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Gurobi Optimizer

The Gurobi Optimizer is a commercial mathematical optimization solver developed by Gurobi Optimization, LLC, designed to address complex prescriptive analytics and decision-making challenges across various industries by solving large-scale linear, quadratic, and nonlinear programming problems. It supports a wide range of problem types, including linear programming (LP), mixed-integer linear programming (MILP), quadratic programming (QP), mixed-integer quadratic programming (MIQP), quadratically constrained programming (QCP), mixed-integer quadratically constrained programming (MIQCP), second-order cone programming (SOCP), bilinear programming, general nonlinear programming (NLP), mixed-integer nonlinear programming (MINLP), and non-convex MINLP. Gurobi Optimization was founded in 2008 by Zonghao Gu, Edward Rothberg, and Robert Bixby, with the explicit goal of creating the world's fastest and most powerful optimization solver; the company's name derives from the first two letters of the founders' surnames. Bixby, a in optimization software with nearly 40 years of experience, previously founded the CPLEX solver, while Rothberg and Gu brought expertise in advanced algorithmic development, enabling rapid innovations in solver performance from the outset. Since its inception, Gurobi has achieved significant milestones, such as a 96-fold performance improvement in MILP solving since version 1.1, and has been rigorously tested on over 10,000 industry and academic models to ensure stability and accuracy. Key capabilities of the Gurobi Optimizer include support for parallel and distributed computing, , and scenario-based analysis, making it suitable for applications in scheduling, , and . It provides flexible interfaces in languages such as (with a rich and pre-built libraries), C++, , .NET, C, , and , and integrates seamlessly with popular modeling tools like AMPL, GAMS, , and Excel plugins. Licensing options include free full-featured academic versions, commercial trials, and cloud-based deployments, underscoring its for both and use.

Development and History

Founding and Early Development

Gurobi Optimization, LLC was founded in 2008 by Zonghao Gu, Edward Rothberg, and Robert Bixby, all of whom had extensive experience in . Prior to establishing , the three served as key contributors to the CPLEX solver during their time at ILOG, where Gu led R&D from 2005 to 2008 after earlier roles at LINDO Systems, Rothberg directed R&D from 1998 to 2005 following his work on sparse linear algebra, and Bixby co-founded CPLEX Optimization in 1987 before joining ILOG after its 1997 acquisition of CPLEX. The 's name, "Gurobi," derives from the first two letters of the founders' last names: Gu, Rothberg, and Bixby. The founders' initial vision was to create the world's fastest and most powerful solver, motivated by perceived limitations in existing commercial tools like CPLEX, including suboptimal performance on modern multi-core architectures. This ambition led them to leave their positions at ILOG shortly before its acquisition by in January 2009, marking a significant transition from stable corporate environments to the uncertainties of a startup. Early development efforts centered on building the solver from the ground up, leveraging the founders' expertise in core algorithms such as dual and barrier methods inherited from their CPLEX work, while redesigning for enhanced speed and parallelism. Version 1.0 of the Gurobi Optimizer was released in May 2009, introducing substantial performance gains over CPLEX through improved heuristics, multi-core support, and seamless integration with languages like . This launch established Gurobi as a competitive alternative in the optimization software market, setting the stage for rapid adoption in industry and research.

