pyHMS

pyHMS is a Python implementation of Hierarchic Memetic Strategy (HMS).

The Hierarchic Memetic Strategy is a stochastic global optimizer designed to tackle highly multimodal problems. It is a composite global optimization strategy consisting of a multi-population evolutionary strategy and some auxiliary methods. The HMS makes use of a dynamically-evolving data structure that provides an organization among the component populations. It is a tree with a fixed maximal height and variable internal node degree. Each component population is governed by a particular optimization engine. This package provides a simple python implementation.

Installation

Installation can be done using pypi:

pip install pyhms

It's also possible to install the current main branch:

pip install git+https://github.com/agh-a2s/pyhms.git@main

Quick Start

from pyhms import minimize
import numpy as np

fun = lambda x: sum(x**2)
bounds = np.array([(-20, 20), (-20, 20)])
solution = minimize(
    fun=fun,
    bounds=bounds,
    maxfun=10000,
    log_level="debug",
    seed=42
)

pyhms provides an interface similar to scipy.optimize.minimize. This is the simplest way to run HMS with default parameters.

import numpy as np
from pyhms import (
    EALevelConfig,
    hms,
    get_NBC_sprout,
    DontStop,
    MetaepochLimit,
    SEA,
    Problem,
)

square_bounds = np.array([(-20, 20), (-20, 20)])
square_problem = Problem(lambda x: sum(x**2), maximize=False, bounds=square_bounds)

config = [
    EALevelConfig(
        ea_class=SEA,
        generations=2,
        problem=square_problem,
        pop_size=20,
        mutation_std=1.0,
        lsc=DontStop(),
    ),
    EALevelConfig(
        ea_class=SEA,
        generations=4,
        problem=square_problem,
        pop_size=10,
        mutation_std=0.25,
        sample_std_dev=1.0,
        lsc=DontStop(),
    ),
]
global_stop_condition = MetaepochLimit(limit=10)
sprout_condition = get_NBC_sprout(level_limit=4)
hms_tree = hms(config, global_stop_condition, sprout_condition)
print(hms_tree.summary())

Relevant literature

• J. Sawicki, M. Łoś, M. Smołka, R. Schaefer. Understanding measure-driven algorithms solving irreversibly ill-conditioned problems. Natural Computing 21:289-315, 2022. doi: 10.1007/s11047-020-09836-w
• J. Sawicki, M. Łoś, M. Smołka, J. Alvarez-Aramberri. Using Covariance Matrix Adaptation Evolutionary Strategy to boost the search accuracy in hierarchic memetic computations. Journal of computational science, 34, 48-54, 2019. doi: 10.1016/j.jocs.2019.04.005