updated hitting set sample

examples/python/hs.py

@@ -1,48 +1,166 @@
 #
 # Unweighted hitting set maxsat solver.
+# interleaved with local hill-climbing improvements
 #
 
+from z3 import *
+import random
+
+
+                
 class Soft:
-    __init__(self, soft):
+    def __init__(self, soft):
         self.formulas = soft
         self.name2formula = { Bool(f"s{s}") : s for s in soft }
-        self.formula2name = { s : v for (v, s) in self._name2formula.items() }
+        self.formula2name = { s : v for (v, s) in self.name2formula.items() }
+
 
 def improve(hi, mdl, new_model, soft):
     cost = len([f for f in soft.formulas if not is_true(new_model.eval(f))])
+    if mdl is None:
+        mdl = new_model
     if cost <= hi:
+        print("improve", hi, cost)
         mdl = new_model
     if cost < hi:
         hi = cost
+    assert mdl
     return hi, mdl
 
-def pick_hs(K, soft):
+#
+# This can improve lower bound, but is expensive.
+# Note that Z3 does not work well for hitting set optimization.
+# MIP solvers contain better
+# tuned approaches thanks to LP lower bounds and likely other properties.
+# Would be nice to have a good hitting set
+# heuristic built into Z3....
+#
+def pick_hs_(K, lo, soft):
+    hs = set()
+    for k in K:
+        ks = set(k)
+        if len(ks & hs) > 0:
+            continue
+        h = random.choice([h for h in k])
+        hs = hs | { h }
+    print("approximate hitting set", len(hs), "smallest possible size", lo)
+    return hs, lo
+
+opt_backoff_limit = 0
+opt_backoff_count = 0
+timeout_value = 6000
+def pick_hs(K, lo, soft):
+    global timeout_value
+    global opt_backoff_limit
+    global opt_backoff_count
+    if opt_backoff_count < opt_backoff_limit:
+        opt_backoff_count += 1
+        return pick_hs_(K, lo, soft)
     opt = Optimize()
     for k in K:
-        opt.add(Or(soft.formula2name[f] for f in k))        
+        opt.add(Or([soft.formula2name[f] for f in k]))        
     for n in soft.formula2name.values():
-        opt.add_soft(Not(n))
+        obj = opt.add_soft(Not(n))
-    print(opt.check())
+    opt.set("timeout", timeout_value)
-    mdl = opt.model()
+    is_sat = opt.check()
-    hs = [soft.name2formula[n] for n in soft.formula2name.values() if is_true(mdl.eval(n))]
+    lo = max(lo, opt.lower(obj).as_long())
-    return hs, True
+    if is_sat == sat:
+        mdl = opt.model()
+        hs = [soft.name2formula[n] for n in soft.formula2name.values() if is_true(mdl.eval(n))]
+        return hs, lo
+    else:
+        print("Timeout", timeout_value, "lo", lo, "limit", opt_backoff_limit)
+        opt_backoff_limit += 1
+        opt_backoff_count = 0
+        timeout_value += 500
+        return pick_hs_(K, lo, soft)
+
+
+
+def local_mss(hi, mdl, s, soft):
+    mss = { f for f in soft.formulas if is_true(mdl.eval(f)) }
+    ps = set(soft.formulas) - mss
+    backbones = set()
+    qs = set()
+    while len(ps) > 0:
+        p = random.choice([p for p in ps])
+        ps = ps - { p }
+        is_sat = s.check(mss | backbones | { p })
+        print(p, len(ps), is_sat)
+        sys.stdout.flush()
+        if is_sat == sat:
+            mdl = s.model()
+            rs = { p }
+            
+# by commenting this out, we use a more stubborn exploration
+# by using the random seed as opposed to current model as a guide
+# to what gets satisfied.
+#
+# Not sure if it really has an effect.
+#           rs = rs | { q for q in ps if is_true(mdl.eval(q)) }
+            rs = rs | { q for q in qs if is_true(mdl.eval(q)) }
+            mss = mss | rs
+            ps = ps - rs 
+            qs = qs - rs
+            hi, mdl = improve(hi, mdl, s.model(), soft)
+        elif is_sat == unsat:
+            backbones = backbones | { Not(p) }            
+        else:
+            qs = qs | { p }
+    return hi, mdl
+
+def get_cores(hi, hs, mdl, s, soft):
+    core = s.unsat_core()
+    remaining = set(soft.formulas) - set(core) - set(hs)
+    num_cores = 0
+    cores = [core]
+    print("new core of size", len(core))    
+    while True:        
+        is_sat = s.check(remaining)
+        if unsat == is_sat:
+            core = s.unsat_core()
+            print("new core of size", len(core))
+            cores += [core]
+            remaining = remaining - set(core)
+        elif sat == is_sat and num_cores == len(cores):
+            hi, mdl = local_mss(hi, s.model(), s, soft)
+            break
+        elif sat == is_sat:
+            hi, mdl = improve(hi, mdl, s.model(), soft)
+
+            #
+            # Extend the size of the hitting set using the new cores
+            # and update remaining using these cores.
+            # The new hitting set contains at least one new element
+            # from the original core
+            #
+            hs = set(hs)
+            for i in range(num_cores, len(cores)):
+                h = random.choice([c for c in cores[i]])
+                hs = hs | { h }
+            remaining = set(soft.formulas) - set(core) - set(hs)
+            num_cores = len(cores)
+        else:
+            print(is_sat)
+            break
+    return hi, mdl, cores
 
 def hs(lo, hi, mdl, K, s, soft):    
-    hs, is_min = pick_hs(K, soft)
+    hs, lo = pick_hs(K, lo, soft)
-    is_sat = s.check(set(soft.formulas) - set(hs))
+    is_sat = s.check(set(soft.formulas) - set(hs))    
     if is_sat == sat:
         hi, mdl = improve(hi, mdl, s.model(), soft)
     elif is_sat == unsat:
-        core = s.unsat_core()
+        hi, mdl, cores = get_cores(hi, hs, mdl, s, soft)
-        K += [set(core)]
+        K +=  [set(core) for core in cores]
-        if is_min:
+        hi, mdl = local_mss(hi, mdl, s, soft)
-            lo = max(lo, len(hs))
+        print("total number of cores", len(K))
     else:
         print("unknown")
-    print(lo, hi)
+    print("maxsat [", lo, ", ", hi, "]")
     return lo, hi, mdl, K
         
-
+#set_option(verbose=1)
 def main(file):
     s = Solver()
     opt = Optimize()
@@ -56,7 +174,8 @@ def main(file):
     while lo < hi:
         lo, hi, mdl, K = hs(lo, hi, None, K, s, soft)
 
-def __main__():
+
-    main(sys.argv[0])
+if __name__ == '__main__':
+    main(sys.argv[1])