pyepo.model.copt

Optimization Model based on Cardinal Optimizer（COPT）

Submodules

Classes

`optCoptModel`	This is an abstract class for a Cardinal Optimizer optimization model
`shortestPathModel`	This class is an optimization model for the shortest path problem
`knapsackModel`	This class is an optimization model for the knapsack problem
`knapsackModelRel`	This class is relaxed optimization model for knapsack problem.
`tspGGModel`	This class is an optimization model for the traveling salesman problem based on Gavish-Graves (GG) formulation.
`tspGGModelRel`	This class is relaxation of tspGGModel.
`tspDFJModel`	This class is an optimization model for the traveling salesman problem based on Danzig-Fulkerson-Johnson (DFJ) formulation and
`tspMTZModel`	This class is an optimization model for the traveling salesman problem based on Miller-Tucker-Zemlin (MTZ) formulation.
`tspMTZModelRel`	This class is relaxation of tspMTZModel.
`portfolioModel`	This class is an optimization model for the portfolio problem

Package Contents

class pyepo.model.copt.optCoptModel

Bases: pyepo.model.opt.optModel

This is an abstract class for a Cardinal Optimizer optimization model

_model

COPT model

Type:: COPT model

__repr__()

setObj(c)

A method to set the objective function

Parameters:: c (np.ndarray / list) – cost of objective function

solve()

A method to solve the model

Returns:: optimal solution (list) and objective value (float)
Return type:: tuple

copy()

A method to copy the model

Returns:: new copied model
Return type:: optModel

addConstr(coefs, rhs)

A method to add a new constraint

Parameters:

coefs (np.ndarray / list) – coefficients of new constraint
rhs (float) – right-hand side of new constraint

Returns:

new model with the added constraint

Return type:

optModel

class pyepo.model.copt.shortestPathModel(grid)

Bases: pyepo.model.copt.coptmodel.optCoptModel

This class is an optimization model for the shortest path problem

_model

COPT model

Type:: COPT model

grid

size of grid network

Type:: tuple of int

arcs

list of arcs

Type:: list

grid

arcs = []

_getModel(): A method to build COPT model

class pyepo.model.copt.knapsackModel(weights, capacity)

Bases: pyepo.model.copt.coptmodel.optCoptModel

This class is an optimization model for the knapsack problem

_model

COPT model

Type:: COPT model

weights

weights of items

Type:: np.ndarray

capacity

total capacity

Type:: np.ndarray

items

list of item index

Type:: list

weights

capacity

items

_getModel(): A method to build COPT model

relax(): A method to get linear relaxation model

class pyepo.model.copt.knapsackModelRel(weights, capacity)

Bases: knapsackModel

This class is relaxed optimization model for knapsack problem.

_getModel(): A method to build COPT model

relax(): A forbidden method to relax MIP model

class pyepo.model.copt.tspGGModel(num_nodes)

Bases: tspABModel

This class is an optimization model for the traveling salesman problem based on Gavish-Graves (GG) formulation.

_model

COPT model

Type:: COPT model

num_nodes

Number of nodes

Type:: int

edges

List of edge index

Type:: list

_getModel()

A method to build COPT model

Returns:: optimization model and variables
Return type:: tuple

setObj(c)

A method to set the objective function

Parameters:: c (list) – cost vector

solve(): A method to solve model

addConstr(coefs, rhs)

A method to add new constraint

Parameters:

coefs (ndarray) – coefficients of new constraint
rhs (float) – right-hand side of new constraint

Returns:

new model with the added constraint

Return type:

optModel

relax(): A method to get linear relaxation model

class pyepo.model.copt.tspGGModelRel(num_nodes)

Bases: tspGGModel

This class is relaxation of tspGGModel.

_model

COPT model

Type:: COPT model

num_nodes

Number of nodes

Type:: int

edges

List of edge index

Type:: list

_getModel()

A method to build COPT model

Returns:: optimization model and variables
Return type:: tuple

solve()

A method to solve model

Returns:: optimal solution (list) and objective value (float)
Return type:: tuple

relax(): A forbidden method to relax MIP model

getTour(sol): A forbidden method to get a tour from solution

class pyepo.model.copt.tspDFJModel(num_nodes)

Bases: tspABModel

This class is an optimization model for the traveling salesman problem based on Danzig-Fulkerson-Johnson (DFJ) formulation and constraint generation.

_model

COPT model

Type:: COPT model

num_nodes

Number of nodes

Type:: int

edges

List of edge index

Type:: list

class _SubtourCallback(x, n, edges)

Bases: coptpy.CallbackBase

A callback class for subtour elimination

_x

_n

_edges

callback()

_getModel()

A method to build COPT model

Returns:: optimization model and variables
Return type:: tuple

setObj(c)

A method to set the objective function

Parameters:: c (list) – cost vector

solve(): A method to solve model

addConstr(coefs, rhs)

A method to add new constraint

Parameters:

coefs (ndarray) – coefficients of new constraint
rhs (float) – right-hand side of new constraint

Returns:

new model with the added constraint

Return type:

optModel

class pyepo.model.copt.tspMTZModel(num_nodes)

Bases: tspABModel

This class is an optimization model for the traveling salesman problem based on Miller-Tucker-Zemlin (MTZ) formulation.

_model

COPT model

Type:: COPT model

num_nodes

Number of nodes

Type:: int

edges

List of edge index

Type:: list

_getModel()

A method to build COPT model

Returns:: optimization model and variables
Return type:: tuple

setObj(c)

A method to set the objective function

Parameters:: c (list) – cost vector

solve(): A method to solve model

addConstr(coefs, rhs)

A method to add new constraint

Parameters:

coefs (ndarray) – coefficients of new constraint
rhs (float) – right-hand side of new constraint

Returns:

new model with the added constraint

Return type:

optModel

relax(): A method to get linear relaxation model

class pyepo.model.copt.tspMTZModelRel(num_nodes)

Bases: tspMTZModel

This class is relaxation of tspMTZModel.

_model

COPT model

Type:: COPT model

num_nodes

Number of nodes

Type:: int

edges

List of edge index

Type:: list

_getModel()

A method to build COPT model

Returns:: optimization model and variables
Return type:: tuple

solve()

A method to solve model

Returns:: optimal solution (list) and objective value (float)
Return type:: tuple

relax(): A forbidden method to relax MIP model

getTour(sol): A forbidden method to get a tour from solution

class pyepo.model.copt.portfolioModel(num_assets, covariance, gamma=2.25)

Bases: pyepo.model.copt.coptmodel.optCoptModel

This class is an optimization model for the portfolio problem

_model

COPT model

Type:: COPT model

num_assets

number of assets

Type:: int

covariance

covariance matrix of the returns

Type:: numpy.ndarray

risk_level

risk level

Type:: float

num_assets

covariance

risk_level

_getRiskLevel(gamma)

A method to calculate the risk level

Parameters:: gamma (float) – risk level parameter
Returns:: risk level
Return type:: float

_getModel()

A method to build COPT model

Returns:: optimization model and variables
Return type:: tuple