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HjaltiThrastarson / Application-of-Pareto-Front-to-Multi-Objective-Genetic-Optimization

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Application of Pareto Front to Multi-Objective Genetic Optimization

Getting Started

  1. Install poetry
    • OSX/Linux/WSL 
      curl -sSL https://install.python-poetry.org | python3 -
    • Windows/Powershell 
      (Invoke-WebRequest -Uri https://install.python-poetry.org -UseBasicParsing).Content | python -
  2. Add poetry to your path
    • OSX/Linux/WSL (add e.g. to .bashrc to make it permanent) 
      export PATH="$HOME/.local/bin:$PATH"
    • Windows/Powershell (add to your $profile to make permanent) or via the GUI 
      $env:Path += ';%APPDATA%\Python\Scripts'
  3. Checkout repo 
    git clone https://github.com/HjaltiThrastarson/Application-of-Pareto-Front-to-Multi-Objective-Genetic-Optimization ofme
cd ofme
  4. Create venv from lockfile and enter shell 
    poetry config virtualenvs.in-project true
poetry install
  5. If you now open the folder in Visual Studio Code it should tell you that no Python Interpreter has been selected and prompt you to choose one. The recommended one should be .venv which is the just installed poetry environment. If not use Ctrl+Shift+P and change Python: Select Interpreter to the .venv in the current directory.
  6. Some poetry commands
    • Add new packages/dependencies 
      poetry add <pkgname>
    • Enter the python venv 
      poetry shell
    • Update all packages 
      poetry update
  7. Running Tests 
    poetry run pytest --cov --black

IDEAS

  1. Implement micro genetic algorithm
  2. Use Chankong and Haimes test func for evaluation
  3. The range is [-20, 20], idea is to map small ranges in that range to binary numbers, for example with 1 bit we would have 0 as -20 and 1 as 20
  4. Shift gray codes and restart to circumvent hamming wall. See Procedures & Encoding
  5. Sort by fitness, if lower than threshold search area.

First implement a mGA

mga

Notes on [3]

  1. "Multiobjective optimization constraints are often handled by penalties that increase the objective function values in propoertion to the constraint violation."
  2. Two approaches:
    1. A priori: Define weights before execution on functions to obtain utility function. Result it a point
    2. A posteriori: Define partial ordering on objective functions, usually Pareto order. Result is minimal set fulfilling the order (e.g. Pareto front)
  3. Pareto dominance: y1 pareto dominates y2 if the first vector is not wores in each of the objectives and better in at least one objective than the second vector.
  4. The solution of a Linear Scalarization Problem is on the Pareto front, no matter which weigths are chosen.

Documentation

Write down any decisions you make, any problems you face and any interesting insights you come across.

Literature

  1. Multi-Objective Optimization (Wiki)
  2. Pareto-Efficiency (Wiki)
  3. A tutorial on multiobjective optimization: fundamentals and evolutionary methods
  4. Multi-objective Optimisation Using Evolutionary Algorithms: An Introduction
  5. Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation
  6. The weighted sum method for multi-objective optimization: new insights

Frameworks/Libraries/Resources