DCC: Distributed Cooperative Coevolution (powered by LM-CMA/CMA-ES under the recently proposed Multi-Level Learning framework).

This is an online companion website for the paper Cooperative Coevolution for Non-Separable Large-Scale Black-Box Optimization: Convergence Analyses and Distributed Accelerations (under review, submitted to Applied Soft Computing).

All the Python source code and data involved in this paper are presented here to ensure repeatability and possible improvements.

Baselines of Black-Box Optimizers (BBO) Used in our Paper

All of the below BBO are given in alphabetical order. Please refer to their references for details according to their open-source code files.

Optimizer | Source Code --------- | ----------- Adaptive Estimation of Multivariate Normal Algorithm | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/eda/aemna.py Annealed Random Hill Climber | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/rs/arhc.py BErnoulli Smoothing | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/rs/bes.py Cholesky-CMA-ES 2009 | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/ccmaes2009.py Cooperative Coevolving Particle Swarm Optimizer | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/pso/ccpso2.py Classic Differential Evolution | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/de/cde.py Comprehensive Learning Particle Swarm Optimizer | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/pso/clpso.py Covariance Matrix Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/cmaes.py CoOperative CO-evolutionary Covariance Matrix Adaptation | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/cc/cocma.py COmposite Differential Evolution | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/de/code.py CoOperative co-Evolutionary Algorithm | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/cc/coea.py CoOperative SYnapse NEuroevolution | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/cc/cosyne.py Corana et al.' Simulated Annealing | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/sa/csa.py Cumulative Step-size self-Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/csaes.py Differentiable Cross-Entropy Method | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/cem/dcem.py Diagonal Decoding Covariance Matrix Adaptation | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/ddcma.py Derandomized Self-Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/dsaes.py Dynamic Smoothing Cross-Entropy Method | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/cem/dscem.py Exact Natural Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/nes/enes.py Enhanced Simulated Annealing | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/sa/esa.py Fast Covariance Matrix Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/fcmaes.py Adaptive Differential Evolution | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/de/jade.py Limited-Memory Covariance Matrix Adaptation | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/lmcma.py Limited-Memory Covariance Matrix Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/lmcmaes.py Limited-Memory Matrix Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/lmmaes.py Matrix Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/maes.py Mixture Model-based Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/mmes.py (1+1)-Active-CMA-ES 2010 | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/opoa2010.py (1+1)-Active-CMA-ES 2015 | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/opoa2015.py (1+1)-Cholesky-CMA-ES 2006 | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/opoc2006.py (1+1)-Cholesky-CMA-ES 2009 | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/opoc2009.py Pure Random Search | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/rs/prs.py Rank-One Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/r1es.py Rank-One Natural Evolution Strategies | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/nes/r1nes.py Rechenberg's (1+1)-Evolution Strategy with 1/5th success rule | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/res.py Random (stochastic) Hill Climber | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/rs/rhc.py Rank-M Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/rmes.py Random-Projection Estimation of Distribution Algorithm | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/eda/rpeda.py Standard Cross-Entropy Method | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/cem/scem.py Separable Covariance Matrix Adaptation Evolution Strategy | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/sepcmaes.py Separable Natural Evolution Strategies | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/nes/snes.py Standard Particle Swarm Optimizer with a global topology | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/pso/spso.py Standard Particle Swarm Optimizer with a Local (ring) topology | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/pso/spsol.py Simple Random Search | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/rs/srs.py Univariate Marginal Distribution Algorithm for normal models | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/eda/umda.py Linear Covariance Matrix Adaptation | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/vdcma.py Projection-based Covariance Matrix Adaptation | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/es/vkdcma.py Exponential Natural Evolution Strategies | https://github.com/Evolutionary-Intelligence/pypop/blob/main/pypop7/optimizers/nes/xnes.py

Configurations of Clustering Computing Platform

Use the following three bash commands to obtain the information of each slave node in the clustering computing platform:

1. Use lsb_release -a to obtain operation system (OS) information,
2. Use cat /proc/cpuinfo | grep name | cut -f2 -d: | uniq -c to obtain CPU information,
3. Use free -mh to obtain memory information.

OS | CPU | Memory -- | --- | ------ Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2650 v3 @ 2.30GHz | 62G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2650 v3 @ 2.30GHz | 62G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2650 v3 @ 2.30GHz | 62G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2650 v3 @ 2.30GHz | 62G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2650 v3 @ 2.30GHz | 62G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2640 v4 @ 2.40GHz | 62G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2640 v4 @ 2.40GHz | 62G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2640 v4 @ 2.40GHz | 32G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2640 v4 @ 2.40GHz | 32G Ubuntu 16.04 LTS | 40 Intel(R) Xeon(R) CPU E5-2640 v4 @ 2.40GHz | 32G

• Increase the limits of open files (by default, 1024) to e.g. 500000 for successful runs:

$ ulimit -n
$ sudo vi /etc/security/limits.conf

• Make sure that all slave nodes use the same versions of all three Python libraries (NumPy, SciPy, and Ray):

$ pip install numpy  # to use the virtual environment to install depended libraries
$ pip install scipy
$ pip install ray
$ export RAY_memory_monitor_refresh_ms=0

• Choose one node as the master node:

$ ray start --head
$ ray status

$ ssh -L 8265:0.0.0.0:8265 <NAME>@<IP-ADDRESS>  # for local access to the remote clustering computing platform
# <NAME> and <IP-ADDRESS> are replaced by user name and IP of the master node
$ python  # local
>>> import ray
>>> ray.init(include_dashboard=True)
# open http://localhost:8265/ in the browser for status of the used clustering computing platform

Guideline for Hyper-Parameter Settings

• n_islands: the total number of islands to be run in parallel (int, must > 0)
  • To maximize the level of parallelism while avoiding disputes with OS management programs, it is suggested to be set as the total number of all available (logical) CPU cores minus the total number of worker nodes at most.
• inner_max_runtime: runtime of each island within each isolation time (float, must > 0.0)
  • By default: 3.0 * 60 (seconds).
• max_runtime: maximal wall-clock time to be run in the distributed computing platform (float, must > 0.0)
  • This hyper-parameter is problem-dependent, depending on the maximally acceptable time of the user obviously.