AMPL Team
March 8, 2024
Transforming Challenges into Solutions: AMPL’s Integration of COPT Solver
Cardinal Optimizer (COPT) incorporates a full suite of solvers for linear and convex quadratic mixed-integer programming. It ranks at the top of benchmark tests on continuous linear programs, and has been fully extended to handle integer variables.
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The COPT solver, developed by Cardinal Operations, represents a significant advancement in the field of mathematical optimization. This solver is specifically designed to address complex linear, integer, and mixed-integer programming problems. Its development reflects a commitment to integrating cutting-edge algorithmic research with practical application needs. COPT is widely recognized for its efficiency and robust performance, particularly in large-scale optimization scenarios. Its application spans various industries, including logistics, finance, energy, and telecommunications, where optimization plays a critical role in strategic decision-making and operational efficiency. The solver’s unique capabilities make it a valuable tool for both academic researchers and industry professionals who require powerful computational resources to solve intricate optimization problems. As such, COPT has gained a reputation for transforming theoretical models into actionable, real-world solutions, pushing the boundaries of what’s possible in optimization technology.
Linear and convex quadratic optimization in continuous and integer variables.
For continuous problems, primal and dual simplex, interior-point (barrier); for integer problems, branch-and-bound with presolve, feasibility heuristics, and cut generators.
For Python enthusiasts, COPT 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 COPT
$ python -m amplpy.modules install copt
Best for individuals running on one machine
$3,000 /year
$3,000 /year
Best for small applications running one process at a time
$4,500 /year
$4,500 /year
Best for large teams or applications to run multiple processes simultaneously
$7,000 /year
+$700 /additional CPU
$4,500 /year
+$450 /additional CPU
Best for individuals running on one machine
$6,000 /purchase
+ $1,200 maintenance annually
$6,000 /purchase
+ $1,200 maintenance annually
Best for small applications running one process at a time
$9,000 /purchase
+ $1,800 maintenance annually
$9,000 /purchase
+ $1,800 maintenance annually
Best for large teams or applications to run multiple processes simultaneously
$14,000 /purchase
+ $2,400 maintenance annually
+1,400 /additional CPU
$9,000 /purchase
+ $1,800 maintenance annually
+$900 /additional CPU
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Best for individuals running on one machine
$3,000 /yearly subscription
$6,000 /purchase
+ $1,200 maintenance annually
$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
$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
$4,500 /yearly subscription
+ $450 additional CPU
$9,000 /purchase
+ $1,800 maintenance annually + $900 additional CPU
COPT downloads are available from the My Downloads page of your account at the AMPL Portal, and are included in the bundles that are used for free trials.
Discover the unmatched efficiency and innovation brought to life by integrating AMPL with the COPT solver. This powerful combination synergizes AMPL’s user-friendly modeling capabilities with COPT’s advanced solving algorithms, delivering a streamlined solution for complex optimization challenges. Ideal for both intricate academic models and large-scale industrial applications, this integration simplifies the transition from model creation to problem-solving, enhancing productivity and precision across diverse industries.
With AMPL’s intuitive interface and COPT’s robust performance, users experience a seamless workflow that minimizes the learning curve and maximizes results. Whether in logistics, finance, or energy management, the AMPL-COPT duo offers scalable, high-performance solutions, transforming the way problems are approached and solved in the realm of optimization.
In today’s world, where resources are often scarce and competition is fierce, making the most of what you have is crucial. This is where COPT (Cardinal Optimizer), a powerful mathematical optimization solver, comes in.
COPT can be your secret weapon in resource allocation, helping you make informed decisions and squeeze the maximum value out of your limited resources.
Think of it as a tireless advisor, constantly crunching numbers and suggesting the best ways to:
Schedule personnel: Whether you’re a hospital managing doctors and nurses, a construction company juggling skilled workers, or a restaurant allocating servers, COPT can create optimal schedules that consider workload, expertise, and availability.
Assign tasks: With COPT, you can ensure the right skills are matched to the right tasks, maximizing efficiency and minimizing wasted resources. Imagine assigning maintenance schedules to technicians based on their skillsets and location, or prioritizing emergency calls based on available resources.
