Introduction

MEALPY (MEta-heuristic ALgorithms in PYthon) is the most comprehensive Python library for cutting-edge, nature-inspired meta-heuristic algorithms. It is officially released under the MIT license.

Note

Current Project Status

• Current version: 3.0.3

• Total algorithms: 233

  • 206 official implementations (originals, hybrids, and variants)

  • 27 custom-developed algorithms by our core development team

Check out all historical updates on the PyPI Releases Page.

Important

Version Compatibility Warning

Different versions of MEALPY introduce significant architectural changes regarding how hyperparameters are defined and passed. Please verify your installed version and adhere to its specific paradigm:

• < 1.0.5: Legacy implementation.

• 1.1.0 - 1.2.2: Stable legacy structures.

• 2.0.0 - 2.1.2: Core framework refactoring.

• 2.2.0: Enhanced parameter mapping.

• 2.3.0: Addition of advanced utility features.

• 2.4.0 - 2.4.2: Native support for discrete problems introduced.

• 2.5.1 - 2.5.4: “Define once, solve multiple problems” architecture.

• >= 3.0.0: Fully Object-Oriented Design (Current Standard).

Goals of this Framework

• To share comprehensive knowledge of the meta-heuristic field with the global community at no cost.

• To help researchers across all domains access robust optimization algorithms as quickly as possible.

• To implement both classical and state-of-the-art meta-heuristics, effectively preserving the entire history of the field.

What MEALPY Offers

• Detailed analysis of algorithm hyperparameters.

• Robust frameworks for qualitative and quantitative performance analysis.

• Convergence rate evaluation across different algorithmic strategies.

• Scalability and robustness testing for varying problem complexities.

Hint

Contributing & Citations

Want to request a new algorithm? Open an Issue ticket or build your own using MEALPY’s modular components.

If you utilize MEALPY in your academic or professional research, please credit our work by citing our main paper:

@article{van2023mealpy,
   title={MEALPY: An open-source library for latest meta-heuristic algorithms in Python},
   author={Van Thieu, Nguyen and Mirjalili, Seyedali},
   journal={Journal of Systems Architecture},
   year={2023},
   publisher={Elsevier},
   doi={10.1016/j.sysarc.2023.102871}
}

Optimization

Optimization is the mathematical process of finding the absolute best solution from a set of feasible solutions. In real-world applications, objective functions are often nonlinear, noisy, non-differentiable, or highly constrained—making traditional gradient-based methods ineffective.

Meta-heuristic algorithms offer a powerful alternative. They do not require analytical gradient information and can seamlessly handle a wide array of optimization types: continuous, discrete, constrained, and multi-objective.

A general continuous optimization problem can be formulated as follows:

Where: * \(x\) is the vector of decision variables (real, integer, or categorical). * \(f(x)\) represents the objective functions to be minimized or maximized. * \(g(x)\) and \(h(x)\) represent the inequality and equality constraints, respectively.

While classical methods (like Newton-Raphson) work exceptionally well for smooth, convex problems, they fail on complex fitness landscapes. Meta-heuristics provide a flexible, robust mechanism to solve challenging problems when deriving exact mathematical solutions is impractical or impossible.

Meta-heuristic Algorithms

Meta-heuristics are high-level algorithmic search strategies designed to strike a delicate balance between exploration (global search across the solution space) and exploitation (local refinement around promising areas). They draw heavy inspiration from natural processes such as evolution, swarm behavior, physics, and chemical reactions.

Note

Key Features of Meta-heuristics:

• Utilize stochastic (random) elements to escape local optima traps.

• Perform exceptionally well on complex, multimodal, and non-differentiable problems.

• Treat the objective function as a “black box,” requiring minimal to no assumptions about the underlying mathematical problem.

Broadly, meta-heuristics can be categorized into two structural paradigms:

1. Population-based Methods: Evolve a set of solutions simultaneously, sharing information across the group (e.g., Genetic Algorithm, Particle Swarm Optimization).

2. Trajectory-based Methods: Trace a single solution path through the search space over time (e.g., Simulated Annealing).

Despite their inherent stochastic nature, well-designed meta-heuristics consistently converge to high-quality solutions. MEALPY provides over 200 standardized implementations of these algorithms, ranging from foundational classical models to the absolute cutting edge of current research.