Nature-inspired Optimization Algorithms: A Comparative Study

nature_inspired_optimization_algorithms_comperative/
│
├── requirements.txt                    # Project dependencies
├── main_simulation.py                  # Entry point for the 1530 statistical runs
├── config.py                           # Global configurations (hyperparameters, FEs, bounds)
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├── src/                                # Source code directory
│   ├── __init__.py
│   │
│   ├── algorithms/                     # Meta-heuristic algorithm implementations
│   │   ├── __init__.py
│   │   ├── base_optimizer.py           # Abstract base class (OOP inheritance)
│   │   ├── pso.py                      # Particle Swarm Optimization
│   │   ├── de.py                       # Differential Evolution
│   │   ├── gwo.py                      # Grey Wolf Optimizer
│   │   ├── abc.py                      # Artificial Bee Colony
│   │   └── es.py                       # Evolution Strategies
│   │
│   ├── benchmarks/                     # Mathematical test environments
│   │   ├── __init__.py
│   │   └── functions.py                # Sphere, Rastrigin, Rosenbrock definitions
│   │
│   └── utils/                          # Helper modules
│       ├── __init__.py
│       ├── logger.py                   # I/O operations (JSON/CSV data logging)
│       ├── statistics_engine.py        # Binom Test, Mean, Median, Std calculations
│       └── visualizer.py               # Convergence curves, boxplots, and 2D animations
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│
└── outputs/                            # Generated artifacts
    ├── figures/                        # Static convergence and boxplot images
    ├── statistics/                     # Output of 1530 runs
    └── animations/                     # 3D surface GIFs/MP4s from showcase runs

This repository contains a comprehensive comparative analysis of nature-inspired meta-heuristic optimization algorithms. The study evaluates performance, scalability, and statistical reliability across multi-dimensional benchmark functions.

1. Project Overview

The core objective is to rationalize the behavior of stochastic optimizers when facing the Curse of Dimensionality ($D \in {10, 20, 30}$). The framework integrates automated simulation pipelines with rigorous statistical validation.

Supported Algorithms

• ABC: Artificial Bee Colony
• DE: Differential Evolution
• ES: Evolution Strategies
• GWO: Grey Wolf Optimizer
• PSO: Particle Swarm Optimization

Benchmark Functions

• Sphere: Unimodal, smooth convex function.
• Ackley: Multimodal, characterized by a large number of local minima.
• Zakharov: Plate-shaped, non-separable function with a flat surface.

2. Methodology & Optimization Logic

Success Criteria & Early Stopping

To ensure computational efficiency, an Early Stopping mechanism is implemented. A run is considered a "Success" if the fitness value $f(x)$ reaches the success threshold $\epsilon$: $$f(x) < \epsilon, \quad \text{where } \epsilon = 10^{-8}$$

Success Rate (SR) Calculation

The Success Rate represents the reliability of the algorithm over $N = 30$ independent runs: $$SR = \left( \frac{\sum_{i=1}^{N} S_i}{N} \right) \times 100$$ where $S_i \in {0, 1}$ denotes the success status of the $i$-th run.

3. Statistical Framework

Two-sided Binomial Test

To prove that results are not due to random chance, a Two-sided Binomial Test is applied to the Success Rate (SR). We test the deviation from a random baseline ($p_{null} = 0.5$):

• Null Hypothesis ($H_0$): The algorithm performs no better/worse than random guessing ($p = 0.5$).
• Alternative Hypothesis ($H_1$): The performance is significantly different from random ($p \neq 0.5$).

The Probability Mass Function (PMF) used for the exact test: $$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $n=30$ and $k$ is the number of successes. A result is considered statistically significant if the $p\text{-value} < 0.05$.

• Reliability Index: Color-coded p-values indicating the deterministic nature of success/failure. ├── algorithms/ # Meta-heuristic implementations ├── benchmarks/ # Mathematical test functions └── utils/ # Statistics engine & visualizer