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adaptive_memory_LS.py
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adaptive_memory_LS.py
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'''
References
[1] Z. Lü and J.-K. K. Hao, “Adaptive Memory-Based Local Search for MAX-SAT,” Elsevier, Aug. 2012. doi: 10.1016/j.asoc.2012.01.013.
'''
from base_solver import Base_Solver
import numpy as np
import random
import time
from itertools import chain
class AMLS(Base_Solver):
def __init__(self, input_cnf_file, verbose):
super(AMLS, self).__init__(input_cnf_file, verbose)
self.initialize_pool()
self.generate()
self.initialize_cost()
self.best_assignment = self.assignment.copy()
self.best_cost = len(self.id_unsat_clauses)
self.p = 0.0
self.wp = 0.0
self.last_move = [-1 for _ in self.assignment]
self.MAX_PERT = 15
self.MAX_FLIPS = int(self.nvars*self.nvars/4)
self.CHECK_FREQ = self.nvars * 10
self.vf = [None for _ in self.list_clauses]
self.vs = [None for _ in self.list_clauses]
self.nf = [0 for _ in self.list_clauses]
self.ns = [0 for _ in self.list_clauses]
self.tabu_tenure = int(self.nvars/10 + 4)
self.stagnation = False
self.no_improvement_step = 0
self.DEFINED_STEP = int(len(self.list_clauses)/6)
def initialize_params(self):
self.p = 0
self.wp = 0
self.last_move = [-1 for _ in self.assignment]
self.nb_tries += 1
self.nb_flips = 0
self.no_improvement_step = 0
def update_params(self):
if self.stagnation:
self.no_improvement_step += 1
if self.no_improvement_step >= self.DEFINED_STEP:
# Increase
self.wp += float((0.05 - self.wp)/5)
self.p += float((1-self.p)/5)
self.no_improvement_step = 0
else:
# Decrease
self.wp -= float(self.wp/10)
self.p -= float(self.p/10)
nb_moves, tb_moves = self.pick_allowed_lits(self.tabu_tenure)
nb_total_moves = len(nb_moves) + len(tb_moves)
self.tabu_tenure = random.randint(1,10) + int(nb_total_moves*0.25)
def pick_unsat_clause(self):
assert len(self.id_unsat_clauses) > 0
random_index = random.choice(self.id_unsat_clauses)
return self.list_clauses[random_index]
def pick_allowed_lits(self, tabu_tenure):
allowed_lits = []
non_allowed_lits = []
'''
GSAT strategy
'''
for ind in self.id_unsat_clauses:
allowed_lits += self.list_clauses[ind]
allowed_lits = list(set(allowed_lits))
if tabu_tenure > 0:
for lit in allowed_lits:
if self.nb_flips - self.last_move[abs(lit)-1] < tabu_tenure: #tabu move
allowed_lits.remove(lit)
non_allowed_lits.append(lit)
'''
WalkSAT strategy
'''
# list_id_unsat_clauses = self.id_unsat_clauses.copy()
# while len(allowed_lits) == 0 and len(list_id_unsat_clauses)>0:
# random_id = random.choice(list_id_unsat_clauses)
# list_id_unsat_clauses.remove(random_id)
# allowed_lits = self.list_clauses[random_id]
# if tabu_tenure > 0:
# for lit in allowed_lits:
# if self.nb_flips - self.last_move[abs(lit)-1] < tabu_tenure: #tabu move
# allowed_lits.remove(lit)
# non_allowed_lits.append(lit)
return allowed_lits, non_allowed_lits
def pick_necessary_flip(self):
oldest_move = min(self.last_move)
if self.nb_flips - oldest_move > self.CHECK_FREQ:
return self.assignment[self.last_move.index(oldest_move)]
else:
return None
def pick_1st_and_2nd_min(self, cost_list):
assert len(cost_list) > 0
x_1, x_2 = cost_list[0], cost_list[0]
id_1, id_2 = 0, 0
for i in range(1,len(cost_list)):
if cost_list[i] <= x_1:
x_1, x_2 = cost_list[i], x_1
id_1, id_2 = i, id_1
elif cost_list[i] < x_2:
x_2 = cost_list[i]
id_2 = i
return id_1, id_2
def penalty(self, y):
list_RS, list_RF = [], []
for i in range(len(self.list_clauses)):
if self.vs[i] is not None and abs(self.vs[i]) == abs(y):
list_RS.append(i)
if self.vf[i] is not None and abs(self.vf[i]) == abs(y):
list_RF.append(i)
cost_RS, cost_RF = 0, 0
for cs in list_RS:
cost_RS += 2**self.ns[cs]
for cf in list_RF:
cost_RF += 2**self.nf[cf]
if len(list_RS)>0:
cost_RS = float(cost_RS/(2*len(list_RS)))
if len(list_RF)>0:
cost_RF = float(cost_RF/(2*len(list_RF)))
pen = cost_RS + cost_RF
return pen
def pick_neighborhood(self, tabu_tenure):
'''
compute allowed literals wrt tabu list
'''
allowed_lits, non_allowed_lits = self.pick_allowed_lits(tabu_tenure)
if len(allowed_lits) == 0: # else take allowed_lits and ignore tabu
allowed_lits, non_allowed_lits = self.pick_allowed_lits(0)
'''
Compute cost of every (tabu and non tabu) moves
Cost = break - make
'''
assert len(allowed_lits) > 0
ntb_cost, tb_cost = [], []
current_cost = len(self.id_unsat_clauses)
for literal in allowed_lits:
ntb_cost.append(self.evaluate_breakcount(literal, bs=1, ms=1))
id_ntb_1st, id_ntb_2nd = self.pick_1st_and_2nd_min(ntb_cost)
