COPT#

Cardinal Optimizer (COPT) incorporates a full suite of solvers for linear, (non-)convex quadratic, second-order and exponential conic mixed-integer programming. It ranks at the top of benchmark tests on continuous linear programs, and has been fully extended to handle integer variables. The driver is built on the MP library, which reformulates logical and other expressions that the solver does not accept natively.

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How to use it#

How to install using amplpy:

# Install Python API for AMPL:
$ python -m pip install amplpy --upgrade

# Install AMPL & solver modules:
$ python -m amplpy.modules install copt # install COPT

# Activate your license (e.g., free ampl.com/ce or ampl.com/academia licenses):
$ python -m amplpy.modules activate <your-license-uuid>

How to use:

from amplpy import AMPL
ampl = AMPL()
...
ampl.solve(solver="copt", copt_options="option1=value1 option2=value2")

Learn more about what we have to offer to implement and deploy Optimization in Python.

AMPL APIs give access to AMPL from a programming language:

AMPLS (AMPL solver libraries) load an AMPL model into the solver in C++ or Python and give direct access to the solver’s own API, for example for callbacks. Python packages: amplpy-gurobi, amplpy-cplex, amplpy-xpress, amplpy-copt.

ampl: option solver copt; # change the solver
ampl: option copt_options 'option1=value1 option2=value2'; # specify options
ampl: solve; # solve the problem

Resources#

Features#

Problem types and algorithms#

Problem types

  • LP, (non-)convex QP, (non-)convex QCP, conic programs (SOCP, exponential cones)

  • MILP, (non-)convex MIQP, (non-)convex MIQCP, mixed-integer conic programs

  • NLP (local)

  • MINLP (approximated)

Received natively: indicator constraints, SOS, quadratic constraints, second-order (also rotated) and exponential cones. With acc:_expr=1, also abs and all nonlinear functions, as expressions; by default they are approximated piecewise-linearly.

All constructs: native constraints and expressions by driver.

LP: simplex, barrier, PDLP

alg:method: -1 automatic (default), 1 dual simplex, 2 barrier, 4 concurrent, 5 simplex or barrier, 6 first-order (PDLP). GPU for barrier and PDLP: alg:gpumode (CUDA, Windows and Linux).

MIP and nonconvex quadratic models: branch-and-cut

Relative gap: mip:gap. For continuous nonconvex quadratic models, alg:nonconvex: -1 default (as of COPT 8 a local search), 1 local, 2 global. Nonlinear functions other than quadratic are approximated piecewise-linearly by default, which allows approximate solving of MINLP.

Nonlinear models: local

With acc:_expr=1, nonlinear functions (exp, log, trigonometric, powers, divisions) are passed to COPT natively as expressions, and its barrier returns a locally optimal solution (solve_result solved?, message “locally optimal solution”); on a nonconvex model, different starting points can give different local optima. For the continuous relaxation of an MINLP, add alg:relax=1. With the default acc:_expr=0, these functions are approximated piecewise-linearly instead.

ampl.solve(solver="copt", copt_options="acc:_expr=1 outlev=1")  # local NLP
print(ampl.solve_result, ampl.get_value("solve_message"))

ampl: option solver copt;
ampl: option copt_options 'acc:_expr=1 outlev=1';  # local NLP
ampl: solve;

Instrumentation#

For a generic summary of the options and features used most often, see Important features in the MP documentation.

For all models

Model export

Option tech:writemodel. Details

Solution export

Option tech:writesolution. Details

Feasibility relaxation

Option alg:feasrelax. Details

Irreducible inconsistent subset (IIS)

Option iis:find. Details

Method: iis:method.

Basis input and output

Option alg:basis. Details

Multiple solutions

Option sol:stub. Details

Multiple objectives

Option obj:multi. Details

Sensitivity analysis

Option alg:sens. Details

Unbounded rays and Farkas certificates

Option alg:rays. Details

Warm start

Option alg:start. Details

For MIP models

Fixed model (duals and basis for a MIP)

Option mip:basis. Details

Lazy constraints and user cuts

Option mip:lazy. Details

MIP gap

Option mip:return_gap. Details

Best dual bound

Option mip:bestbound. Details

Solver options#

Full list of solver options:

More details on solver options: MP solver options.

Retrieving solutions#

The outcome of the last optimization is stored in the AMPL parameter solve_result_num and the relative message in solve_result.

display solve_result_num, solve_result;

COPT solve result codes can be obtained by running copt -! or ampl: shell "copt -!";:

Solve result table for COPT 8.0.6
          0- 99 solved: optimal for an optimization problem,
                feasible for a satisfaction problem 
        100-199 solved? solution candidate returned but error likely 
            150 solved? MP solution check failed (option sol:chk:fail) 
        200-299 infeasible 
        300-349 unbounded, feasible solution returned 
        350-399 unbounded, no feasible solution returned 
        400-449 limit, feasible: stopped, e.g., on iterations or Ctrl-C 
        450-469 limit, problem is either infeasible or unbounded.
                Disable dual reductions or run IIS finder for definitive answer.
        470-499 limit, no solution returned 
        500-999 failure, no solution returned 
            550 failure: numeric issue, no feasible solution

For general information, see MP result codes guide.

Changelog#