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Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

TLDR
This paper provides a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions and shows that elitism is shown to be an important factor for improving evolutionary multiobjectives search.
Abstract
In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

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ETH Library
Comparison of multiobjective
evolutionary algorithms: empirical
results
Working Paper
Author(s):
Zitzler, Eckart; Deb, Kalyanmoy; Thiele, Lothar
Publication date:
1999
Permanent link:
https://doi.org/10.3929/ethz-a-004287264
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
TIK-Report 70
This page was generated automatically upon download from the ETH Zurich Research Collection.
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     
 
 
 
 
 
       !
" 
# $  "  %! 
%&'()* + #
&,

-...
 / 0   /0!
"1 
  "  
 2  *(' (34 
&, -..
 &5  . 6(
 "+  "   % +
/ 78 %& %9'()* + #
 ** 3)))

         
            
        Æ 
           
! "   #   
        $     %
           
     &   #  
      Æ  
 &           
  


                
 !!!  " # "  $
% $   & & ' "& &((
% )$       *
% +$    "(         ,
 
% -$ .      "

£
 "
"  "& &   " &&   / % !0


1& &(" /1.0  " & 

"    ,&
 '"& "& # "2 &"    "&, 
& , "    & (""(  (     &
   &  &  ( & &(   "&&
'"& &3     &&&"   &  ,&
"&  & "   &  ,"  '"&
 (& "2   " &   & (( 
   "& # 1. *    
.   (   & "& # "2  
  "( /%4 !5+3 %4 !5-3 " !5-0 &  4 1.
"&"       !!6!!+ / !!3 7 #&  8 !!3
  &"( !!)3 7 &  9& ( !!+3 %  : !!+0
8   /   "0  && &   "&
 # "2 &" /  ; !!<3 = >&  =
!!3 ?&2&@  A= !!3   &"( !!53 '* 
;&& !!50    "   ( &   &
 "& #    (   '"&  /?&2
 8" !!53 & !!50 ( /> *  *( !!50 
&" /'*  ;&& !!53 > *  *( !!50 &  
  &(  & B /8" &  %
& !!53 C2&  & !!!0  (  & &(" 
"& # "2       /  &"( !!-3
7 !!3 ?&2  8" !!53 = && !!!0
       &*    "  " 
4     &  =B&  B   "&
"       &"       ( 
* &  4 B
       "     >  
&    &"( /!!-0   D  4  ("
(   &   >  &  C2&  & /!!5 !!!0 
' E ** &"  " & "& # 1.
    " " , "& # 1. &(
"  ( &&  (& # 1. (  # (((  
  "&   " && "   
 &&  (    &"  F   &
  /: !!!0  &"   " "* (  1. 
 '"&  Æ&    " "   (
    ((       ( 
, ,  '  "&" &    
 7   &  "&& "     4*
 Æ&   " " ,&   B  (  
&   ,  & ,"    & 2  &"
      &&$ %  *   "& #
"2    "&(      ""&& F  (
    "& # 1.     & " 

 4  "          
 # % +  &&   " "   
B& 4  .  , "& &  % < 
(    &* &" /% 0  & 2 /% 50 &
.   &  &&      (   & 

>"2 &" &( "&& D(  #   
((((   #  &   &(  &( (& #
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Citations
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Journal ArticleDOI

A fast and elitist multiobjective genetic algorithm: NSGA-II

TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
Journal ArticleDOI

Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach

TL;DR: The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface.
Journal ArticleDOI

MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

TL;DR: Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjectives optimization problems.

SPEA2: Improving the strength pareto evolutionary algorithm

TL;DR: An improved version of SPEA, namely SPEA2, is proposed, which incorporates in contrast to its predecessor a fine-grained fitness assignment strategy, a density estimation technique, and an enhanced archive truncation method.
Book ChapterDOI

A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II

TL;DR: Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA--two other elitist multi-objective EAs which pay special attention towards creating a diverse Paretimal front.
References
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Book

Genetic algorithms in search, optimization, and machine learning

TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.

Genetic algorithms in search, optimization and machine learning

TL;DR: This book brings together the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Journal ArticleDOI

Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach

TL;DR: The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface.
Journal ArticleDOI

Muiltiobjective optimization using nondominated sorting in genetic algorithms

TL;DR: Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously are investigated and suggested to be extended to higher dimensional and more difficult multiobjective problems.
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