for literal in non_allowed_lits:
tb_cost.append(self.evaluate_breakcount(literal, bs=1, ms=1))
if len(tb_cost)>0:
x_tb = non_allowed_lits[np.argmin(tb_cost)]
if min(tb_cost) < min(ntb_cost) and current_cost + min(tb_cost) < self.best_cost:
y = x_tb
return y
x_nb = allowed_lits[id_ntb_1st]
x_nsb = allowed_lits[id_ntb_2nd]
if min(ntb_cost) < 0:
y = x_nb
return y
wp = random.random()
if wp < self.wp:
# Random walk on non tabu moves
y = random.choice(allowed_lits)
return y
p = random.random()
least_recent_move = allowed_lits[0] #largest last move
for lit in allowed_lits[1:]:
if self.last_move[abs(least_recent_move)-1] < self.last_move[abs(lit)-1]:
least_recent_move = lit
if p < self.wp and x_nb == least_recent_move:
if self.penalty(x_nsb) < self.penalty(x_nb):
y = x_nsb
return y
y = x_nb
return y
def flip(self, literal):
self.nb_flips += 1
# Flip variable in assignment
ind = 0
if literal in self.assignment:
ind = self.assignment.index(literal)
elif -literal in self.assignment:
ind = self.assignment.index(-literal)
old_literal = self.assignment[ind]
self.assignment[ind] *= -1
# Update cost
# Clause contains literal => cost --
if old_literal in self.pool.keys():
for i in self.pool[old_literal]:
self.costs[i] -= 1
if self.costs[i] == 0: # if SAT -> UNSAT: add to list of unsat clauses
self.id_unsat_clauses.append(i)
if self.vf[i] is not None and self.vf[i] == abs(literal):
self.nf[i] += 1
else:
self.vf[i] = abs(literal)
self.nf[i] = 1
# Clause contains -literal => cost ++
if -old_literal in self.pool.keys():
for j in self.pool[-old_literal]:
if self.costs[j] == 0: # if UNSAT -> SAT: remove from list of unsat clauses
self.id_unsat_clauses.remove(j)
if self.vs[j] is not None and self.vs[j] == abs(literal):
self.ns[j] += 1
else:
self.vs[j] = abs(literal)
self.ns[j] = 1
self.costs[j] += 1
def perturbate(self, tabu_tenure):
nb_pert = 0
while nb_pert < self.MAX_PERT and not self.check():
'''
compute allowed literals wrt tabu list
'''
all_allowed_lits, non_allowed_lits = self.pick_allowed_lits(tabu_tenure)
if len(all_allowed_lits) == 0: # else take all_allowed_lits and ignore tabu
all_allowed_lits, non_allowed_lits = self.pick_allowed_lits(0)
'''
Compute cost of every (tabu and non tabu) moves
Cost = break - make
'''
ntb_cost, tb_cost = [], []
current_cost = len(self.id_unsat_clauses)
for literal in all_allowed_lits:
ntb_cost.append(self.evaluate_breakcount(literal, bs=1, ms=1))
x_ntb = all_allowed_lits[np.argmin(ntb_cost)]
for literal in non_allowed_lits:
tb_cost.append(self.evaluate_breakcount(literal, bs=1, ms=1))
if len(tb_cost) > 0:
x_tb = non_allowed_lits[np.argmin(tb_cost)]
if min(tb_cost) < min(ntb_cost) and current_cost + min(tb_cost) < self.best_cost: #EXCEPTION
x = x_tb
else:
x = x_ntb
else:
x = x_ntb
self.flip(x)
self.last_move[abs(x)-1] = self.nb_flips
if len(self.id_unsat_clauses) < self.best_cost:
self.best_cost = len(self.id_unsat_clauses)
'''
Every 10n iterations, if a variable is not flipped within 10n iterations
=> force X to be flipped !
'''
if self.nb_flips % self.CHECK_FREQ == 0:
x = self.pick_necessary_flip()
if x is not None:
self.flip(x)
self.last_move[abs(x)-1] = self.nb_flips
if len(self.id_unsat_clauses) < self.best_cost:
self.best_cost = len(self.id_unsat_clauses)
'''
TODO: Every n iterations => change randomly tabu tenure
Note: tabu tenure for perturbation phase should be larger than the one used for LS
'''
# if self.nb_flips % self.nvars == 0:
# self.tabu_tenure = random.randint(self.tabu_tenure_MIN, self.tabu_tenure_MAX)
nb_pert += 1
return self.assignment
def solve(self):
initial = time.time()
while self.nb_tries < self.MAX_TRIES and not self.is_sat:
'''
Search Phase
'''
self.initialize_params()
while self.nb_flips < self.MAX_FLIPS and not self.check():
'''
Select move
'''
x = self.pick_neighborhood(self.tabu_tenure)
self.flip(x)
'''
Update best cost and assignment
'''
if len(self.id_unsat_clauses) < self.best_cost:
self.best_cost = len(self.id_unsat_clauses)
self.best_assignment = self.assignment.copy()
self.stagnation = False
else:
self.stagnation = True
'''
Add this move to the tabu list
Update p, wp, tabu tenure
'''
self.last_move[abs(x)-1] = self.nb_flips
self.update_params()
'''
Perturbation Phase
'''
self.assignment = self.perturbate(int(self.nvars/2))
if self.check():
self.is_sat = True
end = time.time()
print('Nb flips: {0} '.format(self.nb_flips))
print('Nb tries: {0} '.format(self.nb_tries))
print('CPU time: {0:10.4f} s '.format(end-initial))
if self.is_sat:
print('SAT')
return self.assignment
else:
print('UNKNOWN')
return None