AMPL Team
March 8, 2024
Unleashing Knitro’s Power through AMPL Integration
Artelys Knitro is an especially powerful nonlinear solver, offering a range of state-of-the-art algorithms and options for working with smooth objective and constraint functions in continuous and integer variables. It is designed for local optimization of large-scale problems with up to hundreds of thousands of variables.
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Artelys Knitro is distinguished as a leading nonlinear solver, celebrated for its robust and efficient algorithms. Initially developed by Ziena Optimization in the early 2000s and subsequently acquired by Artelys, Knitro boasts a legacy of continuous innovation. It excels in handling large-scale nonlinear problems, making it the go-to solution in industries such as finance, energy management, and engineering design, where near-optimal solutions must be achieved swiftly and effectively.
Knitro is renowned for its proficiency in addressing a diverse range of optimization challenges, from straightforward continuous unconstrained problems to the more complex mixed-integer nonlinear programs (MINLPs). Its forte lies in efficiently solving large-scale, smooth convex nonlinear optimization problems, but its capabilities extend to non-convex quadratic programming (QPs) and finding local solutions of general nonlinear programs (NLPs) as well.
Knitro’s integration with AMPL through a user-friendly interface enhances its accessibility, making it an intuitive yet potent tool for professionals and researchers striving to solve demanding optimization problems with efficiency.
Unconstrained, bound constrained, systems of nonlinear equations, linear and nonlinear least squares problems, linear programming problems (LPs), convex and non-convex quadratic programming problems (QPs), quadratically constrained quadratic programs (QCQPs), second order cone programs (SOCPs), mathematical programs with complementarity constraints (MPCCs), both convex and non-convex general nonlinear (smooth) constrained problems (NLP), mixed integer linear programs (MILP) of moderate size, mixed integer (convex) nonlinear programs (MINLP) of moderate size, derivative free (DFO) or black-box optimization.
Complementarity and equilibrium constraints using the AMPL “complements” operator.
At its core, Knitro is powered by four sophisticated optimization algorithms: the direct and conjugate-gradient interior point methods, the active set method, and the sequential quadratic programming method. Mixed-integer nonlinear programs are solved using either a non-linear branch-and-bound (NLPBB) algorithm or mixed-integer sequential quadratic programming (MISQP) algorithm. The MISQP method is designed for problems with expensive function evaluations and can handle non-relaxable integer variables.
Extensive use of shared-memory multi-core computing: concurrent optimization to determine the best choice among multiple algorithms; a parallel multi-start procedure for non-convex problems to prevent users from settling on the initial locally optimal solution encountered; parallel linear algebra and finite-difference gradient computations. Options to keep iterates feasible with respect to bounds and inequalities. Special handling of quadratic objectives and constraints to improve efficiency.
For Python enthusiasts, Knitro is also accessible as a module with amplpy, blending seamlessly with your Python projects. Explore more about this integration at AMPL Python Integration.# Install Python API for AMPL
$ python -m pip install amplpy
# Install Knitro
$ python -m amplpy.modules install knitro
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Best for individuals running on one machine
$3,000 /yearly subscription
$6,000 /purchase
+ $1,200 maintenance annually
$2,000 /yearly subscription
$4,000 /purchase
+ $800 maintenance annually
Best for small applications running one process at a time
$4,500 /yearly subscription
$9,000 /purchase
+ $1,800 maintenance annually
$4,000 /yearly subscription
$8,000 /purchase
+ $1,600 maintenance annually
Best for large teams or applications to run multiple processes simultaneously
$7,000 /yearly subscription
+ $700 additional CPU
$14,000 /purchase
+ $2,800 maintenance annually + $1,400 additional CPU
$6,000 /yearly subscription
+ $600 additional CPU
$12,000 /purchase
+ $2,400 maintenance annually + $1,200 additional CPU
Knitro downloads are available from the My Downloads page of your account at the AMPL Portal, and are included in the trial bundles
The integration of AMPL and Knitro brings together the intuitive modeling capabilities of AMPL with the sophisticated non-linear solving power of Knitro. This collaboration enables users to define complex optimization problems in AMPL’s accessible language, which are then efficiently solved by Knitro’s advanced algorithms. The outcome is a streamlined process that enables users to easily implement, maintain, and solve their models, thereby significantly boosting overall productivity. Particularly beneficial for large-scale, intricate models, this powerful combination ensures that even the most demanding optimization tasks are handled with unmatched efficiency.
