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ZDT 2

Formulation:

Pareto Front:

Relevant Publications:

E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000 (PDF) (bibtex)

Reference Point:

Reference Point used:

Density:

Optimal Distributions:
(see "Maximum Hypervolume" for more plots)

of 5 points:

of 10 points:

of 20 points:

of 50 points:

Maximum Hypervolume:

µ	HV	Values	Plot
2	120.000000	download	plot
3	120.148148	download	plot
4	120.204159	download	plot
5	120.233907	download	plot
10	120.286820	download	plot
20	120.310699	download	plot
50	120.324398	download	plot
100	120.328881	download	plot
1000	120.332834	download	plot
∞	120 1/3

The x-values x_i of the µ points are equally distributed between 0 and 1
The first and last point are known to be extremal, hence only the remaining µ -2 points are optimized.
All points p with 1 < p < µ, starting with point p = 1, are optimized according to the following formulas:

For p > 1 and p < mu (non-extremal points)
The value of x_p is set to bopt(a,c), where a is x_p-1 and b is x_p+1
The Hypervolume-Indicator is calculated. If the value did increase less than a predefined value eps, the distribution of x is returned. Otherwise, step 3 is repeated.