No Rank-0 in Initial Population. And NaN Crowding distance

[abhinavgaur]

Hello David,

I am trying out this bi-objective problem. Based on an earlier code that you shared to collect all population of all generations, I wrote this script that additionally prints ConstraintViolation, Rank and Crowding Distance. The script prints out the Variables, Objectives, Constraints, ConstraintViolation, Rank and CrowdingDistance for each individual of a population and for all generations/FuncEvaluations.

The following is the output for a run.

As you can see in the image, I have three issues.

1) There is no Rank zero individual in the initial population and 1st Generation population. 2) In the second generation, Crowding Distance for one of the individuals is evaluated as NaN. 3) The NFE (# of function evalutations) attribute of accumulator should increase as 11,22,33. Why does it show 11,23,35?

Can you tell me what I may be doing wrong here?

Thanks

[dhadka]

1) This is a mistake on my part. In the PopulationCollector, it needs to create a copy of the solution. Otherwise, the rank and crowding attributes are being changed as that solution is being non-dominated sorted in later generations. Update the collect(...) method as follows:

        @Override
        public void collect(Accumulator accumulator) {
            ArrayList<Solution> list = new ArrayList<Solution>();
            Population population = algorithm.getPopulation();

            for (Solution solution : population) {
                list.add(solution.deepCopy());
            }

            accumulator.add("Population", list);
        }

2) The NaN is occurring because the rank 2 front contains 3 identical solutions. This is handled the same way as Deb's NSGA-II code (in crowddist.c). One question would be: why are there 3 identical solutions? I would guess that "selection with replacement" combined with the small population size (11) is causing this loss of diversity. Using "selection without replacement" would probably help prevent this.

However, having said that, statistical tests on this problem still show the results are statistically indifferent between the two versions:

        Problem problem = new metalCutting2();

        Executor executor = new Executor()
                .withProblem(problem)
                .withProperty("populationSize", 11)
                .withMaxEvaluations(10000);

        Analyzer analyzer = new Analyzer()
                .withProblem(problem)
                .includeHypervolume()
                .includeInvertedGenerationalDistance()
                .includeGenerationalDistance()
                .showStatisticalSignificance();

        analyzer.addAll("NSGA-II with Replacement", executor.withAlgorithm("NSGA-II").withProperty("withReplacement", true).runSeeds(50));
        analyzer.addAll("NSGA-II without Replacement", executor.withAlgorithm("NSGA-II").withProperty("withReplacement", false).runSeeds(50));

        analyzer.printAnalysis();

NSGA-II with Replacement:
    Hypervolume: 
        Min: 0.31609412727099256
        Median: 0.5143054665632678
        Max: 0.5576830030460866
        Count: 50
        Indifferent: [NSGA-II without Replacement]
    GenerationalDistance: 
        Min: 0.005328191697079058
        Median: 0.017774346994537088
        Max: 0.07186860178192847
        Count: 50
        Indifferent: [NSGA-II without Replacement]
    InvertedGenerationalDistance: 
        Min: 0.047127207176900755
        Median: 0.0726838689641357
        Max: 0.22349802834565763
        Count: 50
        Indifferent: [NSGA-II without Replacement]
NSGA-II without Replacement:
    Hypervolume: 
        Min: 0.21978558841920523
        Median: 0.5141349504256087
        Max: 0.5484263066200257
        Count: 50
        Indifferent: [NSGA-II with Replacement]
    GenerationalDistance: 
        Min: 0.01055840214749359
        Median: 0.018784205080687615
        Max: 0.1085387029456017
        Count: 50
        Indifferent: [NSGA-II with Replacement]
    InvertedGenerationalDistance: 
        Min: 0.04785901371042905
        Median: 0.07415195967628987
        Max: 0.337843383915133
        Count: 50
        Indifferent: [NSGA-II with Replacement]

[abhinavgaur]

Hi David,

I updated the previous question after initial posting. Can you also answer the Question-3 that I have put there regarding NFE attribute of Accumulator class?

Thanks

[dhadka]

Absolutely. Since the population size is odd (11) and the crossover operator (SBX) takes two parents and produces two offspring, it ends up producing 12 offspring every generation. Thus, the NFE counts you see are:

11       - Random initialization produces 11 solutions
11+12=23 - First generation with 12 offspring
23+12=35 - Second generation with 12 offspring

[abhinavgaur]

Thanks David. All the above replies make perfect sense.