Manage equipment and facilities: Allocate equipment, classrooms, or even meeting rooms to minimize idle time and optimize resource utilization. COPT can help you avoid bottlenecks and ensure everyone has access to the tools they need, when they need them.
Plan logistics and transportation: Whether you’re delivering goods across a city or managing a fleet of buses, COPT can optimize routes to minimize time, fuel consumption, and operational costs.
The benefits of using COPT for resource allocation are numerous:
Beyond these general examples, COPT can be used in a variety of industries and scenarios:
COPT is not just about crunching numbers; it’s about taking your resource allocation to the next level. By unlocking the power of optimization, you can achieve greater efficiency, reduce costs, and ultimately, gain a competitive edge.
In the complex world of engineering and design, COPT shines as a powerful tool for optimizing processes and achieving peak performance. Its ability to handle diverse optimization problems makes it a valuable asset across various subfields, from conceptual design to detailed analysis and production.
Here are some specific examples of how COPT can be used in engineering and design:
Optimal Design: Minimizing weight and maximizing strength: In aerospace engineering, COPT can be used to design aircraft components that are lightweight but incredibly strong, enhancing fuel efficiency and performance. Imagine optimizing the design of a drone frame or helicopter blades for optimal lift and maneuverability.
Improving energy efficiency: From designing energy-efficient buildings to optimizing power plant layouts, COPT can help engineers find solutions that minimize energy consumption and environmental impact. Think about optimizing wind turbine blade angles or building insulation thickness for maximum energy capture and thermal control.
Maximizing product performance: Whether it’s designing a fuel-efficient car engine or a high-performance sports bike, COPT can help engineers find the perfect balance between functionality and performance. Picture optimizing engine combustion or suspension geometry for optimal power output and handling.
Process Optimization: Chemical engineering: COPT can optimize chemical reaction pathways, reactor designs, and distillation processes to maximize yield and minimize waste. Imagine optimizing the production of a specific pharmaceutical drug or efficiently separating components in a petroleum refinery.
Electrical engineering: COPT can be used to design optimal circuit layouts, minimize power losses, and extend battery life in electronics. Think about optimizing circuit routing in a printed circuit board or designing energy-efficient microchips.
Mechanical engineering: From optimizing production lines to reducing vibration in machinery, COPT can help engineers improve efficiency and reliability in mechanical systems. Envision automating the scheduling of a complex manufacturing process or optimizing the design of a robotic arm for precision and stability.
Beyond these examples, COPT can be used in even broader contexts:
COPT doesn’t just provide numbers; it empowers engineers and designers to make informed decisions based on data-driven insights. By unlocking the potential of optimization, they can:
If you’re an engineer or designer looking for ways to push the boundaries of innovation and efficiency, COPT could be your perfect partner. So, why not explore its capabilities and see how it can help you optimize your next project?
COPT, or the Cardinal Optimizer, is a high-performance mathematical optimization solver. It specializes in solving linear programming (LP), mixed-integer programming (MIP), and other related optimization problems. COPT is designed to provide efficient, accurate solutions for a wide range of complex optimization tasks, making it a valuable tool in various industries and research fields.
COPT excels at handling various linear, mixed-integer linear, quadratic, and conic optimization problems. This includes complex challenges in scheduling, resource allocation, design optimization, and more.
While COPT’s capabilities are powerful, its interface can be intimidating for beginners. Nevertheless, AMPL simplifies model formulation and interaction with COPT.
COPT supports all major 64-bit operating systems (Windows, Linux, macOS) and integrates with various modeling languages and interfaces. This flexibility allows users to choose their preferred environment for working with COPT.
COPT’s advanced algorithmic capabilities make it a valuable asset across various sectors, including logistics, finance, energy, and healthcare. In logistics, for instance, it optimizes routes and resource allocation, reducing costs. In finance, COPT aids in portfolio optimization, effectively balancing risk and return. Its wide applicability underscores COPT’s role in driving operational efficiencies and strategic innovations.
Cardinal Optimizer website
COPT-AMPL interface source code with instructions