问题
I'm using Accord.Net's Cobyla solver to solve a rather simple non-linear problem. In some cases there will be no feasible points for the problem. When I run even a simple problem where the non-feasibility is obvious, the solver return "Success" even though the solution is not feasible.
Consider the following example, written in F#:
open System.Collection.Generics
let obj12 = QuadraticObjectiveFunction("a - a*a");
let c12 = QuadraticConstraint(obj12, Array2D.zeroCreate 1 1, [| 10.0 |], ConstraintType.LesserThanOrEqualTo, 4.0)
let c13 = QuadraticConstraint(obj12, Array2D.zeroCreate 1 1, [| 10.0 |], ConstraintType.GreaterThanOrEqualTo, 45.0)
let p1 = List<NonlinearConstraint>()
p1.Add(c12)
p1.Add(c13)
let solver1 = Cobyla(obj12, p1)
let success = solver1.Maximize()
let value = solver1.Value
let solution = solver1.Solution
let r = solver1.Status
The solution the solver is found is 4.5 which clearly violate the first and second constraints however the solver status is "successful".
Is that a bug/feature? Any workaround?
回答1:
I am the author of the C# COBYLA code that is the basis for the Accord.NET version of COBYLA. The C# implementation is a fairly straightforward translation from FORTRAN 77 of Michael Powell's original code.
The optimization method currently only supports three return statuses:
- Normal termination
- Maximum number of function evaluations reached
- Rounding errors are increasing in an uncontrolled way
There exists no explicit indication saying that constraints are violated. COBYLA strives to meet the constraints, but is not guaranteed to succeed with this and may return without having fulfilled the constraints.
If I interpret your example correctly (my F# knowledge is a little rusty for the moment) you have two contradicting constraints, or? As a possible workaround, I would otherwise suggest that you select a variable start guess that at least approximately fulfills the constraints; that should make it easier for COBYLA to stay within the feasible region.
来源：https://stackoverflow.com/questions/30567946/accord-net-cobyla-solver-returns-success-when-there-are-no-feasiable-solutions