The most advanced solver for nonlinear optimization
— Nonlinear optimization problems arise in numerous business and industry applications: portfolio optimization, optimal power flow, nonlinear model predictive control, Nash equilibrium problems. To solve these challenging problems, customers in hundreds of sites worldwide rely on Artelys Knitro for its efficiency and robustness.
Artelys Knitro has been developed by Ziena Optimization since 2001. Since the acquisition of Ziena and its development team in 2015, Artelys is in charge of the software development and distribution worldwide.
news
The latest versions of Artelys Knitro and CasADi are now compatible!
— CasADi is an open-source tool for general numerical optimization with a strong focus on optimal control and its versions 3.6.2 and higher are now compatible with Artelys Knitro 13.2.
Artelys Knitro 13.2: increased robustness for MINLP
— We are pleased to announce that Artelys Knitro 13.2 is now available! This new version focuses on robustness improvements for mixed-integer general nonlinear programs (MINLP).
Artelys Knitro 13.1: solving MINLP faster than ever!
— We are pleased to announce that Artelys Knitro 13.1 is now available! Check out its improvements, especially on mixed-integer nonlinear problems (MINLP).
widely used in academia and industry
— More than 450 institutions in over 40 countries rely on Artelys Knitro.
Top universities
Berkeley, Columbia, Harvard, MIT, Princeton, Stanford
Cath. Univ. of Chile, Univ. of São Paulo,ESSEC, ETH Zürich, LSE,Nat. Univ. of Singapore, Tsinghua Univ.,Univ. of Melbourne, Univ. of Queensland
Industries
Economic consulting firms
Financial institutions
Mechanical engineering companies
Oil & Gas companies
Regulatory & Policy makers
Software developers (as a third-party)
countries
institutions
algorithms
interfaces
undeniable successes
The MIT Biomimetic Robotics Lab used our nonlinear solver on a quadruped robot.
TotalEnergies owns and operates several refineries worldwide, producing millions of barrels per day by implementing complex refinery operations.
Artelys Knitro and AMPL are used by Masoud Zarepisheh, Assistant professor, at the Memorial Sloan Kettering Cancer Center to plan radiation for cancer patients!
We studied the Federal Reserve Bank of New York DSGE model implemented in MATLAB using the IRIS toolbox by Iskander Karibzhanov, Senior Scientist at Bank of Canada.
The NCL algorithm, designed by Kenneth Judd, Ding Ma, Michael Saunders, addresses the difficulty in solving tax policy models by using Julia with Artelys Knitro.
IPSO, a rich and powerful tool for optimizing the planning and operation of power systems thanks to Artelys Knitro.
See how black-box optimization is used in mining industry.
ORICA: Optimizing resource extraction
The mining industry faces sophisticated engineering problems arising from the need to develop increasingly complex ore deposits. The ORICA delivers value by enabling mining operations to reduce the amount of waste they process, leading to increased sustainability, greater profitability and a smaller environmental footprint.
One of the obstacles to solve the complex engineering problems in the mining industry is the integration of all the processes in the mining value chain. The Integrated Extraction Simulator (IES) is an ORICA developed cloud-based simulation and optimization platform designed to integrate, predict and optimize all mining and mineral processing operations. It provides fast and accurate simulations of key mining process from mine to final product.
ORICA is working to solve various industry challenges, which makes Artelys Knitro an invaluable tool. It allows IES users to efficiently solve a wide range of problems, such as mass balance, calibration, and user-defined optimization problems. Indeed, users can build simulation flowsheets which IES can express as black box functions, without known derivatives. In addition, cloud deployment of Artelys Knitro makes it possible to use thousands of servers in parallel to complete simulations, that would take an individual machine years to do, in the space of a few days.
IES provides productivity breakthroughs and new thinking in mining and metallurgical modelling, by creating a truly integrated virtual mining value chain, enabled by Artelys Knitro.
ENGIE Impact: Optimizing sustainable electric power systems
Electric power systems are at the heart of the energy trilemma: affordability, sustainability and reliability. Powerful optimization software tools are required to plan electric power systems in order to achieve a twofold result: improving profitability of investments and ensuring reliable operating conditions.