Key Milestones and Versions

Gurobi Optimizer's development has been marked by regular major releases that introduce significant enhancements in problem-solving capabilities and performance. Version 5.0, released in May 2012, added support for quadratic constraints, second-order cones, and rotated second-order cones, along with a new barrier solver for second-order cone programming and lazy constraints. Version 9.0, launched in November 2019, introduced bilinear constraint support and the addition of Cluster Manager to Compute Server for improved scalability. These releases built on earlier foundations, with the optimizer achieving a 96x speedup in mixed-integer linear programming (MILP) solve times compared to version 1.1, measured via geometric mean of runtimes on benchmark suites. Subsequent versions focused on advanced nonlinear and features. 11.0, released on December 4, 2023, enabled global optimality for mixed-integer nonlinear programs (MINLPs) using spatial branching and outer approximation techniques, delivering a 5.8x on nonconvex problems relative to prior versions. 12.0, released in November 2024, expanded nonlinear solving with global MINLP optimality guarantees and introduced smarter resource management features, including enhancements to Compute Server and for distributed tuning. Performance across mixed-integer optimizations continued to improve, with version 12.0 offering speedups of up to 68.5% on hard nonconvex MIQCP models and 18.9% on hard MIP models compared to 11.0. Version 13.0, released on November 12, 2025, introduced further performance enhancements in MIP and MINLP solving, support for the PDHG solver with GPU acceleration, and local nonlinear optimization capabilities. In terms of company growth, Gurobi Optimization acquired , a Japan-based mathematical optimization services provider, in June 2023, marking a key expansion into the Asian market and enhancing service capabilities. As of , the company served over 2,500 customers across more than 40 industries, including major organizations in , , and . Gurobi maintains a support policy where major releases from version 10 onward are supported for three years following their initial release date. As of November 2025, actively supported versions include 10.0 (until November 2025), 11.0 (until December 2026), 12.0 (until November 2027), and 13.0 (until November 2028).

Technical Capabilities

Supported Optimization Problems

The Gurobi Optimizer supports (LP) problems, which involve minimizing or maximizing a linear objective function subject to linear constraints. In standard form, an LP problem is formulated as minimizing \mathbf{c}^T \mathbf{x} subject to A\mathbf{x} \leq \mathbf{b} and \mathbf{x} \geq \mathbf{0}, where \mathbf{c} is the coefficient vector for the objective, A is the constraint matrix, \mathbf{b} is the right-hand-side vector, and \mathbf{x} is the vector of decision variables. For problems requiring discrete decisions, Gurobi handles mixed-integer linear programming (MILP), an extension of where some or all variables must take values, including (0-1) variables for yes/no choices and general variables for countable quantities. MILP formulations retain the linear structure of but incorporate integrality constraints on subsets of \mathbf{x}, enabling solutions to challenges like scheduling or network design. Gurobi also solves (QP) and mixed-integer quadratic programming (MIQP) problems, where the objective function or constraints include quadratic terms, such as \mathbf{x}^T Q \mathbf{x} + \mathbf{c}^T \mathbf{x} for the objective, with Q as a . These support both convex and non-convex cases, with non-convex instances addressed through techniques like spatial branch-and-bound. More generally, quadratically constrained programming (QCP) and mixed-integer quadratically constrained programming (MIQCP) allow multiple quadratic constraints alongside linear ones, formulated as \mathbf{x}^T Q_i \mathbf{x} + \mathbf{a}_i^T \mathbf{x} \leq b_i for each constraint i. (SOCP) emerges as a special case of QCP, where constraints take the form \|\mathbf{x}\| \leq t ( norm), useful for and approximation of nonlinear problems. Gurobi further supports general nonlinear programming (NLP) problems, where the objective function and/or constraints involve arbitrary nonlinear functions, formulated as minimizing f(\mathbf{x}) subject to g_i(\mathbf{x}) \leq 0 and h_j(\mathbf{x}) = 0, with f, g_i, and h_j being nonlinear. This includes both and non-convex cases, as well as bilinear programming as a specific form of nonlinearity. Mixed-integer nonlinear programming (MINLP) extends NLP by adding integrality constraints on subsets of variables, enabling the solution of complex problems combining continuous nonlinearities with discrete decisions. These capabilities have been available since Gurobi version 11.0 (released in 2023). Gurobi imposes no inherent limits on model size beyond available and computational resources, routinely handling problems with millions of variables and constraints in practical applications. Models can be input in standard formats such as Mathematical Programming System () for fixed or free variants, or the more readable format, alongside direct construction via Gurobi's without file-based input.

