Lineare Programmierung und gemischt-ganzzahlige lineare Programmierung
Lösen linearer Programmierungsprobleme mit kontinuierlichen und ganzzahligen Variablen
Bevor Sie mit der Lösung eines Optimierungsproblems beginnen, müssen Sie den geeigneten Ansatz wählen: problembasiert oder solverbasiert. Für Details siehe Erster Schritt: Wählen eines problembasierten oder solverbasierten Ansatzes.
Erstellen Sie beim problembasierten Ansatz Problemvariablen und stellen Sie anschließend die Zielfunktion und die Nebenbedingungen anhand dieser symbolischen Variablen dar. Die erforderlichen Schritte beim problembasierten Vorgehen finden Sie unterProblem-Based Optimization Workflow. Lösen Sie das resultierende Problem mithilfe der Funktion solve.
Die erforderlichen Schritte beim solverbasierten Vorgehen, einschließlich der Definition der Zielfunktion und der Nebenbedingungen sowie der Auswahl des geeigneten Solvers, finden Sie unter Solverbasierte Optimierungsproblem-Konfiguration. Lösen Sie das resultierende Problem mithilfe der Funktion intlinprog, wenn erweiterte ganzzahlige Nebenbedingungen vorliegen, bzw. mithilfe von linprog, wenn keine ganzzahligen Nebenbedingungen vorliegen.
Funktionen
Objekte
integerConstraint | Indices of extended integer variables (Seit R2025a) |
SensitivityAnalysis | Sensitivities of linear program coefficients (Seit R2026a) |
Live Editor Tasks
| Optimize | Optimieren oder Lösen von Gleichungen im Live-Editor |
Themen
Problembasierte gemischt-ganzzahlige lineare Programmierung
- 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. - Minimize Makespan in Parallel Processing
Minimize the maximum time for a set of processors to complete a group of tasks. - Solve Sudoku Puzzles via Integer Programming: Problem-Based
This example shows how to solve a Sudoku puzzle using binary integer programming.
Solverbasierte gemischt-ganzzahlige lineare Programmierung
- 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.
Problembasierte lineare Programmierung
- Set Up a Linear Program, Problem-Based
Linear problem formulation using the problem-based approach. - Maximize Long-Term Investments Using Linear Programming: Problem-Based
Optimize a deterministic multiperiod investment problem using linear programming and the problem-based approach. - Optimize Green Hydrogen Production System
Optimize a green hydrogen production system. - Optimal Dispatch of Electric Power
Optimize the power generated or dispatched among renewable and nonrenewable generators in a deterministic system using optimization variables. - Create Multiperiod Inventory Model in Problem-Based Framework
Create an inventory model, where stock is carried between time periods, in the problem-based approach.
Solverbasierte lineare Programmierung
- 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. - Sensitivity Analysis in Linear Programming
Examine sensitivities in a linear program solution. - Maximize Long-Term Investments Using Linear Programming: Solver-Based
Optimize a deterministic multiperiod investment problem using linear programming.
Codegenerierung
- Code Generation for linprog Background
Prerequisites to generate C code for quadratic optimization. - Generate Code for linprog
Learn the basics of code generation for thelinprogoptimization solver.
Modellieren und Analysieren linearer und ganzzahliger Probleme
- Integer and Logical Modeling
Techniques for modeling with integer constraints using "Big-M" and other techniques. - Investigate Linear Infeasibilities
Find out which linear constraints cause a problem to be infeasible.
Problembasierte Algorithmen
- Problem-Based Optimization Algorithms
Learn how the optimization functions and objects solve optimization problems. - Supported Operations for Optimization Variables and Expressions
Explore the supported mathematical and indexing operations for optimization variables and expressions.
Solverbasierte Algorithmen und Optionen
- Linear Programming Algorithms
Minimizing a linear objective function in n dimensions with only linear and bound constraints. - Mixed-Integer Linear Programming (MILP) Algorithms
The algorithms used for solution of mixed-integer linear programs. - Optimization Options Reference
Explore optimization options. - Tuning Integer Linear Programming
Steps for improving solutions or solution time. - intlinprog Output Function and Plot Function Syntax
How to monitor the progress of theintlinprogsolution process.
Verwandte Informationen
- Lösen eines gemischt-ganzzahligen linearen Optimierungsproblems mithilfe der Optimierungsmodellierung
- Mathematische Modellierung mit Optimierung, Teil 1
- Optimierungsmodellierung, Teil 2: Problembasierte Lösung eines mathematischen Modells
- Optimierungsmodellierung, Teil 2: Umwandlung in die Solver-Form
