed-Integer Linear Programming

Mixed-integer linear programming expands the linear programming problem with the additional constraint that some or all of the variables in the optimal solution must be integers. 

For some optimization problems, the variables should not take on fractional values. For instance, if a variable represents the number of stock shares to purchase, it should take on only integer values. Similarly, if a variable represents the on/off state of a generator, it should take on only binary values (0 or 1). The mixed-integer linear programming problem allows this behavior to be modeled by adding the constraint that these variables should take on only integers, or whole numbers, in the optimal solution.

Optimization Toolbox solves mixed-integer linear programming problems using an algorithm that:

  • Performs integer programming preprocessing to tighten the feasible region
  • Applies cutting planes to tighten the feasible region
  • Uses heuristics to search for integer feasible solutions
  • Verifies that no better feasible solution is possible with a branch and bound algorithm that solves a series of linear programming relaxation problems
Using an integer programming problem to determine which investments should be made.
Using an integer programming problem to determine which investments should be made.

Deployment

You can use Optimization Toolbox solvers with MATLAB Compiler™ to create decision support tools that can be shared with users who do not have MATLAB.  These standalone applications can be deployed royalty-free to an unlimited number of end users. You can also integrate MATLAB optimization algorithms with other languages, such as Java® and .NET, using MATLAB Builder™ products.

Next: Multiobjective Optimization

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