Associate Professor Tsung-Che Chiang
Department of Computer Science and Information Engineering
National Taiwan Normal University

Tel: +886-2-77346692    Fax: +886-2-29322378    Email
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Tsung-Che Chiang, nsga3cpp: A C++ implementation of NSGA-III, 2014.

Validation & Issues

v1.2 (2016/1/1)

  • After the modification, now the results for solving DTLZ with more than 5 objectives are somewhat acceptable. :)

¡@ M = 8 (best/median/worst IGD in 20 runs) M = 10 (best/median/worst IGD in 20 runs)
¡@ official nsga3cpp official nsga3cpp
DTLZ1 2.044´10-3
3.979´10-3
8.721´10-3		 3.454´10-3
5.279´10-3
4.290´10-2		 2.215´10-3
3.462´10-3
6.869´10-3		 2.257´10-3
4.235´10-3
2.744´10-2
DTLZ2 1.371´10-2
1.571´10-2
1.811´10-2		 1.540´10-2
1.740´10-2
2.002´10-2		 1.350´10-2
1.528´10-2
1.697´10-2		 1.384´10-2
1.727´10-2
2.004´10-2
DTLZ3 1.244´10-2
2.375´10-2
9.649´10-2		 1.564´10-2
3.014´10-2
1.386´10-1		 8.849´10-3
1.188´10-2
2.083´10-2		 2.014´10-2
3.092´10-2
4.817´10-2
DTLZ4 5.079´10-3
7.054´10-3
6.051´10-1		 3.406´10-3
4.345´10-3
5.496´10-3		 5.694´10-3
6.337´10-3
1.076´10-1		 3.633´10-3
4.601´10-3
5.301´10-3

v.1.1 (2014/8)

  • Again, please note the nsga3cpp is an *unofficial* implementation of NSGA-III. Here is the comparison between the results of nsga3cpp and the original NSGA-III paper.

    ¡@ M = 3 (best/median/worst IGD in 20 runs) M = 5 (best/median/worst IGD in 20 runs)
    ¡@ official nsga3cpp official nsga3cpp
    DTLZ1 4.880´10-4
    1.308    ´10-3
    4.880    ´10-3    		 7.593´10-4
    2.845    ´10-3
    2.053    ´10-2    		 5.116´10-4
    9.799    ´10-4
    1.979    ´10-3    		 7.718´10-4
    2.050    ´10-3
    4.733    ´10-2
    DTLZ2 1.262´10-3
    1.357    ´10-3
    2.114    ´10-3    		 1.585´10-3
    2.731    ´10-3
    6.911    ´10-3    		 4.254´10-3
    4.982    ´10-3
    5.862    ´10-3    		 4.701´10-3
    6.299    ´10-3
    1.547    ´10-2
    DTLZ3 9.751´10-4
    4.007    ´10-3
    6.665    ´10-3    		 1.374´10-3
    4.757    ´10-3
    1.129    ´10-2    		 3.086´10-3
    5.960    ´10-3
    1.196    ´10-2    		 3.462´10-3
    9.447    ´10-3
    1.040    ´10-1
    DTLZ4 2.915´10-4
    5.970    ´10-4
    4.286    ´10-1    		 2.447´10-4
    5.778    ´10-4
    5.330    ´10-1    		 9.849´10-4
    1.255    ´10-3
    1.721    ´10-3    		 4.305´10-4
    7.294    ´10-4
    1.108    ´10-3

    For solving 3- and 5-objective DTLZ problems, nsga3cpp can provide similar IGD performance with the official implementation in most cases. In some cases, the worst-case IGD of nsga3cpp is not so good.

    For problems with 8 and higher objectives, nsga3cpp performs very bad. By some analysis and observations, I think that the bad performance is caused by the situation in which the hyperplane cannot be constructed due to duplicate extreme points. Currently nsga3cpp uses a very simple way to deal with the problem. (You can check the code in ConstructHyperplane() in alg_environmental_selection.cpp.) I do appreciate if you are willing to share with me how to deal with this problem better.

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