Optimization: Searching the Global Maximum¶
In this tutorial we show how to optimize a given function.
Problem Description¶
We are given the function \(f(\vartheta)=-\vartheta^2\) for \(\vartheta\in[-10,10]\). We want to find the maximum of the function in the given interval.
The Objective Function¶
Create a folder named model. Inside, create a file with name directModel.py and paste the following code,
#!/usr/bin/env python
def evaluateModel(p):
x = p["Parameters"][0]
p["Evaluation"] = -x*x
This is the computational model that represents our objective function.
Optimization with CMAES¶
First, open a file (you could name it ‘run-cmaes.py’) and import the korali module
#!/usr/bin/env python3
import korali
Import the computational model,
import sys
sys.path.append('./model')
from directModel import *
The Korali Engine and Experiment Objects¶
Next we construct a korali.Engine and a korali.Experiment object and set the computational model,
k = korali.Engine()
e = korali.Experiment()
e["Problem"]["Objective Function"] = evaluateModel
The Problem Type¶
Then, we set the type of the problem to Direct Evaluation, and the objective to maximization,
e["Problem"]["Type"] = "Evaluation/Direct/Basic"
e["Problem"]["Objective"] = "Maximize"
The Variables¶
In this problem there is only one variable, X, whose domain we set to [-10,10],
e["Variables"][0]["Name"] = "X"
e["Variables"][0]["Lower Bound"] = -10.0
e["Variables"][0]["Upper Bound"] = +10.0
The Solver¶
We choose the solver CMAES, set the population size to be 32 and two termination criteria,
e["Solver"]["Type"] = "Optimizer/CMAES"
e["Solver"]["Population Size"] = 32
e["Solver"]["Termination Criteria"]["Min Value Difference Threshold"] = 1e-7
e["Solver"]["Termination Criteria"]["Max Generations"] = 100
For a detailed description of CMAES settings see CMAES.
Finally, we need to add a call to the run() routine to start the Korali engine.
k.run(e)
Running¶
We are now ready to run our example: ./run-cmaes
Or, alternatively: python3 ./run-cmaes
The results are saved in the folder _korali_result/.
Plotting¶
You can see the results of CMA-ES by running the command, python3 -m korali.plotter