Introduction¶

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

Current version: 3.0.3
Total algorithms: 233 - 206 official (originals, hybrids, and variants) - 27 custom-developed by our developers

Important: Different versions of MEALPY introduce different ways to define and pass hyperparameters. Please check your version carefully:

< 1.0.5
1.1.0 - 1.2.2
2.0.0 - 2.1.2
2.2.0
2.3.0
2.4.0 - 2.4.2: Supports discrete problems
2.5.1 - 2.5.4: Define once, solve multiple problems
>= 3.0.0: Fully object-oriented design

Goals of this framework:

To share knowledge of the meta-heuristic field with everyone at no cost.
To help researchers in all fields access optimization algorithms as quickly as possible.
To implement both classical and state-of-the-art meta-heuristics, covering the entire history of meta-heuristics.

What MEALPY offers:

Analyze the parameters of algorithms.
Perform qualitative and quantitative analyses of algorithms.
Analyze the rate of convergence of algorithms.
Test and analyze the scalability and robustness of algorithms.

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

And please give us credits if you use this library, check some of my previous 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 process of finding the best solution from a set of feasible solutions. In real-world problems, objective functions can be nonlinear, noisy, non-differentiable, or highly constrained—making traditional gradient-based methods ineffective.

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

A general optimization problem can be formulated as:

Where x is the vector of decision variables (real, integer, or categorical), f(x) are the objective functions, and g(x), h(x) are constraints.

Classical methods like Newton-Raphson work well for smooth problems, but fail on complex landscapes. Meta-heuristics provide a flexible, robust way to solve challenging problems when exact solutions are impractical or impossible.

Meta-heuristic Algorithms¶

Meta-heuristics are high-level search strategies that balance exploration (global search) and exploitation (local refinement). They are inspired by natural processes like evolution, swarm behavior, physics, and chemistry.

Key features: - Use randomness to escape local optima - Perform well on complex, multimodal problems - Require minimal assumptions about the problem

Meta-heuristics can be: - Population-based: e.g., Genetic Algorithm, PSO - Trajectory-based: e.g., Simulated Annealing

../../_images/history_metaheuristics.png

Despite their stochastic nature, well-designed meta-heuristics often produce high-quality solutions consistently. MEALPY offers 200+ implementations of such algorithms, from classical to cutting-edge.