def direct_random(T, r, iterations, verbose=False):
"""
Direct random algorithm.
Arguments:
T -- the constraint problem
r -- range [-r, r] of assignments to consider
iterations -- number of maximum random iterations
"""
best_gene = None
best_gene_failed = None
for i in range(iterations):
gene = random_gene(T, r)
gene_failed = verify_witness(gene, T)
if not best_gene or len(gene_failed) < len(best_gene_failed):
best_gene = gene
best_gene_failed = gene_failed
if len(gene_failed) == 0:
break
if verbose:
print(f'num iterations: {i+1}')
print('best gene:', best_gene)
print('constraints failed:', len(best_gene_failed), 'out of:', len(T))
print('failed constraints:', best_gene_failed)
return best_gene, best_gene_failed
def direct_genetic(T, r,
gene_pool_size,
retainment_ratio,
mutation_chance,
max_iterations,
verbose=False):
"""
Direct genetic algorithm.
Arguments:
T -- the constraint problem
r -- range [-r, r] of assignments to consider
gene_pool_size -- number of genes kept in the pool
retainment_ratio -- probability of keeping a gene from one iteration to the other
mutation_chance -- how likely a gene is to be walked
max_iterations -- maximum number of iterations before failure
"""
genes = [random_gene(T, r) for i in range(gene_pool_size)]
for it in range(max_iterations):
genes = select(genes, retainment_ratio, T)
genes = crossover(genes, gene_pool_size)
genes = mutate(T, genes, mutation_chance, r)
best_gene = select(genes, 1, T)[0] # to sort genes such that first is best
best_gene_failed = verify_witness(best_gene, T)
if verbose:
print('best gene:', best_gene)
print('constraints failed:', len(best_gene_failed), 'out of:', len(T))
print('failed constraints:', best_gene_failed)
return best_gene, best_gene_failed
def evaluate(genes, T):
"""
For each gene, compute the failed constraints.
"""
for g in genes:
d_graph = generate_d_graph(g[1]) # costly op.
g[2] = verify_witness(get_middles_sol(d_graph), T)
return genes
def random_gene(T):
"""
Returns a random gene, ie. selection of intervals for the constraints.
The gene is of the form [interval selection, distance graph, failed constraints]
"""
num_variables = max([max(t['i'], t['j']) for t in T])
interval_selection = [
randint(0,
len(constr['intervals']) - 1) for constr in T
]
gene = [interval_selection, discrete_graph(num_variables + 1), None]
update_graph(gene, T)
d_graph = generate_d_graph(gene[1]) # costly op.
failed = verify_witness(get_middles_sol(d_graph), T)
gene[2] = failed
return gene
def meta_walk(T, max_iterations, max_flips, verbose=False):
"""
Meta walk algorithm.
Arguments:
T -- the constraints
max_iterations -- max number of iterations
max_flips -- max number of flips
"""
num_variables = max([max(t['i'], t['j']) for t in T])
graph = discrete_graph(num_variables + 1)
best_gene = None
best_gene_failed = None
for i in range(max_iterations):
gene = random_gene(T)
update_graph(gene, T)
for j in range(max_flips):
# at each iteration we modify
is_consistent, witness = solve_stp(gene[1])
gene_failed = verify_witness(witness, T)
gene[2] = gene_failed
if not best_gene or len(gene_failed) < len(best_gene_failed):
best_gene = gene
best_gene_failed = gene_failed
if is_consistent:
break
walk_gene(gene, T)
if verbose:
print(f'num flips: {i+1}, num iterations: {j+1}')
print('best gene:', best_gene)
print('constraints failed:', len(best_gene_failed), 'out of:', len(T))
print('failed constraints:', best_gene_failed)
return best_gene[0], best_gene_failed
def direct_walk(T, r, max_iterations, max_flips, pick_best_gene, verbose=False):
"""
Direct walk-based algorithm.
Arguments:
T -- the constraint problem
r -- range [-r, r] of assignments to consider
max_iterations -- number of maximum random iterations
max_flips -- maximum number of walks per iteration
pick_best_gene -- whether to do extra work to find best gene to walk
"""
best_gene = None
best_gene_failed = None
for i in range(max_iterations):
gene = random_gene(T, r)
for j in range(max_flips):
gene_failed = verify_witness(gene, T)
if not best_gene or len(gene_failed) < len(best_gene_failed):
best_gene = gene
best_gene_failed = gene_failed
if len(gene_failed) == 0:
break
gene = walk_gene(gene, T, pick_best_gene)
# necessary for double break after flips loop
if len(gene_failed) == 0: break
if verbose:
print(f'num iterations: {i+1}')
print('best gene:', best_gene)
print('constraints failed:', len(best_gene_failed), 'out of:', len(T))
print('failed constraints:', best_gene_failed)
return best_gene, best_gene_failed
def fitness(gene, T):
return -len(verify_witness(gene, T))