Algorithms and Performance Features

Gurobi Optimizer employs a suite of advanced algorithms tailored to different classes of optimization problems. For (LP) problems, it utilizes the dual simplex method, which is particularly efficient for re-optimizations when constraints or objective coefficients are modified, as it leverages the existing optimal basis to quickly restore feasibility and optimality. For large-scale LPs, the interior-point barrier algorithm provides robust performance, solving problems by navigating the interior of the toward the optimum using parallel computations. Mixed-integer linear programming (MILP) problems are addressed through a branch-and-cut framework, which integrates linear programming relaxations at each node, generates cutting planes to tighten bounds, and applies heuristics to find high-quality integer solutions early in the search process. Performance enhancements in Gurobi are driven by extensive parallelism and preprocessing techniques. The solver supports multi-threading across multiple cores for key components, including the for continuous problems and the branch-and-cut tree exploration for MILPs, enabling efficient use of modern hardware with dozens to hundreds of cores per machine. Automatic presolve reductions aggressively simplify models by eliminating redundant variables and constraints, detecting infeasibilities, and tightening bounds before the main optimization phase, often reducing problem size by orders of magnitude. Additionally, distributed allows parameter optimization across multiple machines, accelerating the search for solver settings that improve runtime for specific problem instances. For more challenging formulations, Gurobi incorporates specialized methods such as spatial branch-and-bound for non-convex mixed-integer quadratically constrained programming (MIQCP) problems, where it branches on continuous variables to handle bilinear terms and non-convexities while maintaining global optimality guarantees. This approach extends to (MINLP) problems, combined with outer approximation techniques to manage general nonlinearities. Decomposition approaches like are supported through user callbacks, allowing the addition of cuts in a branch-and-cut to manage large-scale models by separating master and subproblems, which can significantly reduce solve times for structured problems. In benchmarking, Gurobi has historically excelled on standard test sets like MIPLIB, consistently solving a higher percentage of mixed-integer instances to optimality compared to competitors in independent evaluations. While specific 2025 comparisons are not publicly detailed due to the solver's withdrawal from some public benchmarks, Gurobi maintains its position as a leading performer in MILP solving based on prior results from sources like Hans Mittelmann's optimization benchmarks. The built-in parameter tool automates the exploration of Gurobi's extensive parameter space, performing multiple solves with varied settings to identify configurations that minimize for a given model class, often yielding substantial speedups tailored to problem characteristics. This tool supports both and distributed modes, making it scalable for fine-tuning on environments.

Integrations and Interfaces

Programming Language Support

The Gurobi Optimizer provides direct application programming interfaces (APIs) in multiple programming languages, enabling developers to integrate optimization capabilities into custom applications. The core API is implemented in C, serving as the foundation for higher-level interfaces, with the C++ API offering an object-oriented wrapper that is often considered the primary interface for performance-critical applications. Bindings are available for Python via the gurobipy module, which supports high-level, NumPy-compatible modeling; Java, providing object-oriented access; .NET languages including C# and Visual Basic; MATLAB, for matrix-oriented workflows; and R, tailored for statistical computing environments. The modeling workflow in these follows a programmatic approach where users create an empty model object, add decision variables with specified bounds and types (continuous, , or ), define linear or constraints, and set an objective function to minimize or maximize. Once the model is built, the invokes the solver to optimize it, after which values, , and status information can be retrieved through attribute queries. Callbacks allow real-time interaction during the solve process, such as monitoring progress or injecting custom logic. Advanced features enhance flexibility for complex applications. Custom callbacks enable the implementation of user-defined heuristics, such as or heuristics, to guide the solver toward better solutions during branch-and-bound or barrier iterations. Batch solving supports efficient concurrent optimization of multiple models, useful for parameter tuning or scenario analysis. Additionally, the cloud facilitates remote model execution on Gurobi's hosted infrastructure, allowing seamless scaling without local compute resources. For illustration, the following snippet using gurobipy demonstrates a simple setup: maximizing $3x + 4y subject to x + 2y \leq 14, $3x + 2y \leq 18, and non-negativity constraints.
python
import gurobipy as gp
from gurobipy import GRB

