🌟 EvoMO: Bridging Evolutionary Multiobjective Optimization and GPU Acceleration via Tensorization 🌟

Table of Contents

1. Overview
2. Key Features
3. Installation Guide
4. Examples
5. Publications on EvoMO
6. Community & Support
7. Citing
8. Contributors

Overview

EvoMO is a GPU-accelerated library for evolutionary multiobjective optimization (EMO) that leverages advanced tensorization techniques. By transforming key data structures and operations into tensor representations, EvoMO enables more efficient mathematical modeling and delivers significant performance improvements. Designed with scalability in mind, EvoMO can efficiently handle large populations and complex optimization tasks. Additionally, EvoMO includes MoRobtrol, a multiobjective robot control benchmark suite, providing a platform for testing tensorized EMO algorithms in real-world, black-box environments. EvoMO is a sister project of EvoX.

For more details, please refer to our Documentation / 文档.

[!NOTE] To use the JAX version of EvoMO, you can switch to the v0.0.1-dev branch. This branch is fully compatible with EvoX version 0.9.0.

Key Features

💻 High-Performance Computing

🚀 General Tensorization Methodology

• EvoMO adopts a unified tensorization approach, restructuring EMO algorithms into tensor representations, enabling efficient GPU acceleration.

⚡ Ultra Performance

• Supports tensorized implementations of 57 multi-objective optimization algorithms, including NSGA-II, NSGA-III, MOEA/D, RVEA, and HypE, with 48 new algorithms added in v0.3.0, achieving up to 1113× speedup while preserving solution quality.

📈 Scalability

• Handles large populations, scaling to hundreds of thousands for complex optimization tasks, ensuring scalability for real-world applications.

📊 Benchmarking

🤖 MoRobtrol Benchmark

• Includes MoRobtrol, a multiobjective robot control benchmark, for testing tensorized EMO algorithms in challenging black-box environments.

🔧 Easy-to-Use Integration

📦 Standalone EvoMO Package

• EvoMO is now available as an independent repository, allowing users to easily access multiobjective optimization algorithms and benchmark problems via import evomo for improved discoverability and usability.

Installation Guide

To install EvoMO, you need to install EvoX first.

1. Install EvoX:

pip install evox

1. Install EvoMO:

pip install evomo

For the latest development version, you can install from the source:

git clone https://github.com/EMI-Group/evomo.git
cd evomo
python -m pip install -e .

Examples

Numerical optimization problem

Solve the DTLZ2 problem using the TensorMOEA/D algorithm:

import time

import torch
from evox.metrics import igd
from evox.problems.numerical import DTLZ2
from evox.workflows import StdWorkflow

from evomo.algorithms import TensorMOEAD

if __name__ == "__main__":
    torch.set_default_device("cuda" if torch.cuda.is_available() else "cpu")

    algo = TensorMOEAD(pop_size=100, n_objs=3, lb=-torch.zeros(12), ub=torch.ones(12))
    prob = DTLZ2(m=3)
    pf = prob.pf()
    workflow = StdWorkflow(algo, prob)
    workflow.init_step()
    jit_state_step = workflow.step

    t = time.time()
    for i in range(100):
        print(i)
        jit_state_step()
        fit = workflow.algorithm.fit
        fit = fit[~torch.any(torch.isnan(fit), dim=1)]
        print(f"Generation {i + 1} IGD: {igd(fit, pf)}")

    print(f"Total time: {time.time() - t} seconds")

Constrained multi-objective optimization

Solve the DOC1 constrained multi-objective problem using NSGA-II. A solution is feasible when all of its constraint-violation values are zero.

import torch

from evomo.algorithms import NSGA2
from evomo.problems.constrained import DOC1
from evomo.workflows import UnifiedWorkflow


if __name__ == "__main__":
    device = "cuda" if torch.cuda.is_available() else "cpu"
    torch.set_default_device(device)

    problem = DOC1()
    algorithm = NSGA2(
        pop_size=100,
        n_objs=problem.m,
        lb=problem.lb,
        ub=problem.ub,
        device=device,
    )
    workflow = UnifiedWorkflow(algorithm, problem, device=device)
    workflow.init_step()

    compiled_step = torch.compile(workflow.step)
    for _ in range(100):
        compiled_step()

    fitness = workflow.algorithm.fit
    constraint_violation = workflow.algorithm.cv
    feasible = constraint_violation.sum(dim=1) <= 0

    print(f"Fitness shape: {tuple(fitness.shape)}")
    print(f"Constraint violation shape: {tuple(constraint_violation.shape)}")
    print(f"Feasible solutions: {feasible.sum().item()}/{feasible.numel()}")
    print("Feasible objective values:")
    print(fitness[feasible])

UnifiedWorkflow preserves the (fitness, constraint_violation) output returned by constrained problems so that NSGA-II can apply constraint-aware selection.

