picos.modeling.solution¶

Optimization problem solution representation.

Classes

class picos.modeling.solution.Solution(primals, duals=None, problem=None, solver='user', primalStatus=SS_UNKNOWN, dualStatus=SS_UNKNOWN, problemStatus=PS_UNKNOWN, searchTime=0.0, info=None, vectorizedPrimals=False, reportedValue=None)[source]¶

Bases: object

Assignment of primal and dual values to variables and constraints.

Instances are usually returned by a solver (and thus bound to a problem instance), but may be manually created by the user:

>>> import picos
>>> x = picos.RealVariable("x")
>>> s = picos.Solution({x: 1}); s
<detached primal solution from user>
>>> s.apply()
>>> x.value
1.0

If the solution was created by a solver (or attached to a problem via attach_to), more information is available:

>>> P = picos.Problem()
>>> P.minimize = x
>>> P += x >= 2
>>> s = P.solve(solver = "cvxopt", duals = False); s
<feasible primal solution (claimed optimal) from cvxopt>
>>> "{:.2f} ms".format(1000.0 * s.searchTime) 
'0.83 ms'
>>> P += x >= 3; s
<infeasible primal solution (was feasible and claimed optimal) from cvxopt>

__init__(primals, duals=None, problem=None, solver='user', primalStatus=SS_UNKNOWN, dualStatus=SS_UNKNOWN, problemStatus=PS_UNKNOWN, searchTime=0.0, info=None, vectorizedPrimals=False, reportedValue=None)[source]¶

Create a solution to an optimization problem.

Parameters

primals (dict(picos.expressions.BaseVariable, object)) – A mapping of variables to their primal solution value.
duals (dict(picos.constraints.Constraint, object)) – A mapping of constraints to their dual solution value.
problem (picos.Problem) – The problem that was solved to create the solution. If None, then the solution is “detached”.
solver (str) – The name of the solver that was used to create the solution.
primalStatus (str) – The primal solution status as reported by the solver.
dualStatus (str) – The dual solution status as reported by the solver.
problemStatus (str) – The state of the problem as reported by the solver.
searchTime (float) – Seconds that the solution process took.
info (dict) – Additional solution (meta)data.
vectorizedPrimals (bool) – Whether primal solution values are given with respect to the variable’s special vectorization format as used by PICOS internally.
reportedValue (float) – Objective value of the solution as reported by the solver.

apply(primals=True, duals=True, clearOnNone=True, toProblem=None, snapshotStatus=False)[source]¶

Apply the solution to the involved variables and constraints.

Parameters

primals (bool) – Whether to apply the primal solution.
duals (bool) – Whether to apply the dual solution.
clearOnNone (bool) – Whether to clear the value of a variable or constraint if the solution has it set to None. This could happen in case of an error or shortcoming of the solver or PICOS.
toProblem (picos.Problem) – If set to a copy of the problem that was used to produce the solution, will apply the solution to that copy’s variables and constraints instead.
snapshotStatus (bool) – Whether to update the lastStatus attribute with the new (verified) solution status. PICOS enables this whenever it applies a solution returned by a solver.

attach_to(problem, snapshotStatus=False)[source]¶

Attach (or move) the solution to a problem.

Only variables and constraints that exist on the problem (same name or ID, respectively) are kept.

Parameters: snapshotStatus (bool) – Whether to set the lastStatus attribute of the copy to match the new problem.

claimedStatus¶: The primal and dual solution status as claimed by the solver.

dualStatus¶: The dual solution status as claimed by the solver.

duals¶: The dual solution values returned by the solver.

info¶: Additional information provided by the solver.

lastStatus¶: The solution status as verified by PICOS when the solution was applied to the problem.

primalStatus¶: The primal solution status as claimed by the solver.

primals¶: The primal solution values returned by the solver.

problem¶: The problem that was solved to produce the solution.

problemStatus¶: The problem status as claimed by the solver.

reportedValue¶: The objective value of the solution as reported by the solver.

property reported_value¶: The objective value as reported by the solver, or None.

searchTime¶: Time in seconds that the solution search took.

solver¶: The solver that produced the solution.

property status¶: The current solution status as verified by PICOS.

