Again for this example we will use a very simple problem, the 0-1 Knapsack. The purpose of this example is to show the simplicity of DEAP and the ease to inherit from anyting else than a simple list or array.
Many evolutionary algorithm textbooks mention that the best way to have an efficient algorithm to have a representation close the problem. Here, what can be closer to a bag than a set? Lets make our individuals inherit from the set class.
creator.create("FitnessMulti", base.Fitness, weights=(-1.0, 1.0))
creator.create("Individual", set, fitness=creator.FitnessMulti)
That’s it. You now have individuals that are in fact sets, they have the usual attribute fitness. The fitness is a minimization of the first objective (the weight of the bag) and a maximization of the second objective (the value of the bag). We will now create a dictionary of 100 random items to map the values and weights.
# The items' name is an integer, and value is a (weight, value) 2-tuple
items = dict([(i, (random.randint(1, 10), random.uniform(0, 100))) for i in xrange(100)])
We now need to initialize a population and the individuals therein. For this we will need a Toolbox to register our generators since sets can also be created with an input iterable.
toolbox = base.Toolbox()
# Attribute generator
toolbox.register("attr_item", random.choice, items.keys())
# Structure initializers
toolbox.register("individual", tools.initRepeat, creator.Individual, n=30)
toolbox.register("population", tools.initRepeat, list)
Voilà! The last thing to do is to define our evaluation function.
def evalKnapsack(individual):
weight = 0.0
value = 0.0
for item in individual:
weight += items[item][0]
value += items[item][1]
if len(individual) > MAX_ITEM or weight > MAX_WEIGHT:
return 10000, 0 # Ensure overweighted bags are dominated
return weight, value
Everything is ready for evolution. Ho no wait, since DEAP’s developers are lazy, there is no crossover and mutation operators that can be applied directly on sets. Lets define some. For example, a crossover, producing two child from two parents, could be that the first child is the intersection of the two sets and the second child their absolute difference.
def cxSet(ind1, ind2):
"""Apply a crossover operation on input sets. The first child is the
intersection of the two sets, the second child is the difference of the
two sets.
"""
temp = set(ind1) # Used in order to keep type
ind1 &= ind2 # Intersection (inplace)
ind2 ^= temp # Symmetric Difference (inplace)
A mutation operator could randomly add or remove an element from the set input individual.
def mutSet(individual):
"""Mutation that pops or add an element."""
if random.random() < 0.5:
if len(individual) > 0: # Can't pop from an empty set
mutant.pop()
else:
mutant.add(random.choice(items.keys()))
Note
The outcome of this mutation is dependent of the python you use. The set.pop() function is not consistent between versions of python. See the sources of the actual example for a version that will be stable but more complicated.
From here, everything else is just as usual, register the operators in the toolbox, and use or write an algorithm. Here we will use the eaMuPlusLambda() algorithm and the SPEA-II selection scheme.
toolbox.register("evaluate", evalKnapsack)
toolbox.register("mate", cxSet)
toolbox.register("mutate", mutSet)
toolbox.register("select", tools.selSPEA2)
pop = toolbox.population(n=MU)
hof = tools.ParetoFront()
stats = tools.Statistics(lambda ind: ind.fitness.values)
stats.register("Avg", tools.mean)
stats.register("Std", tools.std)
stats.register("Min", min)
stats.register("Max", max)
algorithms.eaMuPlusLambda(toolbox, pop, MU, LAMBDA, CXPB, MUTPB, MAXGEN, stats, hof)
Finally, a ParetoFront may be used to retrieve the best non dominated individuals of the evolution and a Statistics object is created for compiling four different statistics over the generations. The complete Knapsack Genetic Algorithm code is available.