Graph Optimization and Learning by Evolutionary Methods

GOLEM is an open-source AI framework for optimization and learning of structured graph-based models with meta-heuristic methods. It is centered around 2 ideas:

1. The potential of meta-heuristic methods in complex problem spaces.

The focus on meta-heuristics allows approaching the kinds of problems where gradient-based learning methods (notably, neural networks) can't be easily applied, like optimization problems with multiple conflicting objectives or having a combinatorial nature.

2. The importance of structured models in multiple problem domains.

Graph-based learning enables solutions in the form of structured and hybrid probabilistic models, not to mention that a wide range of domain-specific problems have a natural formulation in the form of graphs.

Together this constitutes an approach to AI that potentially leads to structured, intuitive, interpretable methods and solutions for a wide range of tasks.

Core Features

• Structured models with joint optimization of graph structure and properties (node attributes).
• Metaheuristic methods (mainly evolutionary) applicable to any task with a well-defined objective.
• Multi-objective optimization that can take into account both quality and complexity.
• Constrained optimization with support for arbitrary domain-specific constraints.
• Extensible to new domains.
• Interpretable thanks to meta-heuristics, structured models, and visualisation tools.
• Reproducible thanks to rich optimization history and model serialization.

Applications

GOLEM is potentially applicable to any optimization problem structures:

• that can be represented as directed graphs;
• that have some clearly defined fitness function on them.

Graph models can represent fixed structures (e.g. physical models such as truss structures) or functional models that define a data-flow or inference process (e.g. bayesian networks that can be fitted and queried).

Examples of GOLEM applications:

• Automatic Machine Learning (AutoML) with optimal ML pipelines search in FEDOT framework
• Bayesian network structure search in BAMT framework
• Differential equation discovery for physical models in EPDE framework
• Geometric design of physical objects in GEFEST framework
• Neural architecture search

As GOLEM is a general-purpose framework, it's easy to imagine potential applications, for example, finite state automata search for robotics control or molecular graph learning for drug discovery, and more.

Installation

GOLEM can be installed with pip:

$ pip install thegolem

Quick Start Example

Following example demonstrates graph search using reference graph & edit distance metric. Optimizer is set up with a minimal set of parameters and simple single-point mutations. For more details see examples simple_run.py, graph_search.py and tree_search.py in directory examples/synthetic_graph_evolution.

def run_graph_search(size=16, timeout=8):
    # Generate target graph sought by optimizer using edit distance objective
    node_types = ('a', 'b')  # Available node types that can appear in graphs
    target_graph = generate_labeled_graph('tree', size, node_types)
    objective = Objective(partial(tree_edit_dist, target_graph))
    initial_population = [generate_labeled_graph('tree', 5, node_types) for _ in range(10)]

    # Setup optimization parameters
    requirements = GraphRequirements(timeout=timedelta(minutes=timeout))
    gen_params = GraphGenerationParams(adapter=BaseNetworkxAdapter(), available_node_types=node_types)
    algo_params = GPAlgorithmParameters(pop_size=30)

    # Build and run the optimizer
    optimiser = EvoGraphOptimizer(objective, initial_population, requirements, gen_params, algo_params)
    found_graphs = optimiser.optimise(objective)

    # Visualize results
    found_graph = gen_params.adapter.restore(found_graphs[0])  # Transform back to NetworkX graph
    draw_graphs_subplots(target_graph, found_graph, titles=['Target Graph', 'Found Graph'])
    optimiser.history.show.fitness_line()
    return found_graph

Tracing the lineage of the found_graph reveals how genetic operators (mutations, crossovers, etc.) are applied to a random graph one after another, eventually leading to the target graph:

One can also notice that despite the fact that the edit distance generally decreases along the genealogical path, the optimizer sometimes sacrifices local fitness gain of some graphs in order to achieve diversity and thus obtain the best possible solution at the end.

Project Structure

The repository includes the following packages and directories:

• Package core contains the main classes and scripts.
• Package core.adapter is responsible for transformation between domain graphs and internal graph representation used by optimisers.
• Package core.dag contains classes and algorithms for representation and processing of graphs.
• Package core.optimisers contains graph optimisers and all related classes (like those representing fitness, individuals, populations, etc.), including optimization history.
• Package core.optimisers.genetic contains genetic (also called evolutionary) graph optimiser and operators (mutation, selection, and so on).
• Package core.utilities contains utilities and data structures used by other modules.
• Package serializers contains class Serializer with required facilities, and is responsible for serialization of project classes (graphs, optimization history, and everything related).
• Package visualisation contains classes that allow to visualise optimization history, graphs, and certain plots useful for analysis.
• Package examples includes several use-cases where you can start to discover how the framework works.
• All unit and integration tests are contained in the test directory.
• The sources of the documentation are in the docs directory.

Current R&D and future plans

Any contribution is welcome. Our R&D team is open for cooperation with other scientific teams as well as with industrial partners.

Contribution Guide

• The contribution guide is available in the repository.

Acknowledgments

We acknowledge the contributors for their important impact and the participants of the numerous scientific conferences and workshops for their valuable advice and suggestions.

Supported by

The study is supported by the Research Center Strong Artificial Intelligence in Industry of ITMO University as part of the plan of the center's program: Development and testing of an experimental prototype of the library of strong AI algorithms in terms of basic algorithms of automatic ML for structural training of composite AI models, including automation of feature selection

Contacts

• Telegram channel for solving problems and answering questions about FEDOT
• Natural System Simulation Team
• Nikolay Nikitin, AutoML Lead (nnikitin@itmo.ru)
• Newsfeed
• Youtube channel

Citation

If you use our project in your work or research, we would appreciate citations.

@article{nikitin2021automated,

title = {Automated evolutionary approach for the design of composite machine learning pipelines}, author = {Nikolay O. Nikitin and Pavel Vychuzhanin and Mikhail Sarafanov and Iana S. Polonskaia and Ilia Revin and Irina V. Barabanova and Gleb Maximov and Anna V. Kalyuzhnaya and Alexander Boukhanovsky}, journal = {Future Generation Computer Systems}, year = {2021}, issn = {0167-739X}, doi = {https://doi.org/10.1016/j.future.2021.08.022}}

Papers that describe applications of GOLEM:

There are various cases solved with GOLEM's algorithms:

• Algorithms for time series forecasting pipeline design: Sarafanov M., Pokrovskii V., Nikitin N. O. Evolutionary Automated Machine Learning for Multi-Scale Decomposition and Forecasting of Sensor Time Series //2022 IEEE Congress on Evolutionary Computation (CEC). – IEEE, 2022. – С. 01-08.
• Algorithms for acoustic equation discovery: Hvatov A. Data-Driven Approach for the Floquet Propagator Inverse Problem Solution //ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). – IEEE, 2022. – С. 3813-3817.
• Algorithms for PDE discovery: Maslyaev M., Hvatov A. Solver-Based Fitness Function for the Data-Driven Evolutionary Discovery of Partial Differential Equations //2022 IEEE Congress on Evolutionary Computation (CEC). – IEEE, 2022. – С. 1-8.
• Algorithms for structural learning of Bayesian Networks: Deeva I., Kalyuzhnaya A. V., Alexander V. Boukhanovsky Adaptive Learning Algorithm for Bayesian Networks Based on Kernel Mixtures Distributions//International Journal of Artificial Intelligence. – 2023. - Т.21. - №. 1. - С. 90.