Variable object mapping issue in Python Callbacks with Presolve enabled

Your code is actually correct. It is allowed to use xp.var() objects in functions which operate on the original problem space, like model.getCallbackSolution. But if you try to print 'value' (or 'value.name') in your for-loop, the wrong name would be printed, due to the bug I mentioned. I am guessing that is the cause of your confusion. If you want to access the var names (or other properties like bounds), you would need to cache them like this:

class XpressSolver():
    def __init__(self):
        ....
 
    def build(self):
        self.model = xp.problem()
 
        x = self.model.addVariables(..., name='x')
        y = self.model.addVariables(..., name='y')
 
        self.variables['x'] = x
        self.variables['y'] = y
 
        # cache var names for later access from callbacks
        self.var_names = [v.name for v in self.model.getVariable()]
 
        ........
 
    def PreIntSolCallback(self, model, object, soltype, cutoff):
        x = self.variables['x']
        y = self.variables['y']
        ....
 
        x_sol, y_sol = {},{}
        for key, value in x.items():
            x_sol[key] = model.getCallbackSolution(value)
            # use var index to look up its name in the original problem
            name = self.var_names[value.index]
            print(name, x_sol[key])
        for key, value in y.items():
            y_sol[key] = model.getCallbackSolution(value)
            name = self.var_names[value.index]
            print(name, y_sol[key])