optimizing zdt1 multi-objective test problem using Genetic Algorithm - A MATLAB tutorial

In this tutorial, I show implementation of the ZDT1 multi-objective test problem and optimize it using the built-in Multi-objective Genetic Algorithm in MATLAB. The given objective function is a standard test function that helps a beginner user to understand the basic concept of optimization in MATLAB easier. The given objective function or fitness function has one vector input including 'n' variables and two outputs (objective values). I write two separate functions one for the fitness function and one for the main algorithm. I plot the pareto-front that illustrates the obtained solutions in a proper way. We use different setting of the algorithm using the 'optimoptions' function.

A simple optimization using Genetic Algorithm:
A simple constrained optimization using Genetic Algorithm:
A simple multi-objective optimization using Genetic Algorithm:
A mixed-integer optimization using Linear Programming:
A simple single-objective optimization using Particle Swarm Optimization Algorithm:
A simple single-objective optimization using Pattern Search:

[hazemismaeel]

Thank you very much for this tutorial
keep in progress

[addislulu]

can I control the value of x that are selected by the optimizer, to be selected from predefined values?

[morriskiguru]

what if I have a penalty factor? how I include it?

[ghzango]

i have two objective functions one for maximization and the other one is for minimization could you confirm if i can use this method for finding the optimal solution