Optimisation of the Global Calculator using Monte Carlo Markov Chain and Genetic Algorithms

Page structure

This page contains documentation of all the methods used, two usage examples and the code’s license and installation requirements.

To install Jupiter notebooks, go to: https://jupyter.readthedocs.io/en/latest/install.html

To install any missing packages via conda, follow: https://docs.conda.io/projects/conda/en/latest/commands/install.html

To open the notebooks, follow these instructions: https://jupyter-notebook-beginner-guide.readthedocs.io/en/latest/execute.html

Introduction

This project includes four self-contained Jupyter notebooks with detailed step by step guide.

They are located in the root directory and can be executed from their first to their last cell. They are:

• Markov Chain Monte Carlo analysis (MCMC_Analysis.ipynb) [Successful]

• Genetic Algorithms analysis (GA_Analysis.ipynb) [Successful]

• Covariance Matrix Adaption Evolutionary Strategy analysis (CMAES_Analysis.ipynb) [Unsuccessful]

• Artificial Neural Network analysis (ANN_Analysis.ipynb) [Unsuccessful]

Setting the constraints and running the optimiser

To change the optimisation constraints, the cell “Defining the optimisation constraints” in GA_Analysis.ipynb must be edited accordingly, as shown below.

• Sample optimisation constraints

The constraint names are listed here: http://tool.globalcalculator.org

The input constraint values must be in the range [1, 4]. Each output constraint value has its own units and scale.

Note that the optimiser will minimise GHG emissions per capita and maximise economic viability by default.

The 2nd notebook “GA_Analysis.ipynb” can be run to perform the optimisation of the Global Calculator.

User documentation

MCMC

• Monte Carlo Markov Chain analysis

GA

• Genetic algorithms optimiser

CMA-ES

• Covariance Matrix Adaption Evolutionary Strategy analysis

ANN

• Artificial Neural Networks analysis

Usage examples

Genetic algorithms optimisation

• Optimisation of the Global Calculator via Genetic Algorithms
• Set-up
  • Creating a new generation
  • Fitness function
  • Selection
  • Mutation
  • Crossover
  • Enabling multiple constraints
  • Defining the optimisation constraints
• Optimisation
  • Iterations
  • Cost minimisation

Monte Carlo Markov Chain analysis

• Optimisation of the Global Calculator via Monte Carlo Markov Chains
• Set-up
• Temperature sensitivity analysis
• Cost sensitivity analysis
• Generalising MCMC (2 constraints) to all levers
  • Unbounded prior for all levers
  • Generating observations
  • Defining a likelihood function
• Running MCMC and logging results
• Loading pre-computed results (24-hours long Markov Chain)
• Correlation matrix of accepted MCMC lever combinations
• Paired density and scatter plot matrix of lever combinations accepted by MCMC
• Correlation matrix of output values
• Export correlation data to GEPHI
• Posterior distribution of accepted MCMC lever combinations
• Posterior distribution of model outputs accepted by MCMC
  • Evolution of temperature values
  • Evolution of cost values
• Acceptance rate
• Autocorrelation function of accepted model outputs
• Summary of inputs to the Global Calculator

Housekeeping

• License
• Requirements