Warning

Accessing this attribute is expensive for large problems as a copy of the problem needs to be created and valued. If you have just applied the solution to a problem, query the solution’s lastStatus attribute instead.

property value¶: The objective value of the solution as computed by PICOS.

Warning

Accessing this attribute is expensive for large problems as a copy of the problem needs to be created and valued. If you have just applied the solution to a problem, query that problem instead.

vectorizedPrimals¶: Whether primal values refer to variables’ special vectorizations.

Objects

picos.modeling.solution.PS_FEASIBLE¶

The problem is primal (and dual) feasible and bounded.

Default value

'feasible'

picos.modeling.solution.PS_ILLPOSED¶

The problem was found to be in a state that is not amenable to solution.

Default value

'illposed'

picos.modeling.solution.PS_INFEASIBLE¶

The problem is primal infeasible (and dual unbounded or infeasible).

Default value

'infeasible'

picos.modeling.solution.PS_INF_OR_UNB¶

The problem is primal infeasible or unbounded.

Being unbounded is usually infered from being dual infeasible.

Default value

'infeasible or unbounded'

picos.modeling.solution.PS_UNBOUNDED¶

The problem is primal unbounded (and dual infeasible).

Default value

'unbounded'

picos.modeling.solution.PS_UNKNOWN¶

The solver did not make a clear claim about the problem status.

Default value

'unknown'

picos.modeling.solution.PS_UNSTABLE¶

The problem was found numerically unstable or otherwise hard to handle.

Default value

'unstable'

picos.modeling.solution.SS_EMPTY¶

The solver claims not to have produced a solution.

Default value

'empty'

picos.modeling.solution.SS_FAILURE¶

The search was termined due to a solver failure.

Default value

'failure'

picos.modeling.solution.SS_FEASIBLE¶

The solution is feasible.

Default value

'feasible'

picos.modeling.solution.SS_INFEASIBLE¶

No feasible solution exists.

In the case of a primal solution, the problem is infeasible. In the case of a dual solution, the problem is unbounded.

Default value

'infeasible'

picos.modeling.solution.SS_OPTIMAL¶

The solution is optimal.

Default value

'optimal'

picos.modeling.solution.SS_PREMATURE¶

The search was prematurely terminated due to some limit.

Default value

'premature'

picos.modeling.solution.SS_UNKNOWN¶

The solver did not make a clear claim about the solution status.

Default value

'unknown'

picos.modeling.solution.VS_DETACHED¶

The solution is not attached to a problem (it was given by the user).

Default value

'detached'

picos.modeling.solution.VS_DETACHED_EMPTY¶

The solution is both detached and empty.

Default value

'detached empty'

picos.modeling.solution.VS_EMPTY¶

The solution is empty; there are neither primals nor duals.

Default value

'empty'

picos.modeling.solution.VS_FEASIBLE¶

The solution is primal feasible; there is no dual solution.

Default value

'feasible'

picos.modeling.solution.VS_INCOMPLETE¶

The primal (dual) solution does not concern all variables (constraints).

Default value

'incomplete'

picos.modeling.solution.VS_INFEASIBLE¶

The solution is primal infeasible; there is no dual solution.

Default value

'infeasible'

picos.modeling.solution.VS_OUTDATED¶

The solution does not fit the problem formulation any more.

Variables or constraints were removed from the problem.

Default value

'outdated'

picos.modeling.solution.VS_PRIMAL_FEASIBLE¶

The solution is primal feasible; a dual solution was not verified.

Default value

'primal feasible'

picos.modeling.solution.VS_PRIMAL_INFEASIBLE¶

The solution is primal infeasible; a dual solution was not verified.

Default value

'primal infeasible'

picos.modeling.solution.VS_UNKNOWN¶

PICOS failed to verify the solution.

Default value

'unverified'

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