OP_002

Objective

Topology	ZDT3 function
Models	Multiobjective optimization module LAB.CMO NSGA-II Algorithm
Outputs	Distance to theoritical Pareto Front
Parameters	Optimization parameters: 10 Population Size: 100 Generations Number: 200
See also	OP_001 OP_003 How to use MANATEE to optimize an external function

The objective of this validation case is to validate the NSGA-II algorithm used in MANATEE with the multi-objective function ZDT3 with 10 parameters.

Equations

The ZDT3 multi-objective function si defined by:

$x_{i} \in [0, 1]$
$f_{1} = x_1$
$f_{2} = g.(1-\sqrt{f_{1}/g})-f_1/g.sin(10\pi f_{1})$
$g= 1 + {9\over{n-1}}\sum_{i=2}^{n}{x_i}$

The theoretical Pareto front of this problem is discontinuous. The theoretical Pareto front equation is:

$f_{1} \in [0, 0.083] \cup [0.182,0.258]\cup {[0.409,0.454]} \cup [0.618,0.653] \cup [0.823,0.852]$
$f_{2}=1-\sqrt{f_1}-f_1.sin(10\pi f_1)$

Results


Optimization results with MANATEE vs theoritical results

Reference

Zitzler, E., Kalyanmoy, D., & Thie. (2000). Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation, 8(2), 173–195. https://doi.org/10.1162/106365600568202