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] x_{i} \in [0, 1]](local/cache-vignettes/L80xH25/4a316b0090f0c2fbeedf1e031a7d8794-0d372.png?1589161773)



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_{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]](local/cache-vignettes/L662xH26/305fd05404e93b53015af236f751b5c7-b126b.png?1589161773)

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