Gurobi Articles
AMPL Team
December 7, 2023
AMPL Brings You the Power of Gurobi
Gurobi’s outstanding performance has been demonstrated through leadership in public benchmark tests and dramatic improvement in solve times year after year. Built using the latest algorithmic developments and large-scale computing techniques, Gurobi’s extremely robust code ensures correctness and scalability of results.
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Gurobi Optimization, founded in 2008, is a renowned developer of advanced software for linear, mixed-integer, quadratic, and more general nonlinear optimization. Its flagship product, the Gurobi Optimizer, is highly regarded for its exceptional combination of speed and robustness in determining optimal solutions for problems in thousands to millions of decision variables.
Gurobi was created by three prominent experts in the optimization field — Dr. Zonghao Gu, Dr. Edward Rothberg, and Prof. Robert Bixby — who sought to create a high-performance solver that could address the growing demands of complex data-driven decision-making, while integrating readily with popular programming languages and platforms. This adaptability has made Gurobi a preferred choice in numerous industries, including logistics, finance, energy, telecommunications, and manufacturing.
The Gurobi Optimizer has continuously evolved, integrating cutting-edge research and algorithms to maintain its position at the forefront of optimization technology, expanding the variety of problem types addressed, and broadening the range of on-premise and cloud-based solutions available. Gurobi’s commitment to innovation, coupled with strong customer support and community engagement, underscores its role as a key player in advancing the practice of mathematical optimization.
Linear and quadratic optimization in continuous and integer variables, for both convex and nonconvex cases, with extensions to widely used nonlinear and logical expressions.
Convex and nonconvex quadratic expressions in objectives and constraints; conic quadratic constraints; convenient nonlinear and logical operators.
For continuous linear and convex quadratic problems, primal and dual simplex methods and interior-point (barrier) methods. For integer problems, advanced branch-and-cut with presolve, feasibility heuristics and cut generators. For general nonlinear problems, spatial branch-and-bound and outer approximation.
Global optimization of nonconvex quadratic and select nonlinear problems. Shared-memory processing for barrier and for branch-and-cut. Distributed concurrent optimization and tuning to leverage multiple machines. Streamlined access to cloud services. Special facilities for multi-objective optimization and infeasibility diagnosis.
For Python enthusiasts, Gurobi 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 Gurobi
$ python -m amplpy.modules install gurobi
Best for individuals running on one machine
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+$700 /additional CPU
Best for individuals running on one machine
$6,000 /purchase
+ $1,200 maintenance annually
Best for small applications running one process at a time
$9,000 /purchase
+ $1,800 maintenance annually
Best for large teams or applications to run multiple processes simultaneously
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Best for individuals running on one machine
$3,000 /yearly subscription
$6,000 /purchase
+ $1,200 maintenance annually
Best for small applications running one process at a time
$4,500 /yearly subscription
$9,000 /purchase
+ $1,800 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
AMPL’s enhanced Gurobi interface provides significantly extended modeling support for logical and nonlinear operators, both natively through Gurobi’s built-in “general constraints” and through linearizations performed by our advanced “MP” interface.
Gurobi Optimization and AMPL have formed a synergistic partnership, leveraging their respective strengths to provide comprehensive solutions in the realm of mathematical optimization. AMPL, a powerful and flexible algebraic modeling language and system, lets people formulate complex optimization problems the way they think about them, while facilitating integration with enterprise applications. When linked to Gurobi’s high-performance optimization solvers, this combination becomes a potent tool for tackling a wide array of challenging decision problems tasks in large-scale optimization.
This partnership is particularly beneficial in supply chain management, logistics, finance, energy, and many other applications that must set thousands or even millions of interrelated decision variables to guarantee effective and profitable results. The union of AMPL’s modeling prowess with Gurobi’s solving efficiency creates a robust platform for users who need to formulate and solve optimization problems rapidly and accurately. This collaboration highlights the commitment of both companies to advancing the practice of optimization and providing users with tools that are both powerful and accessible, thus enabling better data-driven decision-making across locations, facilities, and time horizons.
In the energy and utilities sector, the Gurobi solver plays a crucial role in optimizing various complex operations, significantly enhancing efficiency and sustainability. One of the key applications is in the optimization of power generation and distribution. This includes the scheduling of power plants to meet fluctuating energy demands while minimizing fuel costs and adhering to environmental regulations. Gurobi helps in integrating renewable energy sources like wind and solar power into the grid, balancing the intermittent nature of these sources with demand. Additionally, it’s used for optimizing the maintenance schedules of power plants and distribution networks to ensure reliability and minimize downtime.
The users of Gurobi in this sector are typically operations research analysts, electrical engineers, and energy managers who are responsible for ensuring optimal energy production, distribution, and efficient use of resources.
Another important application in this sector is in the optimization of gas and water distribution networks. Gurobi helps in planning and operating these networks, ensuring efficient flow and reducing losses. It can also be combined with demand forecasting, helping utilities to optimize their operations accordingly. This aspect of optimization is particularly crucial in times of peak demand or during emergency situations, where the efficient distribution of resources can have significant impacts.
The roles that commonly use Gurobi for these purposes include network engineers, utility planners, and environmental analysts, who focus on optimizing network performance while considering economic and environmental factors.
