Introduction into Matrix Adaptation Evolution Strategies
The IEEE World Congress on Computational Intelligence (WCCI 2022), 18 July - 23 July 2022, Padua, Italy
Since the recent successes of Evolution Strategies (ES) in the field of Reinforcement Learning, ESs have attracted interest also outside the ES community. Matrix Adaptation Evolution Strategies are regarded as state-of-the-art in evolutionary real-valued parameter optimization. These strategies are able to learn correlations between the different decision variables in order to generate suitable mutations that allow for an efficient approximation of the optimizer of the problem to be optimized. Until recently, correlation learning has been realized by covariance matrix adaptation (CMA). Only recently it has been shown that there is no need to learn the covariance matrix. Instead a mutation matrix can be learned directly. As a result, the algorithms get simpler and can be easily modified to also tackle large scale optimization problems and constrained optimization problems. One such ES was the winner in the 2018 CEC constrained optimization benchmark competition regarding the high-dimensional problem instances.
This tutorial provides a gentle introduction into Matrix Adaptation Evolution Strategies (MA-ES) explaining the design principles. Being based on these principles, it will be shown how one can modify the MA-ES in order to:
- incorporate self-adaptive behavior,
- handle large scale optimization problems with thousands of variables,
- treat constrained optimization problems.
The tutorial will also show some 2D and 3D graphical demonstrations
of the working of MA-ES handling restricted optimization problems with
non-linear equality and inequality constraints.
This tutorial is intended as an introduction, the target audience is not restricted to Evolutionary Computation specialist. The topic can be of interest for Fuzzy and Neural Network specialist as well. No special mathematical background is needed to understand this presentation.
- The building blocks of Evolution Strategies:
- Design principles for mutation, recombination, and selection
- Adaptiveness in Evolution Strategies:
- Path cumulation
- Learning correlations
- The Matrix Adaptation Evolution Strategy:
- basic idea
- reduction of internal algorithmic costs
- live demonstration: optical lens shape optimization
Limited Memory Matrix Adaptation Evolution Strategy
- Design principles for constrained optimization problems:
- equality constraints (inner point methods, linear and non-linear)
- live 2D and 3D demonstrations (examples: area maximization, Tamme's problem
- inequality constraints: matrix adaptation and repair strategies
- live 3D demonstration (Tamme's problem revisited)
Outlook and Open Problems