MoRobtrol

MoRobtrol evaluates PyTorch policies on multiobjective control tasks using Brax (default) or Playground/MJX. For Playground (Python 3.11+):

pip install 'evomo[playground]'

Solve the MoSwimmer problem in MoRobtrol using the TensorMOEA/D algorithm:

import time

import torch
import torch.nn as nn
from evox.utils import ParamsAndVector
from evox.workflows import EvalMonitor, StdWorkflow

from evomo.algorithms import TensorMOEAD
from evomo.problems.neuroevolution import MoRobtrol


class SimpleMLP(nn.Module):
    def __init__(self):
        super(SimpleMLP, self).__init__()
        self.features = nn.Sequential(nn.Linear(8, 4), nn.Tanh(), nn.Linear(4, 2))

    def forward(self, x):
        return torch.tanh(self.features(x))


def setup_workflow(model, pop_size, max_episode_length, num_episodes, device):
    adapter = ParamsAndVector(dummy_model=model)
    model_params = dict(model.named_parameters())
    pop_center = adapter.to_vector(model_params)
    lower_bound = torch.full_like(pop_center, -5)
    upper_bound = torch.full_like(pop_center, 5)

    problem = MoRobtrol(
        policy=model,
        env_name="mo_swimmer",
        max_episode_length=max_episode_length,
        num_episodes=num_episodes,
        pop_size=pop_size,
        device=device,
        num_obj=2,
        observation_shape=8,
        obs_norm=torch.tensor([5.0, 1e-6, 1e6], device=device),
    )

    algorithm = TensorMOEAD(pop_size=pop_size, lb=lower_bound, ub=upper_bound, n_objs=2, device=device)
    monitor = EvalMonitor(device=device)

    workflow = StdWorkflow(
        algorithm=algorithm,
        problem=problem,
        monitor=monitor,
        opt_direction="max",
        solution_transform=adapter,
        device=device,
    )
    return workflow


def run_workflow(workflow, compiled=False, generations=10):
    workflow.init_step()
    step_function = torch.compile(workflow.step) if compiled else workflow.step
    for index in range(generations):
        print(f"In generation {index}:")
        t = time.time()
        step_function()
        print(f"\tFitness: {-workflow.algorithm.fit}.")
    print(f"\tTime elapsed: {time.time() - t: .4f}(s).")


if __name__ == "__main__":
    device = "cuda" if torch.cuda.is_available() else "cpu"

    model = SimpleMLP().to(device)
    workflow = setup_workflow(model, 12, 100, 2, device)
    run_workflow(workflow)

Publications on EvoMO

• Hao Li, Zhenyu Liang, and Ran Cheng, “GPU-accelerated evolutionary many-objective optimization using tensorized NSGA-III,” in IEEE Congress on Evolutionary Computation, 2025. [📄 Paper] | [🧐 Read More]
• Zhenyu Liang, Tao Jiang, Kebin Sun, and Ran Cheng, “GPU-accelerated evolutionary multiobjective optimization using tensorized RVEA,” in Proceedings of the Genetic and Evolutionary Computation Conference, 2024, pp. 566–575. [📄 Paper] | [🧐 Read More]

Community & Support

We welcome contributions and look forward to your feedback!

• Engage in discussions and share your experiences on GitHub Issues.
• Join our QQ group (ID: 297969717).

Citing EvoMO

If you use EvoMO in your research and want to cite it in your work, please use:

@article{evomo,
  title = {Bridging Evolutionary Multiobjective Optimization and {GPU} Acceleration via Tensorization},
  author = {Liang, Zhenyu and Li, Hao and Yu, Naiwei and Sun, Kebin and Cheng, Ran},
  journal = {IEEE Transactions on Evolutionary Computation},
  year = 2025,
  doi = {10.1109/TEVC.2025.3555605}
}

Contributors

Thanks to the following people who contributed to this project: Zhenyu2Liang, Nam-dada, LiHao-MS, XU-Boqing, sherry-zx, rotarygirl-zxy, BillHuang2001, ranchengcn.