IPSO (Integrated Power System Optimizer) is a planning and analysis tool, developed by ENGIE Impact, for solving advanced Optimal Power Flow (OPF) problems. The tool allows users flexibility to tackle various problems that extend beyond traditional applications of OPF. Potential applications are the computation of the maximum power that can be securely transferred, the definition of an optimal investment plan to compensate the reactive power and keep the voltage within bounds and, lastly, the identification of preventive and/or corrective control actions needed to deal with failing equipment.
These applications consider the full complexity of real power systems, such as the nonlinearities of power flow equations and the discrete nature of numerous control variables. The resulting complex nonlinear and non-convex problems require a powerful nonlinear solver able to handle very large optimization problems. Artelys Knitro is the right answer to tackle these. Indeed, its state-of-the-art interior point method allows IPSO to optimize power systems with thousands of generation and transmission elements (e.g. power system of a country or of a part of a continent).
IPSO is used to plan and operate sustainable electric power systems all over the world, thanks to its efficiency in solving diverse OPF problems and its comprehensive diagnosis on the main constraining factors.
See how large-scale optimization models can be used in the healthcare industry!
Artelys Knitro and AMPL are used by Masoud Zarepisheh, Assistant Professor, at the Memorial Sloan Kettering Cancer Center (MSKCC) to plan radiation for cancer patients! The approach consists in prioritizing clinical objective in order to maximize tumor radiation coverage while minimizing the impact on healthy tissues.
The ECHO project (Expedited Constrained Hierarchical Optimization) is an automated planning process developed at MSKCC based on hierarchical constrained optimization technique to prioritize clinical objective. The automation relies on complex large-scale optimization models solved with Artelys Knitro. One key feature that speeds up the resolution of such complex models is the problem structure exploitation to automatically apply convex specializations.
The automation of radiation therapy cancer treatment results in faster treatment delivery, more accurate tumor irradiation and healthy tissue sparing. The method has been implemented by the hospital since April 2017 and was already successfully used in the treatment process of more than 800 patients!
Artelys Knitro and AMPL are used by Masoud Zarepisheh, Assistant Professor, at the Memorial Sloan Kettering Cancer Center (MSKCC) to plan radiation for cancer patients! The approach consists in prioritizing clinical objective in order to maximize tumor radiation coverage while minimizing the impact on healthy tissues.
The ECHO project (Expedited Constrained Hierarchical Optimization) is an automated planning process developed at MSKCC based on hierarchical constrained optimization technique to prioritize clinical objective. The automation relies on complex large-scale optimization models solved with Artelys Knitro. One key feature that speeds up the resolution of such complex models is the problem structure exploitation to automatically apply convex specializations.
The automation of radiation therapy cancer treatment results in faster treatment delivery, more accurate tumor irradiation and healthy tissue sparing. The method has been implemented by the hospital since April 2017 and was already successfully used in the treatment process of more than 800 patients!
See how tax policy models in Julia can be solved efficiently with Artelys Knitro!
Economists work routinely with tax policy models formulated as inequality-constrained nonconvex optimization problems. They have a degeneracy feature: the number of active inequality constraints at a solution is typically several times larger than the number of variables in the problem, which makes them particularly difficult to solve.
The NCL algorithm, designed by Kenneth Judd, Ding Ma, Michael Saunders, and Dominique Orban as part of Ding Ma’s PhD thesis at Stanford, addresses the difficulty in solving such models. The idea is to approximate the ill-posed problem with a sequence of well-posed subproblems without the degeneracy feature. Early subproblems can be solved loosely. Accuracy is only required as we approach a solution of the original model.
The first version of NCL is implemented entirely in AMPL and calls Artelys Knitro’s barrier algorithm with appropriate options to solve the subproblems tackling tax policy models with thousands of variables and half a million constraints.
NCL’s success on the tax models prompted them to investigate a generalization for any optimization model. The Julia language offers the requisite tools: the Julia interface to Artelys KNITRO and the JuliaSmoothOptimizers (JSO) infrastructure for optimization. In particular, JSO’s generic modeling features gives access to large test sets by way of the Julia interface to the CUTEst collection and to AMPL models.
