OP_001

Objective

Topology ZDT1 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_002
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 ZDT1 with 10 parameters.

Equations

The ZDT1 multi-objective function si defined by:

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


The theoretical Pareto front of this problem is met when g=1. The theoretical Pareto front equation is:

f_{2}=1-\sqrt{f_1}

Results

200. Optimization results with MANATEE vs theoritical 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

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