Differential Evolution

Modify from blake01/fyp. Thanks a lot.

I want to improve differential evolution algorithm by reinforcement learning but it failed. Sad...

What is it

Differential Evolution(DE) algorithm is a powerful evolutionary optimizer for the continuous parameter spaces which utilizes NP D-dimensional parameter vectors, so-called individuals. The canonial DE algorithm as followed:

• Initialization

  $x_{i,0}^j=x^j_{min}+rand(0,1)*(x^j_{max}-x^j_{min})\ j=1,2,..,D$

• Mutation operation

  After initialization, DE employs the mutation operation to produce a mutant vector. There are many mutation strategies like "DE/best/1": $$ V_{i,G}=X_{best,G}+F*(X_{r_1^j,G}-X_{r^i_2,G}) $$

• Crossover operation

  After the mutation phase, crossover operation is applied to each pair of the target vector $X_{i,G}$ and its corresponding mutant vector $V_{i,G}$ to generate a trial vector $U_{i,G}$: $$ u_{i,G}^j=\left{\begin{matrix} v_{i,G}^j\quad if (rand_j[0,1]\leq CR) or (j=j_{rand}) \ x_{i,G}^j\quad otherwise \end{matrix}\right. j=1,2,..,D $$

• Selection operation

  After crossover operation, keep individuals with lower fitness value. $$ X_{i,G+1}=\left{\begin{matrix} U_{i,G},\quad if f(U_{i,G})\leq f(X_{i,G}) \ X_{i,G},\quad otherwise \end{matrix}\right. $$

You can know more about DE by reading this or related paper.

File Structure

• 'population.py' provides a general population class, suitable for use in any population-based evolutionary algorithm. 'tests.py' are unit tests for this file.
• 'deBase.py' contains object-oriented versions of the traditional, non-adaptive DE algorithms, as originally proposed by Storn and Price.
• 'mixins.py' provides mixins to extend/edit the DE classes in some way, e.g. logging output.
• 'sade.py', 'jade.py' and 'jde.py' contain adaptive variants of DE from literature, implemented as subclasses of one or more of the deBase.py classes.
• 'hybrids.py' contains cannibalised algorithms derived from SaDE, JADE and jDE.
• 'deAbaqus.py' contains AbaqusJADE and the AbaqusProblem class.
• 'testFunctions' contains the benchmark cost functions detailed in Appendix 2 of the main report.
• 'study.py' is the file used to perform the benchmarking analysis undertaken in Section 2 of the main report.
• 'beamProblem.py' and 'bloodhoundProblem.py' are the trial and objective FEA optimisation files.
• 'abaqusFiles/bloodhound.cae' is the Abaqus CAE file for the Bloodhound jet fuel tank baffle.
• 'DE_DDQN.py' is invented by me. It uses DDQN(one of reinforcement algorithms) to improve DE.
• 'DE_RL.py' is also invented by me. It uses Q-learning(one of reinforcement algorithms) to improve DE. However, all of them are not performed well.

Outputs

You can see some metrics in the following files to check your algorithm performence.

study.out: run_name, bestVector

xlsx file：functionEvaluations, bestVector.cost, cr, f

Connect

[email protected]

blog: WinterColor blog

Good luck