Thanks to the work of Pierre-Élie Personnaz during his internship at GERAD, numerical results on realistic tax problems were presented at the ICCOPT 2019 conference in Berlin with performance that surpass all previous results. The NCL solver showcases how powerful the combination of Julia, JSO, and Artelys Knitro can be for optimization. Ongoing improvements include primal and dual warm starts, progressive tolerances, and parameter tuning.
See how derivative-free optimization
is used in Macro-economics!
Among the domain of macroeconomics are a series of models called DSGE (Dynamic Stochastic General Equilibrium), that try to explain the effects of economic policies on economic growth. Such models are frequently used by Central Banks to predict global growth of a country.
We studied the Federal Reserve Bank of New York DSGE model implemented in MATLAB using the IRIS toolbox by Iskander Karibzhanov, Senior Scientist at Bank of Canada. This model is highly nonlinear, with no access to exact derivatives. In such cases, one cannot expect the solver to find a solution with as much precision as for a problem for which exact derivatives are provided.
The parallel finite-differencing feature of Artelys Knitro is used to speed up the computation. Using Knitro 11.1 out-of-the-box, the computation time is further decreased by a factor of 5 while achieving the same value of the objective function.
TotalEnergies: optimize oil blending in a refinery
TotalEnergies owns and operates several refineries worldwide, producing millions of barrels per day by implementing complex refinery operations. In order to improve processes within its refineries, TotalEnergies wished to provide its planners with an operations management tool based on an optimization engine.
A refinery has to satisfy product deliveries contracted with its customers over a given time period. Several products such as fuel or diesel can be shipped through various shipment types like trucks or pipelines. As a consequence, a set of operations is planned to meet the product delivery requirements.
The main operation type consists of hydrocarbon blends for which components are blended to generate the final product to be delivered. The calculation engine based on Artelys Knitro optimizes the blend recipes as well as the planning of these mixtures in order to minimize the costs of the operations carried out as well as the delays of the customer deliveries while meeting the product quality requirements.
The model complexity comes from the quality specification constraints of the blends and deliveries which involve complex nonlinear equations. The project leverages the advanced black box capabilities of Artelys Knitro to efficiently tackle instances with dozens of product qualities, specifications and planned operations over several weeks.
See how the MIT Biomimetic Robotics Lab uses Artelys Knitro to achieve High speed landing of quadruped robots
There are various and fascinating projects adopting Artelys Knitro. The MIT Biomimetic Robotics Lab used our nonlinear solver on quadruped robot. Artelys Knitro has been found to be the only non-linear solver capable of performing fast enough to be deployed onboard their robot for a real-time Optimal Landing Control.
Trajectory optimization
The Biomimetic Robotics Lab at the Massachusetts Institute of Technology (MIT) has been using Artelys Knitro for real-time control of their legged robots: the MIT Mini Cheetah and the MIT Humanoid. Trajectory optimization is an essential process for real-time control of the legged robots. Optimal control for legged systems is a challenging problem that must contend with nonlinear, hybrid dynamics and complicated, high degree-of-freedom kinematics. In the case of the Mini Cheetah, this optimization process is used to plan complicated motions such as jumps, aerial spins, back flips, and barrel rolls.
The ability to perform these motions greatly expands the range of environments the robot is capable of traversing, which is crucial as these robots are meant to be deployed operationally. Since incorporating Artelys Knitro into the software, the lab has been able to implement a number of new, real-time controllers on their robots using nonlinear optimization. Even after testing other state-of-the-art nonlinear optimization solvers, Artelys Knitro was the only one capable of performing fast enough to be deployed onboard their robot.
Model-predictive controllers
For the Mini Cheetah, a nonlinear model predictive controller (MPC) was implemented for landing. The optimization was formulated with complementarity constraints, which make the nonlinear program (NLP) challenging for many solvers, but Artelys Knitro was able to find solutions at roughly 5-10 Hz (i.e., between 5 and 10 problems are solved every second). The team used a nonlinear trajectory optimization including contact complementary constraints to find optimal landing postures. Because real-time performance is so important in the short duration of a fall, Artelys Knitro was used over other solvers for its speed and reliable convergence.
