z3 minimization and timeout

问题

I try to use the z3 solver for a minimization problem. I was trying to get a timeout, and return the best solution so far. I use the python API, and the timeout option "smt.timeout" with

set_option("smt.timeout", 1000) # 1s timeout

This actually times out after about 1 second. However a larger timeout does not provide a smaller objective. I ended up turning on the verbosity with

set_option("verbose", 2)

And I think that z3 successively evaluates larger values of my objective, until the problem is satisfiable:

(opt.maxres [0:6117664])
(opt.maxres [175560:6117664])
(opt.maxres [236460:6117664])
(opt.maxres [297360:6117664])
...
(opt.maxres [940415:6117664])
(opt.maxres [945805:6117664])
...

I thus have the two questions:

• Can I on contrary tell z3 to start with the upper bound, and successively return models with a smaller value for my objective function (just like for instance Minizinc annotations indomain_max http://www.minizinc.org/2.0/doc-lib/doc-annotations-search.html)
• It still looks like the solver returns a satisfiable instance of my problem. How is it found? If it's trying to evaluates larger values of my objective successively, it should not have found a satisfiable instance yet when the timeout occurs...

edit: In the opt.maxres log, the upper bound never shrinks.

For the record, I found a more verbose description of the options in the source here opt_params.pyg

Edit Sorry to bother, I've beed diving into this recently once again. Anyway I think this might be usefull to others. I've been finding that I actually have to call the Optimize.upper method in order to get the upper bound, and the model is still not the one that corresponds to this upper bound. I've been able to add it as a new constraint, and call a solver (without optimization, just SAT), but that's probably not the best idea. By reading this I feel like I should call Optimize.update_upper after the solver times out, but the python interface has no such method (?). At least I can get the upper bound, and the corresponding model now (at the cost of unneccessary computations I guess).

回答1:

Z3 finds solutions for the hard constraints and records the current values for the objectives and soft constraints. The last model that was found (the last model with the so-far best value for the objectives) is returned if you ask for a model. The maxres strategy mainly improves the lower bounds on the soft constraints (e.g., any solution must have cost at least xx) and whenever possible improves the upper bound (the optional solution has cost at most yy). The lower bounds don't tell you too much other than narrowing the range of possible optimal values. The upper bounds are available when you timeout. You could try one of the other strategies, such as the one called "wmax", which performs a branch-and-prune. Typically maxres does significantly better, but you may have better experience (depending on the problems) with wmax for improving upper bounds.

I don't have a mode where you get a stream of models. It is in principle possible, but it would require some (non-trivial) reorganization. For Pareto fronts you make successive invocations to Optimize.check() to get the successive fronts.

来源：https://stackoverflow.com/questions/35203432/z3-minimization-and-timeout