All classes NSGA-II MOPSO Hybrid Multi-Objective Optimization Syllabus · Episode 4 of 6

Class NSGA-II MOPSO Hybrid Multi-Objective Optimization #4: Designing Hybrid NSGA-II + MOPSO / Local Search

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Tutorial on designing a hybrid algorithm of NSGA-II, MOPSO, and local search for multi-objective optimization using Python. Episode 4 of the series on large-scale hybrid multi-objective metaheuristics.

Software: Python (NumPy, SciPy, Matplotlib)
Level: Advanced
Duration: ± 11 min
Series total: 59 min · 6 videos
Published: October 25, 2026

Episode 4 of 6 · view syllabus

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Introduction

Here is the final result, our self-designed hybrid algorithm. With exactly the same number of evaluations, the hybrid has already attached to the Pareto front by generation 100, while NSGA2 and MO-PSO are still far above. Let's get started. Hello, welcome to episode four of the hybrid multi-objective metaheuristics series. NSGA2 maintains diversity well but is slow at the beginning, while the PSO step moves toward the leader very quickly, approaching the front. Today, we are designing a hybrid that combines both, plus local search, and compare them fairly.

Step 1: PSO & Local Search

Create file hybrid.py The PSO step function moves solutions toward the leader with velocity that preserves momentum, like the MO-PSO particle. The local search function adds a small Gaussian disturbance to 20% of variables, to refine solutions without jumping too far.

Step 2: Hybrid Framework

The hybrid function uses the NSGA2 framework. Each generation, 44 offspring are created with SBX and mutation for exploration, 46 offspring are created with the PSO step toward the leader from the best front selected based on crowding, and 10 offspring from local search on the sparsely populated front solutions. Total is exactly 10,000 offspring, same as NSGA2, so the comparison is fair. The elitist selection of NSGA2 selects the next generation, and velocity is reset every 50 generations to prevent it from becoming too wild.

Step 3: Test Convergence Speed

Create file test_underscore hybrid.py All three algorithms run for 300 generations on ZDT1 and ZDT3, and the actual front distance is recorded every 25 generations. Run At generation 50, NSGA2's distance on ZDT1 is still 1.42, MoPSO is 0.36, and the hybrid is already 0.068. At generation 100, the hybrid reaches 0.01, while NSGA2 only breaks below 0.02 at generation 300. On the broken ZDT3, the hybrid also reaches 0.011 at generation 100, and NSGA2 does not go below 0.02 within 300 generations.

Step 4: Convergence Curve & Front

Let's look at the graphs. The convergence curve scale lock shows the hybrid drops the steepest on both test functions. The other two panels show the front at generation 100, the hybrid points have already attached to the actual front with good spread, including the five segments of ZDT3, while NSGA2 is still far above. The combination of SBX exploration, PSO convergence, and local refinement has proven to complement each other.

Done!

Done. We have designed a hybrid algorithm of NSGA2, PSO, and local search, with the same number of evaluations, and proved that its convergence is much faster. In the next episode, we will measure its performance using standard metrics, hypervolume, IGD, and spread. 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, hybrid algorithm design, up to hypervolume and IGD metrics as well as statistical comparison tests between algorithms, as well as opening 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 one-time payment of Rp999.000 for lifetime access. Want just one class? 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

0:43Step 1: PSO & Local Search

2:15Step 2: Hybrid Framework

5:05Step 3: Test Convergence Speed

7:26Step 4: Convergence Curve & Front

9:07Done!

Ask the class material

My notes

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Need more than a video?

Transcript

0:03Introduction

0:43Step 1: PSO & Local Search

2:15Step 2: Hybrid Framework

5:05Step 3: Test Convergence Speed

7:26Step 4: Convergence Curve & Front

9:07Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: PSO & Local Search

Step 2: Hybrid Framework

Step 3: Test Convergence Speed

Step 4: Convergence Curve & Front

Done!

Introduction

Step 1: PSO & Local Search

Step 2: Hybrid Framework

Step 3: Test Convergence Speed

Step 4: Convergence Curve & Front

Done!