Xpress ignore LP warm starts

[odow]

It looks like it does, but I couldn't find any evidence these are actually passed to the solver

Xpress.jl/src/MOI/MOI_wrapper.jl

Lines 2866 to 2886 in e325c68

	function MOI.set(
	model::Optimizer,
	::MOI.VariablePrimalStart,
	x::MOI.VariableIndex,
	value::Union{Nothing, Float64}
	)
	info = _info(model, x)
	info.start = value
	return
	end
	function MOI.get(
	model::Optimizer, ::MOI.VariablePrimalStart, x::MOI.VariableIndex
	)
	return _info(model, x).start
	end
	function MOI.supports(
	::Optimizer, ::MOI.VariablePrimalStart, ::Type{MOI.VariableIndex})
	return true
	end

Reported on Discourse: https://discourse.julialang.org/t/warmstarting-variables-does-not-work-with-xpress/60989

[henriquebecker91]

I would like to get this working as soon as possible. Someone has already tried something? Is there some hint from what is the source of the bug? I will probably work this weekend on this problem. I am almost sure the warm start is really being ignored because I currently warm start a model with a feasible solution of a subset of the model (a model with less columns) and the XPress spends hours without finding any feasible solution.

[metab0t]

https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/HTML/XPRSaddmipsol.html
I think this function can solve that issue. You need to pass the start value to Xpress solver with this function.

[henriquebecker91]

Before making the change, let me confirm if I understood correctly. The solution is to call the aforementioned XPRESS function inside MOI.optimize, before the actual solve, using the values saved in the start field of the Variable wrapper, correct?

Is the aforementioned XPRESS function already wrapped or do I need to write the CCall myself?

Ah, I found it, is this addmipsol(prob::XpressProblem, ilength, mipsolval, mipsolcol, solname).

[metab0t]

You can write as follows:

function MOI.set( 
     model::Optimizer, 
     ::MOI.VariablePrimalStart, 
     x::MOI.VariableIndex, 
     value::Union{Nothing, Float64} 
 ) 
     info = _info(model, x)
     info.start = value
     if value !== nothing
         Xpress.addmipsol(model.inner, 1, [value], [info.column], C_NULL)
     end
     return 
 end

[henriquebecker91]

Created a PR (#148) to solve the problem. The solution is considerably more complex. Not only because I believe that Xpress.addmipsol does not work one-variable-at-time (I am almost sure it adds a whole solution, even if incomplete, each time; so each variable would be considered a distinct incomplete solution in your example.), but mainly because of another reasons discussed in the PR.

[joaquimg]

Since #148, MIP warmstart is accepted.

LP warmstart for xpress is harder because we need a basis (see https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/HTML/XPRSloadbasis.html)

[henriquebecker91]

If I can raise two questions:

1. Currently solving an LP multiple consecutive times (adding variables between solves) does reuse the previous base, right? At least this is my impression in practice.
2. Does JuMP have an API for LP warmstarts? Because set_start_value seems to be only for MIP-starts and I found nothing equivalent for LP.

[joaquimg]

Yes, xpress does re-use the last solution for LPs.

JuMP API for start values is not restricted to MIP by definition. Although it fits well on Xpress' mip start and fits poorly on xpress lp start because it would require converting the solution into a basis.
JuMP also accepts generic atributes if we want to pass something else useful.