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Linear Programming and Mixed-Integer Linear Programming
There are two approaches to linear programming and mixed-integer linear programming. This table helps you choose the best approach. Examples appear toward the bottom of the page.
| Approaches | Characteristics |
|---|---|
| Problem-Based Optimization Setup | Easier to create and debug |
| Only for linear or quadratic problems with linear or integer constraints | |
| Represent the objective and constraints symbolically | |
| Solution time is longer because of translation time from problem form to matrix form | |
| See the steps in Problem-Based Workflow | |
| Basic example: Mixed-Integer Linear Programming Basics: Problem-Based or the video Solve a Mixed-Integer Linear Programming Problem using Optimization Modeling | |
| Solver-Based Optimization Problem Setup | Harder to create and debug |
| Represent the objective and constraints as functions or matrices | |
| Solution time is shorter because there is no translation time to matrix form | |
| To save memory in large problems, allows use of Hessian multiply function or Jacobian multiply function. See Quadratic Minimization with Dense, Structured Hessian or Jacobian Multiply Function with Linear Least Squares. | |
| See the steps in Solver-Based Optimization Problem Setup | |
| Basic example: Mixed-Integer Linear Programming Basics: Solver-Based |
For the problem-based approach, create problem variables, and then
represent the objective function and constraints in terms of these symbolic
variables. For the problem-based steps to take, see Problem-Based Workflow. To
solve the resulting problem, use solve.
For the solver-based steps to take, including defining the objective
function and constraints, and choosing the appropriate solver, see Solver-Based Optimization Problem Setup. To solve the
resulting problem, use intlinprog when there are
integer constraints, or use linprog when there are no
integer constraints.
Functions
Topics
Problem-Based Mixed-Integer Linear Programming Applications
Mixed-Integer Linear Programming Basics: Problem-Based
Simple example of mixed-integer linear programming.
Factory, Warehouse, Sales Allocation Model: Problem-Based
This example shows how to set up and solve a mixed-integer linear programming problem.
Traveling Salesman Problem: Problem-Based
This example shows how to use binary integer programming to solve the classic traveling salesman problem.
Optimal Dispatch of Power Generators: Problem-Based
This example shows how to schedule two gas-fired electric generators optimally, meaning to get the most revenue minus cost.
Office Assignments by Binary Integer Programming: Problem-Based
This example shows how to solve an assignment problem by binary integer programming using the optimization problem approach.
Mixed-Integer Quadratic Programming Portfolio Optimization: Problem-Based
This example shows how to solve a Mixed-Integer Quadratic Programming (MIQP) portfolio optimization problem using the problem-based approach.
Cutting Stock Problem: Problem-Based
This example shows how to solve a cutting stock problem using linear programming with an integer linear programming subroutine.
Solve Sudoku Puzzles Via Integer Programming: Problem-Based
This example shows how to solve a Sudoku puzzle using binary integer programming.
Solver-Based Mixed-Integer Linear Programming Applications
Mixed-Integer Linear Programming Basics: Solver-Based
Simple example of mixed-integer linear programming.
Factory, Warehouse, Sales Allocation Model: Solver-Based
Example of optimizing logistics in a small supply chain.
Traveling Salesman Problem: Solver-Based
The classic traveling salesman problem, with setup and solution.
Optimal Dispatch of Power Generators: Solver-Based
Example showing how to schedule power generation when there is a cost for activation.
Office Assignments by Binary Integer Programming: Solver-Based
Solve an assignment problem using binary integer programming.
Mixed-Integer Quadratic Programming Portfolio Optimization: Solver-Based
Example showing how to optimize a portfolio, a quadratic programming problem, with integer and other constraints.
Cutting Stock Problem: Solver-Based
Solve a cutting stock problem using linear programming with an integer programming subroutine.
Solve Sudoku Puzzles Via Integer Programming: Solver-Based
Sudoku is a type of puzzle that you can solve using integer linear programming.
Problem-Based Linear Programming Applications
Set Up a Linear Program, Problem-Based
Linear problem formulation using the problem-based approach.
Maximize Long-Term Investments Using Linear Programming: Problem-Based
This example shows how to use the problem-based approach to solve an investment problem with deterministic returns over a fixed number of years T.
Create Multiperiod Inventory Model in Problem-Based Framework
This example shows how to create a multiperiod inventory model in the problem-based framework.
Solver-Based Linear Programming Applications
Set Up a Linear Program, Solver-Based
Problem formulation using the solver-based approach.
Typical Linear Programming Problem
This example shows the solution of a typical linear programming problem.
Maximize Long-Term Investments Using Linear Programming: Solver-Based
Optimize a deterministic multiperiod investment problem using linear programming.
Problem-Based Algorithms
Problem-Based Optimization Algorithms
How the optimization functions and objects solve optimization problems.
Supported Operations on Optimization Variables and Expressions
Lists all available mathematical and indexing operations on optimization variables and expressions.
Solver-Based Algorithms and Options
Minimizing a linear objective function in n dimensions with only linear and bound constraints.
Mixed-Integer Linear Programming Algorithms
The algorithms used for solution of mixed-integer linear programs.
Optimization Options Reference
Describes optimization options.
Tuning Integer Linear Programming
Steps for improving solutions or solution time.
intlinprog Output Functions and Plot Functions
How to monitor the progress of the intlinprog solution
process.
