# 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.plot