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Introduction
Here is the final result, Mo-PSO, a swarm of particles chasing the leader from the Pareto Archive. After 400 generations, Mo-PSO finds a well-distributed front, but NSGA-2 is closer to the actual front. Each algorithm has different strengths, and that is the basis for hybrid algorithms. Let's get started. Hello, welcome to episode three of the Hybrid Multi-Objective Meta Heuristics series. Particle Swarm Optimization is known for being fast on single-objective problems, as each particle directly moves toward the best solution. In multi-objective problems, there is no single best solution, so Mo-PSO stores the Pareto Archive and selects leaders from there. Today, we are going to write it.
Step 1: Pareto Archive & Leader
Create a file MOPSO.py The update archive function combines the old archive with new solutions, discards duplicates and dominated solutions. Then, if the archive exceeds capacity, solutions with the highest crowding distance are discarded one by one to maintain an even spread. The select leader function uses a binary tournament on crowding distance, so leaders in areas of the front that are still sparse are more often selected, and particles are pushed to fill the gaps.
Step 2: Particle Movement & Personal Best
The MOPSO function moves 100 particles. New velocity is inertia plus attraction to personal best and attraction to the leader from the archive. Particles that go out of bounds are reflected, and in the first phase of the search, turbulence is added in the form of polynomial mutation to prevent premature convergence. Personal best is replaced if the new solution dominates it, or randomly if neither dominates the other. The archive is updated every iteration, and its size is recorded. Create a test file underscore mobso.py and run it.
Step 3: MOPSO vs NSGA-II
MOP, and NSGA2 are run for 400 generations on the three test functions. The MOPSO archive is filled with 100 solutions on ZDT1 and ZDT2, and 97 on ZDT3. The distance of MOPSO to the actual front is 0.0249 for ZDT1, 0.0273 for ZDT2, and 0.0479 for ZDT3. Meanwhile, NSGA2 is closer, around 0.005, 0.003, and 0.01.
Step 4: Front & Archive Size
Let's look at the graphs. The cross signs of MOPSO are neatly spread along the front, but slightly above the points of NSGA2, meaning its convergence is less dense on 30 variables. The right graph shows the archive being fully populated in a few dozen iterations. However, in the next episode, we will see that MOPSO is actually much faster in the early generations, and this property will be combined with NSGA2.
Done!
Done. We have already written MOPSO with a Pareto archive, crowding-based leader selection, multi-objective personal base, and turbulence, then compared it with NSGA2. In the next episode, we will design a hybrid algorithm that combines the strengths of both. 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 metrics and IG, statistical test comparisons, and opens Python programming courses for engineers. 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 just one class? Buy single classes 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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