# Create model
m = gp.Model("simple_lp")

# Add variables
x = m.addVar(lb=0, name="x")
y = m.addVar(lb=0, name="y")

# Set objective
m.setObjective(3*x + 4*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x + 2*y <= 14, name="c1")
m.addConstr(3*x + 2*y <= 18, name="c2")

# Optimize
m.optimize()

# Retrieve results
print(f"Optimal value: {m.ObjVal}")
print(f"x = {x.X}, y = {y.X}")
This yields an optimal objective value of 36 with x = 4, y = 5. The APIs are designed to be thread-safe, permitting parallel model construction across multiple threads within a single process, which is particularly beneficial for large-scale applications involving dynamic model generation. Multiple environments can be created to isolate solves and avoid interference in multithreaded contexts.

Compatibility with Modeling Tools

Gurobi Optimizer offers seamless compatibility with several algebraic modeling languages (AMLs), enabling users to formulate complex optimization models declaratively and interface directly with the solver. It provides full support for AMPL, allowing models to be solved via the Gurobi solver through installation of a and of solver options within the AMPL . Similarly, Gurobi integrates with GAMS and MPL, where users can specify Gurobi as the solver and export models in formats like .rlp for direct processing, facilitating easy migration from other solvers without altering the model code. users can also link to Gurobi for solving linear, , and mixed-integer problems, leveraging the language's procedural extensions alongside Gurobi's computational engine. For enterprise environments, Gurobi includes plugins and integrations tailored to major platforms, enhancing deployment in large-scale operations. It supports through direct embedding, enabling optimization within SAP's for and planning applications. Integration with Oracle Retail products, such as the Advanced Science Engine and Order Broker, allows Gurobi to be configured as the underlying solver for retail optimization tasks, including inventory and assortment planning. Additionally, tools for migrating from ILOG CPLEX Optimization Studio are available, providing compatibility layers to adapt models and parameters to Gurobi without significant rework. Cloud connectivity is supported via Gurobi Instant Cloud, which offers connectors for AWS and environments, allowing scalable, on-demand solving with flexible resource allocation across these platforms. In workflows, Gurobi integrates effectively with popular Python-based tools, bridging optimization with data analysis and . The gurobipy-pandas wrapper enables efficient model construction from DataFrames, streamlining data import and variable definition for users in exploratory analytics. Support for Jupyter Notebooks allows interactive model building and , with pre-built examples for common optimization scenarios. For pipelines, Gurobi Machine Learning provides compatibility with models, extracting constraints and objectives from trained regressors or classifiers to incorporate them into larger optimization problems. Gurobi handles a range of standard file formats for model input and output, ensuring interoperability with legacy systems and other solvers. It reads and writes (Mathematical Programming System) files, the most widely used for linear and mixed-integer models, as well as files for human-readable representation of linear programs. Gurobi's RLP format (rewritable LP with trailing data) supports advanced features like storing attributes and basis information for iterative solving. Models from open-source solvers like can be imported via or formats, maintaining variable ordering and precision during transfer. Migration utilities further enhance compatibility by providing detailed guides and code conversion tools for transitioning from competitors. Users can convert CPLEX models by mapping parameters and APIs, with Gurobi offering equivalent functionalities for barrier methods and branch-and-cut algorithms. Similar resources exist for Xpress, including parameter translation tables and example scripts to ensure seamless model porting and performance equivalence. These tools minimize disruption, often requiring only license installation and solver specification changes in modeling environments.

