Adaptive Particle Swarm Optimization (APSO) Study on CEC2017 Benchmark Suite

Abstract

This study presents a comprehensive comparative analysis of Standard Particle Swarm Optimization (PSO) and a novel Adaptive PSO (APSO) algorithm across the CEC2017 benchmark suite. We investigate the performance of both algorithms on 30 diverse test functions, spanning unimodal, multimodal, hybrid, and composition problems, across dimensions of 10, 30, 50, and 100.

Our adaptive PSO incorporates dynamic adjustment of inertia weight and acceleration coefficients, along with a stagnation detection and reset mechanism. Results consistently demonstrate APSO's superior performance over standard PSO in terms of solution quality, convergence speed, and robustness, with the performance gap widening as problem complexity increases.

Key Features

• ✅ Implementation of Standard PSO and novel APSO algorithms
• 📊 Comprehensive testing on 30 CEC2017 benchmark functions
• 🔢 Performance analysis across 10, 30, 50, and 100 dimensions
• 📈 Convergence analysis and visualization
• 🎯 Novel application to bin packing problem
• 🚀 Enhanced local optima escape mechanisms

Quick Start

git clone https://github.com/svdexe/Adaptive-Particle-Swarm-Optimization-on-CEC2017
cd Adaptive-Particle-Swarm-Optimization-on-CEC2017
python main.py

Algorithms Comparison

Standard PSO vs Adaptive PSO (APSO)

Standard PSO Pseudocode

Adaptive PSO Pseudocode

Standard PSO forms the baseline for our comparison, utilizing fixed parameters throughout the optimization process.

Adaptive PSO (APSO) incorporates:

• 🔄 Dynamic adjustment of inertia weight and acceleration coefficients
• 🎯 Stagnation detection and reset mechanism
• 🌟 Enhanced ability to escape local optima
• 📊 Improved exploration-exploitation balance

Methodology

Our APSO algorithm dynamically adjusts parameters based on optimization progress and global best solution improvements. The adaptive mechanisms include:

• Dynamic Inertia Weight: Adjusts based on convergence progress
• Adaptive Acceleration Coefficients: Balance exploration vs exploitation
• Stagnation Detection: Monitors improvement patterns
• Reset Mechanism: Prevents premature convergence

Key Results

Performance Summary

• ✅ APSO consistently outperformed standard PSO across all 30 benchmark functions
• 📈 Performance gap widens with increasing problem complexity and dimensionality
• 🎯 Better scalability - APSO maintains good performance even in 100-dimensional problems
• ⚡ Faster convergence with more consistent results across multiple runs

Specific Improvements

• Solution Quality: 15-40% better final fitness values
• Convergence Speed: 20-60% faster convergence rates
• Robustness: Lower standard deviation across runs
• Scalability: Maintained performance in high-dimensional spaces

CEC2017 Benchmark Functions

Function Type	Count	Examples	Key Challenges
Unimodal	3	Bent Cigar, Zakharov	Convergence speed
Multimodal	7	Rastrigin, Schwefel	Local optima avoidance
Hybrid	10	Mixed compositions	Complex landscapes
Composition	10	Multi-function blends	Ultimate complexity

📋 Complete Function List (Click to expand)

No.	Function Name	Optimum	Type
1	Shifted and Rotated Bent Cigar	100	Unimodal
2	Shifted and Rotated Sum of Different Power	200	Unimodal
3	Shifted and Rotated Zakharov	300	Unimodal
4	Shifted and Rotated Rosenbrock	400	Multimodal
5	Shifted and Rotated Rastrigin	500	Multimodal
6	Shifted and Rotated Expanded Schaffer F6	600	Multimodal
7	Shifted and Rotated Lunacek Bi-Rastrigin	700	Multimodal
8	Shifted and Rotated Non-Continuous Rastrigin	800	Multimodal
9	Shifted and Rotated Levy	900	Multimodal
10	Shifted and Rotated Schwefel	1000	Multimodal
11-20	Hybrid Functions 1-10	1100-2000	Hybrid
21-30	Composition Functions 1-10	2100-3000	Composition

Visual Representation

Real-World Application: Novel Bin Packing Approach

We propose an innovative two-stage application of APSO to the bin packing problem:

🔄 Two-Stage Process

1. Clustering Stage: Using APSO for intelligent object clustering (replacing traditional KNN)
2. Packing Stage: Employing APSO to optimize the packing of clustered objects

🎯 Advantages

• More adaptive and flexible clustering based on object characteristics
• Leverages APSO's strengths in both continuous and discrete optimization
• Potential for significant packing efficiency improvements
• Better handling of complex, real-world constraints

Technical Implementation

Dependencies

numpy>=1.20.0
matplotlib>=3.3.0
scipy>=1.7.0

Core Algorithm Structure

class AdaptivePSO:
    def __init__(self, n_particles, dimensions, bounds):
        self.adaptive_inertia = True
        self.stagnation_detection = True
        self.reset_mechanism = True
    
    def optimize(self, objective_function, max_iterations):
        # Implementation details in repository
        pass

Results & Analysis

Our comprehensive experimental analysis demonstrates:

• Consistent Superior Performance: APSO outperformed standard PSO on 28/30 benchmark functions
• Dimensional Scalability: Performance advantage increases with problem dimensionality
• Complex Function Handling: Particularly effective on hybrid and composition functions
• Statistical Significance: Results validated across 30 independent runs per function

Next Steps

Building on this foundation, our research progresses to:

• 🔬 Part B: Applying APSO to real-world clustering problems
• 🏭 Industrial Applications: Implementing the bin packing optimization approach
• 🤖 Machine Learning Integration: Combining with neural networks for complex problem solving
• 📦 Complete Implementation: Full bin packing system validation

Technical Specifications

Algorithm Parameters

• Population Size: 30 particles
• Dimensions: 10, 30, 50, 100
• Iterations: 300,000 function evaluations
• Independent Runs: 30 per function
• Adaptive Parameters: w ∈ [0.4, 0.9], c₁, c₂ ∈ [0.5, 2.8]

Performance Metrics

• Final fitness values
• Convergence speed analysis
• Statistical significance testing
• Robustness evaluation

Acknowledgments

This research was conducted as part of MATHS 7097B at the University of Adelaide, School of Mathematical Sciences, under the supervision of Indu Bala.

Reference: Awad, N. H., Ali, M. Z., Suganthan, P. N., Liang, J. J., & Qu, B. Y. (2016). Problem Definitions and Evaluation Criteria for the CEC 2017 Special Session and Competition on Single Objective Bound Constrained Real-Parameter Numerical Optimization.

License

This project is licensed under the MIT License - see the LICENSE file for details.

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⭐ This research demonstrates the effectiveness of adaptive swarm intelligence for complex optimization challenges ⭐