OP_003

Objective

Topology ZDT6 function
Models Multiobjective optimization module OP2
NSGA-II Algorithm
Outputs Distance to theoritical Pareto Front
Parameters Optimization parameters: 10
Population Size: 100
Generations Number: 200
See also OP_001
OP_002
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 ZDT6 with 10 parameters.

Equations

The ZDT6 multi-objective function si defined by:

x_{i} \in [0, 1]
f_{1} = 1-e^{-4x_{1}}sin^6(6\pi x_{1})
f_{2} = 1-(f_{1}/g)
g= 1 + 9 \left[{{\sum_{i=2}^{n}{x_i}}\over{n-1}}\right]^{1/4}

The theoretical Pareto front of this problem is given by:


f_1 \in [0.2807753191,1]
f_2=1-f_1^2

Results

Optimization results with MANATEE vs theoritical results
Optimization results with MANATEE vs theoritical results

The results show a good agreement with the theoritical front. The first points fail to capture properly the beginning of the front.

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

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