Applications and Use Cases

Industry Applications

The Gurobi Optimizer is widely applied in and to optimize , management, and scheduling, enabling companies to minimize costs and improve in . For instance, implemented Gurobi-powered models to solve intricate challenges, transforming multi-step planning processes into one-click solutions that reduced computation time from hours to seconds and enhanced overall responsiveness. Similarly, Suzano utilized Gurobi for , aligning profitability with goals and unlocking approximately R$76 million in new business opportunities through better . These applications leverage Gurobi's advanced mixed-integer (MILP) capabilities to handle large-scale, real-world constraints effectively. In the finance sector, Gurobi supports , , and by solving large-scale quadratic and linear models to balance returns against . The tool enables financial institutions to develop compliant, data-driven strategies, such as tax-efficient portfolios. A notable example is 55ip, which used Gurobi to accelerate of tax-smart solutions, allowing rapid adjustments to regulatory changes while maintaining optimization integrity. In 2025, Canadian MyGoals harnessed Gurobi to transform personal financial planning, delivering tailored, tax-optimized retirement strategies that improved decision-making for users seeking long-term financial goals. Gurobi plays a critical role in the for grid optimization, scheduling, and refining operations, where it models stochastic and nonlinear problems to maximize profitability amid fluctuating demands. Croatia, for example, employed Gurobi to devise a profit-maximizing strategy for battery energy storage systems, optimizing market operations and dispatch decisions to enhance revenue from energy arbitrage. In oil and gas, Gurobi facilitates strategic planning and for manufacturers, supporting daily operations like scheduling to reduce and operational costs. Within manufacturing, Gurobi aids in workforce scheduling, facility location, and by solving multi-objective problems that integrate constraints and variability. Cosentino, a global leader in surface materials, integrated Gurobi to optimize routes and production lines, eliminating bottlenecks and boosting for over 1,000 members. Toyota's corporate IT division also leveraged Gurobi in an for , enabling precise allocation of resources across global facilities to meet targets while minimizing waste. Yutong Bus, China's largest bus manufacturer, applied Gurobi to address a challenging multi-objective problem, improving output and reducing scheduling conflicts. In healthcare, Gurobi is used for and operational modeling, such as optimizing staffing, facility capacity, and supply distribution to improve patient outcomes and reduce costs. PATH, a global health organization, utilized Gurobi to standardize oxygen plant sizes for low- and middle-income countries, reducing lead times by 6-8 months and meeting 80-95% of hospital oxygen demands with fewer plant variants, thereby accelerating delivery of life-saving equipment. During the response, Gurobi models optimized temporary healthcare facility locations and capacities to efficiently allocate patients and minimize setup costs, demonstrating its utility in crisis .

Research and Academic Use

Gurobi Optimizer provides free, full-featured academic licenses to students, faculty, and researchers at accredited degree-granting institutions for use in , , and non-commercial . These licenses, including named-user, web license service, and site-wide options, allow unrestricted access to the solver's capabilities without time limits or feature restrictions, enabling academic users to explore complex optimization problems without financial barriers. In research, Gurobi plays a key role in operations research benchmarks, such as the Mixed Integer Programming Library (MIPLIB) 2017, where it is used to evaluate solver performance on challenging mixed-integer programming instances. This involvement supports the development and validation of optimization algorithms by providing reliable, high-performance solving for large-scale test sets. Additionally, Gurobi facilitates large-scale experiments in AI-hybrid optimization, integrating with large language models to automate model formulation and solve combinatorial problems, as demonstrated in frameworks like OptiChat that combine generative AI with mathematical optimization for practical decision-making. For education, Gurobi offers extensive resources including interactive tutorials and a library of Jupyter notebooks that guide users through building and solving optimization models in , covering topics from to advanced mixed-integer formulations. These materials integrate with online courses, such as the specialization in , where Gurobi is used to implement and solve optimization algorithms efficiently. Notable research applications include , where Gurobi optimizes hyperparameter selection for models like k-nearest neighbors and decision trees in stochastic settings, outperforming traditional predictive validation by aligning tuning with prescriptive outcomes in power market trading scenarios. In sustainability modeling, Gurobi supports carbon capture system design by optimizing process families and deployment strategies, incorporating surrogates to evaluate across multiple similar units for efficient CO2 management. Gurobi's community impact in is evident through its widespread in scholarly publications and strategic partnerships with universities for solver advancement and educational initiatives, such as collaborations via the Gurobi Innovation Lab to foster cross-disciplinary optimization research. These efforts, including joint development of tools like optimization simulators with institutions such as , enhance solver capabilities and promote optimization literacy among researchers.

