[Paper Review] Cardinal Optimizer (COPT) User Guide

Dongdong Ge, Qi Huangfu+3 more|arXiv (Cornell University)|Aug 30, 2022

Topology Optimization in Engineering8 citations

TL;DR

This user guide details Cardinal Optimizer (COPT), a high-performance optimization solver supporting linear, mixed-integer, quadratic, and second-order cone programming. It provides comprehensive documentation for installing, licensing, and using COPT via multiple interfaces (C, C++, C#, Java, Python, AMPL, Pyomo, PuLP, CVXPY), with emphasis on efficient modeling through helper functions like quicksum and tupledict, and advanced features such as MIP starts, solution pool, and parameter tuning.

ABSTRACT

Cardinal Optimizer is a high-performance mathematical programming solver for efficiently solving largescale optimization problem. This documentation provides basic introduction to the Cardinal Optimizer.

Motivation & Objective

• To provide a complete, standardized user guide for the Cardinal Optimizer (COPT) solver to support researchers and practitioners in deploying optimization models.
• To enable seamless integration of COPT into diverse programming environments, including Python, C++, C#, Java, and modeling languages like AMPL and Pyomo.
• To offer best practices for high-performance modeling, including efficient expression construction and multi-threaded computation.
• To document advanced features such as MIP starts, solution pool, and parameter tuning for improved solver performance.
• To ensure cross-platform compatibility and robust error handling across Windows, Linux, and macOS systems.

Proposed method

• COPT exposes a C API as the core interface, with language-specific wrappers for C, C++, C#, Java, and Python, enabling interoperability across platforms.
• The Python interface uses helper classes like quicksum, psdquicksum, tupledict, and tuplelist to streamline expression construction and variable management.
• Modeling is facilitated through object-oriented abstractions: environments, models, variables, constraints, and objectives are created and modified via method calls.
• COPT supports multiple input/output formats (MPS, LP, SDPA, CBF, binary, and binary blob) for problem exchange and persistence.
• Advanced features include MIP start loading, solution pool management, and the COPT Tuner for automated parameter optimization.
• Licensing is managed via local or floating licenses, with dedicated tools for server and client configuration, and support for running as a system service on Linux and macOS.

Experimental results

Research questions

• RQ1 How can a high-performance optimization solver be effectively integrated into diverse programming environments and modeling frameworks?
• RQ2 What are the most efficient programming patterns and data abstractions for constructing large-scale optimization models in Python and other languages?
• RQ3 How does COPT’s parameter tuning and MIP start functionality improve solution quality and convergence speed?
• RQ4 What mechanisms ensure cross-platform compatibility and robust error handling in production deployment?
• RQ5 How can advanced modeling features like second-order cone and positive semi-definite constraints be efficiently expressed and solved?

Key findings

• COPT supports a wide range of optimization problems, including linear, mixed-integer, quadratic, second-order cone, and semidefinite programs, with high performance across all types.
• The Python interface achieves efficient modeling through helper functions like quicksum and tupledict, which reduce code complexity and improve execution speed.
• COPT’s MIP start feature allows users to provide initial solutions, which can significantly reduce solution time when feasible solutions are known.
• The COPT Tuner enables automated parameter tuning, improving solver performance by up to several orders of magnitude in some test cases.
• The solver supports persistent storage and exchange of models and solutions in standard formats such as MPS, LP, and binary, enabling interoperability with other tools.
• COPT provides detailed solution information, including dual Farkas certificates, primal rays, and basis status, supporting advanced analysis and infeasibility diagnosis.