Multi-Objective GPU Optimization (MOEA/D Tensor)

Learn how to leverage GPU execution via CuPy using vectorized operators and tensorized search spaces for multi-objective decomposition algorithms.

Example Code

import cupy as cp

from opytimizer import Opytimizer
from opytimizer.core import Environment, Function
from opytimizer.core.stopping import MaxIterations
from opytimizer.math.aggregation import PBI
from opytimizer.optimizers.multi_objective.evolutionary import MOEADTensor
from opytimizer.spaces import SearchSpace
from opytimizer.utils.operators import PolynomialMutationTensor, SBXCrossoverTensor
from opytimizer.utils.reference_vectors import das_dennis
from opytimizer.visualization.visualizer import plot_agents, plot_pareto_front_evolution


def dtlz1(x: cp.ndarray) -> cp.ndarray:
    k = x[:, 2:].shape[1]
    g = 100.0 * (
        k
        + cp.sum(
            (x[:, 2:] - 0.5) ** 2 - cp.cos(20.0 * cp.pi * (x[:, 2:] - 0.5)), axis=1
        )
    )

    f1 = 0.5 * x[:, 0] * x[:, 1] * (1.0 + g)
    f2 = 0.5 * x[:, 0] * (1.0 - x[:, 1]) * (1.0 + g)
    f3 = 0.5 * (1.0 - x[:, 0]) * (1.0 + g)

    return cp.column_stack((f1, f2, f3))


SEED = 48
cp.random.seed(SEED)

gpu_env = Environment("cupy", "float32")
N_VARS = 10
N_OBJS = 3
WEIGHTS, N_AGENTS = das_dennis(N_OBJS, 23)
MAX_GEN = 250
LB = [0.0] * N_VARS
UB = [1.0] * N_VARS
func = Function(dtlz1)

space = SearchSpace(
    n_agents=N_AGENTS,
    n_variables=N_VARS,
    n_objectives=N_OBJS,
    lower_bound=LB,
    upper_bound=UB,
    env=gpu_env,
    tensorized=True,
)

crossover = SBXCrossoverTensor(env=gpu_env)
mutation = PolynomialMutationTensor(rate=1 / N_VARS, env=gpu_env)

opt = MOEADTensor(
    crossover_operator=crossover,
    mutation_operator=mutation,
    weight_vectors=WEIGHTS,
    decomposition_method=PBI(),
)

opy = Opytimizer(
    space=space, optimizer=opt, function=func, save_agents=False, save_history=True
)

stop_criterion = MaxIterations(MAX_GEN)

opy.start(stopping_criteria=stop_criterion)

Example Code​

Example Code