Using AMPL and Knitro in unison offers unparalleled flexibility and robustness in tackling various optimization challenges.
Utilizing KNITRO alongside AMPL significantly accelerates the development cycle by eliminating the need for user-provided derivatives—a process that is not only tedious but also prone to errors. This relieves modelers of a substantial burden as AMPL automatically generates derivatives for KNITRO, thereby streamlining the modeling process. The result is enhanced efficiency, enabling rapid prototyping and testing. Users benefit from Knitro’s capability to handle complex non-linearities and its advanced features like constraint programming, mixed-integer programming, and globalization techniques. AMPL’s clear syntax and structure complement these strengths, making it easier to implement, modify, and maintain complex models. Together, AMPL and Knitro not only solve problems more effectively but also empower users to explore innovative optimization strategies, making this combination a valuable asset for researchers, analysts, and decision-makers across diverse sectors.
In today’s complex and fast-paced global market, efficient supply chain management is crucial for maintaining competitive advantage. A leading multinational corporation, specializing in consumer electronics, faced challenges in optimizing its vast supply chain network. The network included multiple manufacturing sites, distribution centers, and retail outlets spread across different continents. The key challenges were minimizing costs, managing the non-linear dynamics of supply and demand, and navigating logistical constraints.
The Knitro Solution: The corporation employed Knitro to tackle these optimization challenges. Knitro’s advanced non-linear problem-solving capabilities were employed to solve a comprehensive model that considered various factors such as production costs, transportation logistics, demand forecasting, inventory management, and delivery timelines.
Implementation and Results:
Conclusion: The use of Artelys Knitro to optimize the corporation’s supply chain resulted in streamlined operations, cost savings, and a more agile response to market changes. This case study demonstrates Knitro’s prowess in managing and optimizing complex, non-linear systems prevalent in global supply chain networks.
In the dynamic field of telecommunications, optimizing network layouts and bandwidth allocation is crucial for maintaining an edge in technology and customer satisfaction. This case study explores the theoretical application of Knitro in transforming network optimization for a telecommunications company.
Here are some specific examples of how Knitro can be used in engineering and design:
Challenge: The hypothetical challenge involves managing complex, large-scale network infrastructures, ensuring optimal bandwidth allocation, and enhancing overall network performance to improve user experience.
Solution with Knitro: Artelys Knitro, with its proficiency in solving non-linear optimization problems, was theoretically employed to restructure the network layout and optimize bandwidth distribution. This involved intricate calculations considering various factors like user demand, geographical constraints, and existing infrastructure.
Results: The theoretical utilization of Knitro led to an optimized network design that efficiently managed data flow, reducing bottlenecks and improving the quality of service. This resulted in enhanced user satisfaction and a competitive advantage in the telecommunications market.
Knitro is specifically designed for solving large-scale, complex non-linear optimization problems. It excels in areas like mixed-integer, quadratic, and nonlinear programming, making it ideal for applications in finance, energy management, engineering design, and more.
Knitro seamlessly integrates with AMPL, allowing users to define their optimization models in AMPL’s user-friendly language, which Knitro then solves using its advanced algorithms. This integration provides an efficient workflow for formulating, solving, and analyzing optimization problems.
Yes, Knitro is renowned for its ability to efficiently solve large-scale optimization problems. Its advanced algorithms and techniques are specifically designed to handle the complexities and size of large-scale, real-world problems.
Knitro provides comprehensive documentation, including user guides, example problems, and technical references. Additionally, users have access to a dedicated support team for technical assistance and guidance in both using Knitro and integrating it with AMPL.
Yes, a trial version of Knitro is available for evaluation purposes. Prospective users can request a trial to assess Knitro’s capabilities and determine how it meets their specific optimization needs.
Knitro uses rigorously tested algorithms and numerical methods to ensure the accuracy and reliability of its solutions. It employs advanced techniques to verify solution quality and provides detailed diagnostic information to aid in model evaluation and troubleshooting.
Knitro stands out for its specialized focus on non-linear problems, its ability to handle a wide range of problem types, and its seamless integration with modeling languages like AMPL. Its robustness, speed, and advanced features make it a preferred choice for complex optimization tasks.
Yes, Knitro is widely used in academic research for solving complex optimization problems across various disciplines. Special licensing options are available for academic institutions, supporting research and educational use.