All classes NSGA-II MOPSO Hybrid Multi-Objective Optimization Syllabus · Episode 6 of 6

Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #6: Large-Scale Case Study & Algorithm Comparison Statistical Test

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Tutorial for large-scale multi-objective optimization case study and Wilcoxon statistical test for algorithm comparison using Python. Episode 6, the closing part of the large-scale hybrid multi-objective metaheuristics series.

Software: Python (NumPy, SciPy, Matplotlib)
Level: Advanced
Duration: ± 7 min
Series total: 59 min · 6 videos
Published: October 25, 2026

Episode 6 of 6 · view syllabus

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Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #6: Large-Scale Case Study & Algorithm Comparison Statistical Test: Cover: Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #6: Case Study at Large Scale & Algorithm Comparison Statistical Test

Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #6: Large-Scale Case Study & Algorithm Comparison Statistical Test: Before you start, steps list, and Step 1

Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #6: Large-Scale Case Study & Algorithm Comparison Statistical Test: Step 1: Ten experiments & Wilcoxon

Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #6: Large-Scale Case Study & Algorithm Comparison Statistical Test: Step 2: Boxplot IGD & hypervolume

Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #6: Large-Scale Case Study & Algorithm Comparison Statistical Test: Done: Final Result and Further Practice

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Introduction

Here is the final result, on a problem with 200 variables, NSGA2 and MOPSO have not even reached the hypervolume reference region, while the hybrid achieves an IGD 11 times smaller. 10 experiments and a Wilcoxon test prove that this superiority is significant. Let's start. Hello, welcome to the final episode of the hybrid multi-objective metaheuristics series. Real-world problems such as power plant scheduling or network design can have hundreds of variables. The more variables, the harder the search. Today we are testing the three algorithms on a large scale and statistically proving the results, according to journal standards.

Step 1: Ten experiments & Wilcoxon

Create a large underscore file dot pay. There are two cases, ZDT1 with 200 variables and DTLZ23 objectives with 50 variables. Each algorithm is run 10 times with different SID, 300 generations. Then we calculate IGD and hypervolume for each experiment and perform a Wilcoxon rank-sum test between the hybrid and the two competitors. Run. On ZDT1 with 200 variables, IGD NSGA2 is 1.85, MoPSO is 1.37, and the hybrid is only 0.16, with a hypervolume of 0.63. Meanwhile, the two competitors have a value of 0 because their fronts are still outside the reference points. On DTLZ2 with 50 variables, IGD hybrid is 0.108 compared to MoPSO 0.36, and NSGA2 0.67. All Wilcoxon tests resulted in P equal to 1.57 x 10-4, the smallest possible value for 10 vs 10 experiments, meaning the hybrid is better in every experiment.

Step 2: Boxplot IGD & hypervolume

Proceed to the box plot of IGD and hypervolume for both cases. Let's look at the graphs. The hybrid box is much lower in IGD and much higher in hypervolume, without overlapping with the competitors, and the boxes are narrow, meaning the results are consistent in every experiment. The hybrid's superiority actually increases on a large scale, because the PSO step towards the leader brings all variables simultaneously in the right direction.

Done!

Done, and the series is complete. We have built a complete research on multi-objective optimization, the Pareto concept and test functions, NSGA2 and MoPSO from scratch, hybrid algorithms, hypervolume metrics, IGD, and spread, up to large-scale case studies with statistical tests. For further research, try problems with constraints, objective functions with NSGA3, applications to real technical problems such as power plant placement, or adaptive parameter settings. Thank you for following this series. Currently working on a thesis, dissertation, or research in the field of optimization and artificial intelligence? Cerdas Inovasi Digital helps implement optimization algorithms, from NSGA2 and MoPSO, algorithm design hybrid, up to hypervolume metrics and IGD, as well as statistical testing for algorithm comparison, and opens Python programming courses for engineering. Want to master the entire series, from Pareto concepts to large-scale case studies? All 6 episodes, complete with PDF step-by-step guides and source code, are available to premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or pay once Rp999.000 for lifetime access. Want a single class only? Buy the single class with lifetime access. Subscribe now at the premium page cerdasinovasidigital.com Contact our WhatsApp or visit cerdasinovasidigital.com Thank you for watching, see you in the next episode.

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Transcript

0:03Introduction

0:47Step 1: Ten experiments & Wilcoxon

3:43Step 2: Boxplot IGD & hypervolume

4:55Done!

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0:03Introduction

0:47Step 1: Ten experiments & Wilcoxon

3:43Step 2: Boxplot IGD & hypervolume

4:55Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: Ten experiments & Wilcoxon

Step 2: Boxplot IGD & hypervolume

Done!

Introduction

Step 1: Ten experiments & Wilcoxon

Step 2: Boxplot IGD & hypervolume

Done!