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

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

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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