For the MIT Humanoid, a nonlinear predictive controller was implemented that leverages the MIT Humanoid’s arms to improve balance and locomotion. The complex nonlinear optimization can solve complex arm motions in response to large disturbances. Artelys Knitro solved these motions at 40 Hz and helped demonstrate successful landings in both simulation and hardware.
problems classes solved
— Artelys Knitro is specialized in solving large scale nonlinear mathematical optimization problems. It is the only nonlinear solver with 7 different algorithms, allowing it to solve a large range of complex optimization problems.
applications
— Artelys Knitro is currently used in many application areas, thus demonstrating its versatility.
This section details some of the typical applications of Artelys Knitro with references to the academic literature. From fundamental mathematics to sustainable development, Artelys Knitro was found useful by a large range of Operations Research practitioners.
Financial & Banking
Optimal control & dynamic optimization
Computational economics & game theory
Telecommunications
Statistics & data analysis
Optics & spectroscopy
Energy
Mathematics & geometry
Sustainable development
Financial & banking
Optimization methods play a vital role in option pricing, portfolio selection and strategic bidding. Modeling and software solutions lend valuable assistance in decision making.
— Typical uses of Artelys Knitro
• Portfolio optimization with transactions costs
• Optimal pricing and risk management
• Volatility estimation
• Credit risk
• Strategic bidding and auctions (Nash equilibrium)
— In the literature
• Byrd, J. R., and Liu, Z. (2007): “Nonlinear Optimization Methods with Financial Applications“, Case Studies in Optimization, Ziena.
• Nocedal, J. (2008): “The ZIENA Solver for American Options Pricing“, Case Studies in Optimization, Ziena.
— Business Case
Computational economics & game theory
— Typical uses of Artelys Knitro
• Design of economic policies
• Yield management
• Demand modeling
• Maximum-likelihood estimation
• Nash equilibrium
— In the literature
• Conlon, C. T. (2009): “A Dynamic Model of Costs and Margins in the LCD TV Industry“, Unpublished manuscript.
• Hanson, D. A., Kryukov, Y., Leyffer, S., and Munson, T. S. (2009): “Optimal Control Model of Technology Transition“, No 2009-E24, GSIA Working Papers from Carnegie Mellon University, Tepper School of Business.
• Dubé, J.-P., Fox, J. T., and Su, C.-L. (2012): “Improving the numerical performance of static and dynamic aggregate discrete choice random coefficients demand estimation“, in Econometrica, 80 (5), 2231-2267.
• Egesdal, M., Lai, Z., and Su, C.-L. (2012): “Estimating Dynamic Discrete-Choice Games of Incomplete Information“, Working paper.
Statistics & data analysis
— Typical uses of Artelys Knitro
• Nonlinear least squares analysis (regression / data fitting)
• Support vector machines
• Data mining
• Data clustering
• Inference analysis
• Parameter estimation
• Inverse problems
— In the literature
• Wang, G., Zhu, Z., Du, W., and Teng, Z. (2008): “Inference Analysis in Privacy-Preserving Data Re-publishing“, Data Mining, 2008, ICDM ’08, Eight IEEE International, 1079-1084.
• Fuchs, M., and Neumaier, A. (2010): “Optimization in latent class analysis“, Technical Report TR/PA/10/89, CERFACS.
• Rauchs, G., and Dumitriu, D. (2010): “Indentation testing parameter identification using an optimization procedure based on genetic algorithms“, in Proc. of the Romanian Academy, Series A: Mathematics, 10 (2), 165-172.
Energy
Management of distribution networks, optimal plant operations, revenue and risk management, and strategic pricing play an increasingly important role in the energy sector.
— Typical uses of Artelys Knitro
• Nonlinear optimal flow problems in electrical networks (OPF)
• Security-Constrained OPF (SCOPF) problems
• Optimisation of generation costs and transmission losses
• Modeling of head effects in the optimal management of water reservoirs Nonlinear OPF (optimal power flow) problem
• Oil & Gas production optimization
— In the literature
• Plantenga, T. (2006): “KNITRO for Nonlinear Optimal Power Flow Applications“, Case Studies in Optimization, Ziena.
