The Max-Min algorithm for maximising the spread of Pareto...

The Max-Min algorithm for maximising thespread of Pareto fronts.

Arturo Hernández Aguirre

ERCOFTAC 2006DESIGN OPTIMIZATION:

METHODS AND APPLICATIONSApril 5 – 7, 2006

Gran Canaria, Spain

CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS

A joint work with:

Dr. Salvador Botello Rionda

Dr. David Greiner Sánchez

Sergio Ivván Valdéz Peña


Index

Issues in spreading vectors on the Pareto front

How do (some) EMO algorithms promote thespreading of vectors on the Pareto front?

A view of Pareto front – Pareto set

The Max-Min Algorithm

Experiments


Issues in spreading vectors alongthe Pareto front


Two main goals of EMO algorithms

-Pareto front convergence.reach the true Pareto front

-Pareto front spread.- two components:

end vectors of the frontuniform distribution along the front


Spread over the front


Desired spreading over the front


Two issues of spreading over the front


A Spreading measure (Deb)


How do EMO algorithms promotespreading on the Pareto front?


NSGA-II Algorithm


NSGA-II spreading strategy


SPEA-2 Algorithm


SPEA-2 spreading mechanism


PAES, ISPAES, PASSSS Algorithms


PAES, ISPAES, PASSSS spreading strategy


Experiment: the spreading mechanisms


A view ofPareto front – Pareto set


A plane truss optimization problem


The objective functions


The constraint functions


Pareto fronts and Pareto setsreturned by non-dominated sorting


Relationship Pareto set – Pareto front


MAX-MIN

The Max of Min distanceAlgorithm.


MAX of the MIN of distances


MAX-MINAlgorithm


BASIC APPROACH TOenhance an EMO algorithm with MAXMIN

EE(µ+λ)Pt ~ initial populationRepeatλ ~ reproduction of µ padresλ ~ mutation of λ hijosP ~ determine Pareto SetPt+1 ~ MAXMIN(P)

Until termination


EXPERIMENTS


Function ZDT6. MaxMin vs NSGA-IIPopulation: 16 - 16


Function ZDT6. MaxMin vs NSGA-IIPopulation: 32 - 32


Bycicle frame design experiment


Bycicle frame design experiment

Design front Reference front


Simple supported plate


Final remarks

-Max Min is easy to program-We are working on a proof of theuniformity of the spread-Max Min is being compared to algorithmsbased on epsilon dominance


Thank you !!


The Max-Min algorithm for maximising the spread of Pareto...

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