Solving Portfolio Optimization Problems Using MOEA/D and Lévy Flight

Python version and libraries

• Python 3.7.4 are used in the experiments.
• Check alias for python3 and edit .sh files. (If the alias is python3, change python to python3. A better way is to use pyenv and set pyenv global 3.7.4.)
• Following libraries are required,
  • numpy
  • scipy
  • pandas
  • matplotlib
  • seaborn

How to use

1. Open terminal
2. Run run.sh
3. Program will create a folder named tmp and save simulation results in this folder
4. Copy folder process_script into tmp
5. Enter process_script
6. Run file run.sh in process_script folder
7. Program will create images, num_res and report folders, containing images, metrics and statistical issues, respectively.

Experimental data

The data is included in file DATA.tar.gz in this repository. After unzip, there are three folders namely, experimental_results, discussion and parameter_tuning_results, for the data (numerical values and graphs) of experiments, discussion and parameter tuning, respectively.

Notice

• This program does not contain statistical test. Please use R or other statistical software to implement Wilcoxon Rank-Sum Test.
• You may get a slight difference in numerical results, for machine epsilon issues. But the statistical conclusion should not change.
• The autoscripts can only run for all algorithms on all datasets. If you want to get results on single dataset or single algorithm, please edit and run run_xxx.py files. You may also edit processing scripts. However, to compute hypervolume, you may need get results for all algorithms on one dataset at first.
• Please feel free to contact at heyf95318@yahoo.co.jp or s1820747@s.tsukuba.ac.jp if you have any problem about the code.

Plotting sample

File tree

.
├── dat ........................................ Folder for benchmark
│   ├── port1.txt .............................. Hangseng
│   ├── port2.txt .............................. DAX 100
│   ├── port3.txt .............................. FTSE 100
│   ├── port4.txt .............................. S&P 100
│   ├── port5.txt .............................. Nikkei
│   ├── portef1.txt ............................ Hangseng Pareto Front
│   ├── portef2.txt ............................ DAX 100 Pareto Front
│   ├── portef3.txt ............................ FTSE 100 Pareto Front
│   ├── portef4.txt ............................ S&P 100 Pareto Front
│   └── portef5.txt ............................ Nikkei Pareto Front
├── DATA.tar.gz ................................ Raw data for experimental results and discussion
├── dec_reprod.py .............................. Mutation for MOEA/D
├── domina.py .................................. Tools for NSGA-II
├── dom_reprod.py .............................. Mutation for NSGA-II
├── LICENSE
├── metric.py .................................. Evaluation metrics
├── moead.py ................................... NBI-MOEA/D framework
├── nbi_decomp.py .............................. NBI-style Tchebycheff
├── nsga2.py ................................... NSGA-II framework
├── plotting_sample.svg ........................ Sample plot for experimental results
├── prob.py .................................... Mean-Variance model
├── process_script ............................. Folder for post processing
│   ├── compute_metric.py ...................... Metrics calculation
│   ├── dat .................................... Folder for Pareto Front
│   │   ├── portef1.txt ........................ Hangseng Pareto Front
│   │   ├── portef2.txt ........................ DAX 100 Pareto Front
│   │   ├── portef3.txt ........................ FTSE 100 Pareto Front
│   │   ├── portef4.txt ........................ S&P 100 Pareto Front
│   │   └── portef5.txt ........................ Nikkei Pareto Front
│   ├── get_best.py ............................ Retrieve runs with best IGD
│   ├── metric.py .............................. Evaluation metrics
│   ├── plot.py ................................ Plotting scripts
│   ├── run.sh ................................. Run file to do post processing
│   └── stat.py ................................ Statistical processing
├── README.md .................................. Instruction
├── repair_tool.py ............................. Constraint handling technique
├── run_benchmark.sh ........................... Run file to test on one benchmark
├── run_dem.py ................................. Run MOEA/D-DEM
├── run_de.py .................................. Run MOEA/D-DE
├── run_ga.py .................................. Run MOEA/D-GA
├── run_lvxm.py ................................ Run MOEA/D-Levy
├── run_lvx.py ................................. Run LEVY
├── run_norm.py ................................ Run NORM
├── run_nsga2.py ............................... Run NSGA-II
├── run.sh ..................................... Run file to do whole experiments
└── run_unif.py ................................ Run UNIF

Figures of Results (Unconstrained)

Hangseng

• Experiment I
  • Convergence Graph
  • Population Graph
  • Scaled population Graph
• Experiment II
  • Convergence Graph
  • Population Graph
  • Scaled population Graph

DAX 100

• Experiment I
  • Convergence Graph
  • Population Graph
  • Scaled population Graph
• Experiment II
  • Convergence Graph
  • Population Graph
  • Scaled population Graph

FTSE 100

• Experiment I
  • Convergence Graph
  • Population Graph
  • Scaled population Graph
• Experiment II
  • Convergence Graph
  • Population Graph
  • Scaled population Graph

S&P 100

• Experiment I
  • Convergence Graph
  • Population Graph
  • Scaled population Graph
• Experiment II
  • Convergence Graph
  • Population Graph
  • Scaled population Graph

Nikkei

• Experiment I
  • Convergence Graph
  • Population Graph
  • Scaled population Graph
• Experiment II
  • Convergence Graph
  • Population Graph
  • Scaled population Graph