• Eka Suwartadi, Stein Krogstad, Bjarne Foss (2010): “Second-Order Adjoint-Based Control for Multiphase Flow in Subsurface Oil Reservoirs“, 49th IEEE Conference on Decision and Control.
• Hu, B., Cañizares, C. A., and Liu, M.(2010): “Secondary and Tertiary Voltage Regulation Based on Optimal Power Flows”, Bulk Power System Dynamics and Control (iREP) – VIII (iREP), 2010 iREP Symposium, 1-6.
• Gutierrez-Martinez, V. J., Cañizares, C. A., Fuerte-Esquivel, C. R., Pizano-Martinez, A., and Gu, X. (2011): “Neural-Network Security-Boundary Constrained Optimal Power Flow”, IEEE Transactions on Power Systems, 26 (1), 63-72.
• Ferreira, E. C., Baptista, E. C., and Soler, E. M. (2012): “An investigation about barrier parameters update strategy and the Optimal Power Flow Solution”, EngOpt 2012, 3rd International Conference on Engineering Optimization.)
• Barragan Hernandez, A., Vazquez-Roman, R., Rosales-Marines, L., Garcia-Sanchez, F. : “A strategy for simulation and optimization of gas and oil production”, Computers and Chemical Engineering 30, 2005, 215–227.
• Liu, Z., Wang, S., and Ouyang, Y. (2017): “Reliable Biomass Supply Chain Design under Feedstock Seasonality and Probabilistic Facility Disruptions”, Energies 2017, 10, 1895.
• Stock, D.S.; Sala, F.; Berizzi, A.; Hofmann, L. (2018): “Optimal Control of Wind Farms for Coordinated TSO-DSO Reactive Power Management”, Energies 2018, 11, 173.
Sustainable development
— Typical uses of Artelys Knitro
• Virtual population analysis
• Population growth management
• Transition path control
— In the literature
• Tahvonen, O. (2008): “Optimal harvesting of age-structured fish populations”, CEMARE Research Paper, P165.
• Tahvonen, O., Pukkala, T., Laiho, O., Lähde, E., and Niinimäki, S. (2010): “Optimal management of uneven-aged Norway spruce stands”, in Forest Ecology and Management, 260 (1), 106-115.
• Rosa, R., Vaz, J., Mota, R. et al. (2017): “Preference for Landings’ Smoothing and Risk of Collapse in Optimal Fishery Policies: The Ibero-Atlantic Sardine Fishery“, in Environmental and Resource Economics.
• Hänsela, M. C., Quaasa, M. F. (2018): ” Intertemporal Distribution, Sufficiency, and the Social Cost of Carbon”, in Ecological Economics 146, 520–535.
Optimal control & dynamic optimization
— Typical uses of Artelys Knitro
• Trajectory optimization
• Optimization with partial differential equations
• PDE-Constrained optimization with discret decisions
• Variational Analysis
— In the literature
• Abdallah, L., Haddou, M., and Khardi, S. (2010): “Optimization of operational aircraft parameters reducing noise emission“, in Applied Mathematical Sciences, 4 (11), 515-535.
• Nahayo, F., Khardi, S., Ndimubandi, J., Haddou, M., and Hamadiche, M. (2010): “Two-Aircraft Acoustic Optimal Control Problem: SQP algorithms“, in ARIMA, 14, 101-123.
• You, F., and Leyffer, S. (2011): “Mixed-Integer Dynamic Optimization for Oil-Spill Response Planning with Integration of a Dynamic Oil Weathering Model“, in AIChE Journal, 57 (12), 3555-3564.
• Kone, B., Diedhiou, I., Diallo, C., Gueye Diagne , S., and Ndiaye, G. (2018): “Optimization of the Containers Train Loading Operations at Abidjan Terminal“, in Journal of Mathematics Research, 10(4), p19.