Learn more about how Gurobi is being used in combination with AI and machine learning programs >
In finance and banking, Gurobi provides sophisticated tools for a range of optimization problems, notably in portfolio optimization and risk management. Portfolio managers use Gurobi to construct investment portfolios that maximize returns while controlling for risk. This involves solving complex mixed-integer linear programming problems to determine the optimal mix of assets. Gurobi’s solver is capable of handling the large, complex datasets typical in financial markets, providing solutions that take into account various constraints and objectives, such as liquidity requirements, regulatory constraints, and market impact costs.
Risk managers also use Gurobi to model and mitigate financial risks. This includes credit risk modeling, where Gurobi helps in optimizing credit portfolios by assessing the risk of defaults and balancing them against expected returns.
Another significant application in this sector is in asset and liability management (ALM), where financial institutions use Gurobi to match their assets and liabilities in a way that minimizes risk and maximizes profitability. This includes interest rate risk management, currency risk management, and ensuring regulatory compliance. Gurobi is also employed in algorithmic trading, where it’s used to develop strategies that respond to real-time market conditions to maximize trading profits.
The roles utilizing Gurobi in these contexts include financial analysts, quantitative analysts, and asset managers. These professionals rely on Gurobi’s robust optimization capabilities to make data-driven decisions in a fast-paced and ever-changing financial landscape, where accuracy and speed are critical.
Gurobi is designed to solve various types of mathematical optimization problems, including Linear Programming (LP), Mixed-Integer Linear Programming (MILP), Quadratic Programming (QP), Mixed-Integer Quadratic Programming (MIQP), and Mixed-Integer Nonlinear Programming (MINLP). It is highly effective in handling large-scale, complex optimization problems across different industries.
Learn more about Gurobi with our training notebooks and it’s applications with mixed integer programming (learn more here).
Combining AMPL’s modeling simplicity with Gurobi’s powerful optimization engine creates an ideal environment for newcomers to optimization. AMPL’s intuitive modeling language allows users to express optimization problems naturally and concisely, which is particularly beneficial for those just starting out. This simplicity, paired with AMPL’s extensive range of interfaces supporting popular programming languages like Python, C++, Java, .NET, and MATLAB, opens up accessibility to a wider audience. While beginners might find optimization challenging initially, the joint use of AMPL and Gurobi eases this learning curve. Both offer comprehensive documentation, illustrative examples, and vibrant user communities for support. Furthermore, their commitment to education is evident through the provision of educational licenses and resources, making AMPL and Gurobi a popular combination in academic circles. Together, they provide a more integrated and user-friendly approach to learning and applying optimization.
AMPL and Gurobi are designed to work in tandem, offering a powerful and seamless integration with a wide range of software and systems. AMPL’s strength in model formulation and Gurobi’s robust optimization capabilities complement each other perfectly. This synergy is further enhanced by their support for APIs in several popular programming languages, including Python. This allows users to embed AMPL models directly within custom applications that utilize Gurobi as the solver. This level of flexibility is particularly advantageous in various industrial applications, where they can serve as the core of larger decision-support systems or data analytics platforms. The combination of AMPL’s modeling ease and Gurobi’s optimization strength ensures that users can not only develop solutions efficiently but also integrate these solutions effortlessly with existing systems and workflows, providing a comprehensive and versatile toolset for optimization challenges.
Gurobi is widely used in various sectors for LP and MIP applications. Common uses include supply chain optimization, logistics planning, production scheduling, financial portfolio optimization, and energy distribution. In these applications, Gurobi helps in optimizing resources, minimizing costs, and improving decision-making processes by finding the best possible solutions to complex linear and integer-constrained problems.
Gurobi is designed for high performance and can handle large-scale LP problems efficiently. It utilizes advanced algorithms and techniques such as dual simplex, barrier methods, and concurrent optimization to solve problems quickly. Gurobi’s ability to provide parallel processing also significantly speeds up the solution of large-scale problems by utilizing multiple cores and processors.
While Gurobi is primarily known for linear and mixed-integer linear programming, it can also handle mixed-integer quadratic programming (MIQP) and mixed-integer nonlinear programming (MINLP) to a certain extent. For non-linear constraints, Gurobi can linearize certain types of non-linear functions, enabling the solver to handle a wider range of MIP problems. However, the capability to solve complex non-linear problems might be limited compared to specialized non-linear solvers.
Gurobi provides several features to enhance MIP modeling and solving. This includes advanced presolving to reduce problem size, cutting planes to improve solution bounds, and heuristics for finding good feasible solutions quickly. Gurobi also offers tuning tools to optimize solver parameters for specific problem types, and its branch-and-cut algorithm is highly effective for solving MIPs efficiently.
Gurobi aids decision-making by providing optimal solutions to complex problems in various industries. For instance, in logistics and supply chain management, it helps in route optimization and inventory management. In finance, Gurobi is used for asset allocation and risk management. In manufacturing, it assists in production planning and resource allocation. These solutions help businesses make data-driven decisions, reduce costs, and improve operational efficiency.
Gurobi for AMPL User’s Guide including option descriptions
Gurobi-AMPL interface source code
What’s New in Gurobi 11.0