Finding suboptimal solution (best solution so far) with Z3 command line tool and timeout

Question

I saw a post which spoke about how Z3's python API can be used to get suboptimal solution for a minimization problem

I have a MAXSMT problem, and I want to know how Z3 command line tool can be used to find a suboptimal solution when timeout is specified?

Is using -t:timeout option alone suppose to give me a suboptimal solution?

The Z3 solver took 150 seconds to find an optimal solution for my MaxSMT problem

I used z3 -t:140000 smt2 <filename> to set the timeout as 140 seconds. But the z3 solver returns unknown (instead of sat and an non zero objective value). I also tried with timeout 145 seconds and saw similar result. When I set timeout as > 150, I got the optimal solution

Am I suppose to add something more to get suboptimal solutions?

Answer 1

The maxres engine, presented in νZ - Maximal Satisfaction with Z3 and Maximum Satisfiability Using Core-Guided MaxSAT Resolution, approaches the optimal solution from the unsatisfiable region through a sequence of relaxations. Therefore, the maxres engine should not be able to find any sub-optimal model: the first model of the input formula that it finds is also the optimal model.

If you don't need a sub-optimal model but only a sub-optimal value, then you might consider taking the latest approximation of the upper-bound value found by maxres.

From the command line, it appears that one can make maxres print any lower/upper bound improvement by enabling the verbose option:

~$ ./z3 -v:1 smtlib2_maxsmt.smt2 
(optimize:check-sat)
(optimize:sat)
(maxsmt)
(opt.maxsat mutex size: 2 weight: 1)
(opt.maxres [1:2])
(opt.maxres [1:1])
found optimum
is-sat: l_true
Satisfying soft constraints
1: |(not (<= y 0))!1| |-> true 
1: |(not (<= y 0))!2| |-> true 
1: |(not (<= 0 y))!3| |-> false 
sat
(objectives
 (goal 1)
)
(model 
  (define-fun y () Int
    1)
  (define-fun x () Int
    (- 1))
)

If I interpret it correctly, in (opt.maxres [1:2]), 1 is the latest lower bound and 2 is the latest upper bound for the given objective. Note that in the linked post Nikolaj Bjorner states that maxres may update the upper bound along the maxres search, but I can't tell how frequently that happens so this solution might not be very effective in practice.

Alternatively, you might want to try to use some other MaxSMT engine which approaches the optimal solution from the satisfiable region, e.g. wmax, though it might be slower than maxres.

The MaxSAT engine used by z3 can be selected using the following option:

(set-option:opt.maxsat_engine [wmax|maxres|pd-maxres])

One can also set it through the command-line, as follows:

~$ ./z3 -v:1 opt.maxsat_engine=wmax smtlib2_maxsmt.smt2 
(optimize:check-sat)
(optimize:sat)
(maxsmt)
(opt.maxsat mutex size: 2 weight: 1)
(opt.wmax [1:2])
(opt.wmax [1:1])
is-sat: l_true
Satisfying soft constraints
1: |(not (<= y 0))!1| |-> true 
1: |(not (<= y 0))!2| |-> true 
1: |(not (<= 0 y))!3| |-> false 
sat
(objectives
 (goal 1)
)
(model 
  (define-fun y () Int
    1)
  (define-fun x () Int
    (- 1))
)

Note that there is also an option to enable wmax within the maxres engine, though I am unsure what it is supposed to do as the output doesn't seem to change:

(set-option:opt.maxres.wmax true)