Licensing and Availability

Commercial Licensing Model

Gurobi Optimizer offers a flexible licensing model designed for deployment, featuring both perpetual and subscription options tailored to organizational needs. Perpetual licenses provide indefinite access to a specific version of the software, while subscription licenses grant time-bound usage with automatic access to updates. for these licenses is primarily based on the number of CPU cores (or threads) utilized, with base configurations typically supporting up to 8 cores and additional fees for exceeding this limit to accommodate larger-scale computations. Annual maintenance fees, required for perpetual licenses, include support and upgrades, ensuring ongoing access to enhancements and technical assistance. Deployment options under the commercial model support on-premises, , and environments to fit diverse setups. On-premises installations include named-user licenses for individual workstations and floating licenses for networked access across multiple users. The Gurobi Compute Server enables shared resource queuing, allowing multiple clients to submit optimization jobs to a central for efficient processing on dedicated . For cloud deployment, Gurobi Instant Cloud facilitates seamless integration with AWS and , where users can provision virtual machines on-demand via a web-based manager, streamlining licensing and billing without hardware management overhead. configurations combine local and cloud resources, supporting containerized deployments in environments like . Standard technical support is included with all commercial licenses, offering and assistance with response times ranging from 2 hours for urgent issues to 3 days for standard queries, along with benchmarking and model services to optimize . Premium support options are available for enterprises requiring custom or dedicated expert consultation beyond the standard package. Commercial users can evaluate the full-featured optimizer through a 30-day , which includes unrestricted access to all capabilities, , and services without or size limitations during the period. The licensing model emphasizes for multi-site enterprises, with floating and Web License Service (WLS) options allowing portability across machines, regions, and users without fixed bindings. Core-based ensures that s can expand to match computational demands, from single-user setups to distributed clusters handling thousands of variables and constraints in production environments. This structure supports both development and deployment phases, enabling organizations to once for comprehensive use across integrations like modeling tools.

Academic and Trial Options

Gurobi Optimization provides free, full-featured licenses through its Academic Program to support teaching, coursework, and at accredited degree-granting institutions. These licenses, available at no cost to eligible students, faculty, and staff, offer unlimited model size and access to all solver capabilities, including advanced algorithms for linear, mixed-integer, , and non-convex optimization problems. The program includes several license types tailored to different needs: the Named-User License for individual local installations, the Web License Service (WLS) for internet-accessible use across devices, and the Site License for departmental or institutional deployment on networked systems. Additionally, the Take Gurobi With You (TGWY) program extends free access to recent graduates for up to two years post-graduation, allowing continued non-commercial use for personal or job applications. Eligibility for the Academic Program requires with a recognized degree-granting , encompassing students, faculty, and staff for non-commercial purposes only. Verification typically involves registering for a free Gurobi account as an user, often confirmed through an institutional (such as .edu) or by connecting to the institution's network during activation. Licenses are issued for up to one year and can be renewed annually by requesting a new license through the Gurobi portal, provided the user remains eligible; for WLS licenses, extensions may be self-managed by reconnecting to the network. If an individual's changes, such as upon , the license expires, necessitating a transition to a commercial or other appropriate option. In addition to academic options, Gurobi offers trial licenses for evaluation, enabling users to test the full suite of features without commitment. The standard evaluation license provides 30 days of unrestricted access to the complete Gurobi Optimizer, including complimentary , model services, and . For those preferring no local installation, web-based cloud trials are available, offering up to 50 hours of compute time (equivalent to $50 in machine credits) on Gurobi's cloud infrastructure, with the same full-featured capabilities and support services. These trials are intended for qualified users exploring the software for potential commercial adoption and require a simple registration and approval process. All academic and trial options are strictly limited to non-commercial use, prohibiting any application in production environments or revenue-generating activities. Violations of these terms may result in license revocation, emphasizing Gurobi's commitment to distinguishing educational and exploratory access from commercial deployment.

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