Implement PSO, DE, and JADE to Solve the Ackley Function

( I ) Introduction

• Programming language: C++
• Metaheuristic algorithms: PSO, DE, and JADE (adaptive DE)
• Benchmark function: Ackley function (dim = 2, 10, 30)
• Visualization: gnuplot
• Supports configurable parameters: dimension, population size, etc.

( II ) Main Functionality

Particle Swarm Optimization (PSO)

• void RunALG(int dim, int pop_size)
  Runs PSO

• void Init()
  Initializes pop_size solutions of dim dimensions and sets up personal_best & global_best

• void Transition()
  Updates velocity and position of particles

• void Evaluation()
  Calculates fitness values of new solutions

• void Determination()
  Updates personal_best and global_best

Differential Evolution (DE)

• void RunALG(const int& dim, const int& pop_size, const double& CR, const double& F)
  Runs DE

• void Init()
  Initializes dim * pop_size candidate solutions

• void Mutation()
  Applies the "DE/rand/1" mutation strategy to generate donor vectors

• void Crossover()
  Performs crossover between original and donor vectors to create trial vectors

• void Evaluation()
  Calculates fitness of trial vectors

• void Determination()
  Determines whether original or trial vector survives and updates best_fit

Adaptive Differential Evolution with External Archive (JADE)

• void RunALG(const int& dim, const int& pop_size, const double& CR, const double& F, const double& c, const double& p)
  Runs JADE

• void Init()
  Initializes dim * pop_size candidate solutions

• void Mutation()
  Applies the "DE/current-to-pbest/1" strategy to generate donor vectors

• void Crossover()
  Performs crossover between original and donor vectors to create trial vectors

• void Evaluation()
  Calculates fitness of trial vectors

• void Determination()
  Selects the better individual and updates best_fit

• void ParaAdaptation()
  Adapts control parameters mCR and mF

( III ) Input

Command-line arguments:

• dim: Problem dimensionality (2 / 10 / 30)
• pop_size: Population size (e.g., 100)
• For DE & JADE only:
  • CR: Crossover rate (default = 0.9 for DE, 0.5 for JADE)
  • F: Donor rate / scaling factor (default = 0.5 for DE, 0.5 for JADE)
• For JADE only:
  • c: Adaptation rate (range = 0.05 ~ 0.2)
  • p: Top p% used to select x_pbest (range = 0.05 ~ 0.2)

( IV ) Output

PSO

• fitness_PSO_dim(2 or 10)_pop100.txt
• plot_PSO.plt
• result_Ackley_PSO_dim(2 or 10)_pop100.png

DE

• fitness_DE_dim(2 or 10)_pop100_CR9_F5.txt
  (CR9 = CR 0.9, F5 = F 0.5)
• plot_DE.plt
• result_Ackley_DE_dim(2 or 10)_pop100_CR9_F5.png

JADE

• fitness_JADE_dim(2 or 10)_pop100_c20_p20.txt
  (c20 = c 0.2, p20 = p 0.2)
• plot_JADE.plt
• result_Ackley_JADE_dim(2 or 10)_pop100_c20_p20.png

( V ) How to Compile, Run and Result Visualization

Compile

Visual Studio

1. Open the project ackleyfunction.sln
2. Press Ctrl + F5 to build

VSCode

1. Open PowerShell or Windows CMD
2. Navigate to the correct folder
3. Compile with:

g++ main.cpp DE.cpp JADE.cpp PSO.cpp Ackley.cpp -o ackleyfunction.exe

Run

1. Open PowerShell or Windows CMD
2. Navigate to the correct folder
3. Run the program with:

.\ackleyfunction.exe 2 100 0.9 0.5

You will be prompted:

Choose Algorithm ( PSO / DE / JADE )

If you select JADE, you will be further prompted:

Please enter the value of adaptation rate c =
Please enter the value of the top % pop chosen for pbest =

Result Visualization

1. Install gnuplot
2. Open CMD or PowerShell
3. Run with:

gnuplot plot_PSO.plt
gnuplot plot_DE.plt
gnuplot plot_JADE.plt

Output PNGs will appear in the working directory

( VI ) File Structure

ackleyfunction/
│
├── main.cpp
├── PSO.cpp / PSO.h
├── DE.cpp / DE.h
├── JADE.cpp / JADE.h
├── Ackley.cpp / Ackley.h
│
├── results/            ← output files (.txt, .png)
├── docs/               ← algorithm notes (.md)
└── README.md           ← this file

( VII ) Experimental Results

Convergence Comparison (dim = 2, pop = 100)

Convergence Comparison (dim = 30, pop = 100)

( VIII ) Observations

• JADE converges faster and avoids premature convergence in high-dimensional scenarios
• Adaptive control of parameters (CR, F) significantly enhances JADE's performance
• For more insights, refer to docs/JADE_Algo_Note.md

( IX ) Key Features

• Object-oriented design in C++
• DE strategy: DE/rand/1/bin
• JADE strategy: DE/current-to-pbest/1
• Adaptive learning of control parameters (mCR, mF)
• Command-line parameter tuning
• Automated result visualization with gnuplot

( X ) Skills Demonstrated

• Modular C++ programming
• Metaheuristic algorithm implementation
• Benchmarking and convergence analysis
• Parameter sensitivity study
• Visualization scripting with gnuplot

( XI ) Related Documents

• JADE_Algo_Note.md