Optics & spectroscopy
— Typical uses of Artelys Knitro
• Light polarization control
• Isomer conformational analysis
— In the literature
• Lott, G. A., Perdomo-Ortiz, A., Utterback, J. K., Widom, J. R., Aspuru-Guzikb, A., and Marcus, A. H. (2011): “Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2D fluorescence spectroscopy“, in Proceedings of the National Academy of Sciences, 108 (40), 16521-16526.
• Tripathi, S., Paxman, R., Bifano, T., and Toussaint, K. C. Jr. (2012): “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media“, in Optics Express, 20 (14), 16067-16076.
Mathematics & geometry
— Typical uses of Artelys Knitro
• Shape curvature minimization via contour regularization
• Independent proof check
• Counterexample detection
— In the literature
• Hales, T. C., and McLaughlin, S. (2010): “The dodecahedral conjecture”, in Journal of the american mathematical society, 23 (2), 299-344.
• Bretin, E., Lachaud, J.-O., and Oudet, E. (2011): “Regularization of discrete contour by Willmore energy”, in Journal of mathematical imaging and vision, 40 (2), 214-229.
Telecommunications
— Typical uses of Artelys Knitro
• Transmission network optimization
• Resource allocation
— In the literature
• Sosa-Paz, C., Ruckmann, J., and Sánchez-Meraz, M. (2010): “Joint Routing, Link Scheduling and Power Control for Wireless Multi-hop Networks for CDMA/TDMA Systems“, in Científica, 14 (4), 165-172.
key features
— The optimization techniques used by Artelys Knitro offer the leading combination of computational efficiency and robustness. Thanks to several key features, Artelys Knitro can efficiently solve a wide range of optimization problems.
Parallel multistart feature for global optimization +
Ability to run multiple algorithms concurrently +
Automatic and parallel tuning of option settings +
Automatic computation of approximate first-order and second-order derivatives +
Smart initialization strategies and fast infeasibility detection +
interfaces
— Artelys Knitro and AMPL
AMPL is a popular modeling language for optimization that allows users to represent their optimization problems in a user-friendly, readable, intuitive format. Artelys Knitro provides a dedicated driver “knitroampl” to use it from AMPL. Knitroampl gives access to all the solver features. Extensive example and documentation on using knitroampl are provided with the Knitro distribution and described in the Artelys Knitro User’s Manual.
— Artelys Knitro and MATLAB
Artelys Knitro presents an interface to the MATLAB® computing environment that supports all major features in Knitro, including the ability to model and solve mixed-integer programming (MIP) models and mathematical programs with equilibrium constraints (MPEC). This interface, called “knitromatlab”, supersedes the previous ktrlink interface provided by the MATLAB Optimization Toolbox. Knitromatlab uses an API very similar to the MATLAB fmincon nonlinear optimization tool, providing an easy mechanism for porting code between the two, while also making available the enhanced features in Artelys Knitro. Extensive example and documentation on using knitromatlab are provided with the Knitro distribution and described in the Artelys Knitro User’s Manual.
— Artelys Knitro and R
R is an open-source software environment for statistical computing, available under GNU General Public License. It is developed and maintained by the R Foundation. Artelys Knitro provides a dedicated library to use it from R. The Artelys Knitro R library gives access to all the solver features and includes a dedicated function for solving nonlinear least-squares. Extensive example and documentation on using Knitro from R are provided with the Knitro distribution and described in the Artelys Knitro User’s Manual.
operating systems
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testimony
— “Artelys Knitro and AMPL performance enables the automation of radiation therapy cancer treatment, resulting in faster treatment delivery and more accurate tumor irradiation and healthy tissue sparing. Thanks to the resolution of complex large scale optimization models more than 800 patients were treated since the beginning of the project.”
— “The use of robust, innovative and powerful components enables us to carry out reliable analyses about sensitive issues such as network security.”
— “Our software incorporates Knitro to solve very complex mixed integer nonlinear programming (MINLP) optimization problems. These problems must be solved in near-real time (at the 5 minute level), and we have found no other solver that matches the speed and accuracy of Knitro. In addition, the customer support at Artelys has been fantastic. They have been very responsive to our needs, have worked closely with us in product development, and have been very flexible in product implementation and licensing.”
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