Optimization-Techniques

Description

This collection of scripts was created for the scope of an assignment in a Optimization-Techniques cource of the Aristotle University of Thessaloniki during the 2019-20 academic year. The main purpose of these projects is to give some intuition about how some famous multivariate minimization algorithms work.

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Algorithms

Part 1: Uncostrained Single Variable Optimization

  • Bisection Method
  • Golden Section Method
  • Fibonacci Method
  • Bisection Derivative Method

Part 2: Uncostrained Multivariate Optimization

  • Steepest Descent Method
  • Newton's Method
  • Levenberg-Marquardt Method
  • Conjugate Gradients Method
  • Quasi Newton Method

Part 3: Costrained Multivariate Optimization

  • Barrier Method
  • Penalty Method

Project: Genetic Algorithm Implementation (Constrained Minimization Problem)

Minimize Traffic of a road network, given constant or variable input vehicle flow. Genetic Operations implemented:

  • Selection
  • Crossover
  • Mutation
  • Elitism

Setup

The provided code was created using MATLAB R2019a, however older MATLAB versions should work fine. All of the .m scripts provided, are commented for higher readability and maintenance.