A comparative study of the effect of parameter scalability in multi-objective metaheuristics

Abstract

Some real-world optimization problems have hundreds or even thousands of decision variables. However, the effect that the scalability of parameters has in modern multi-objective metaheuristic algorithms has not been properly studied (the current benchmarks are normally adopted with ten to thirty decision variables). In this paper, we adopt a benchmark of parameter-wise scalable problems (the ZDT test problems) and analyze the behavior of six multi-objective metaheuristics on these test problems when using a number of decision variables that goes from 8 up to 2048. The computational effort required by each algorithm in order to reach the true Pareto front is also analyzed. Our study concludes that a particle swarm algorithm provides the best overall performance, although it has difficulties in multifrontal problems.

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A Comparative Study of the Effect of Parameter Scalability in
Multi-Objective Metaheuristics
IEEE Congress on Evolutionary 2008, June 1-6, 2008
J. J. Durillo1
A.J. Nebro1
C. A. Coello2
F. Luna1
E. Alba1
1Department of Languages and Computer Science, University of M´ alaga, Spain
{durillo,antonio,flv,eat}@lcc.uma.es
2Department of Computer Science, CINVESTAV-IPN, Mexico
coello@cs.cinvestav.mx
May 27, 2008

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Outline of the talk
1 Introduction
Motivation
Contributions
2 Experimentation
Parameterization and Methodology
Scalability and speed
Discussion
3 Conclusions and Future Work

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Introduction
Experimentation
Conclusions and Future Work
Motivation
Contributions
Motivation
Parameter scalability in MO metaheuristics
MO community is paying much attention to many-objective optimization
Few works devoted to dimensionality (number of decision variables)
Real-world engineering problems → thousands of variables
Performance assessment of MO algorithms
Standard benchmarks: usually, 30 decision variables
Only 10 decision variables for the hardest problems (e.g., ZDT4)
Convergence speed of MO metaheuristics
1 A predefined maximum number of function evaluations is normally used
2 Goal: study computational effort to reach the true Pareto front
3 Practical interest when solving time-consuming MOPs
J. J. Durillo, A.J. Nebro, C. A. Coello, F. Luna, E. AlbaParameter Scalability in MO Metaheuristics 3/13

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Introduction
Experimentation
Conclusions and Future Work
Motivation
Contributions
Contributions of this work
1 Scalability and convergence speed in-depth analysis of MO metaheuristics
2 Six state-of-the-art algorithms
1 Three GAs: NSGA-II, SPEA2, and PESA-II
2 An evolution strategy: PAES
3 A particle swarm optimization: OMOPSO
4 A cellular GA: MOCell
3 The ZDT problem family
1 Keep the same Pareto front with different number of decision variables
2 Experiments that range from 8 up to 2048 decision variables
J. J. Durillo, A.J. Nebro, C. A. Coello, F. Luna, E. AlbaParameter Scalability in MO Metaheuristics4/13

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Introduction
Experimentation
Conclusions and Future Work
Parameterization and Methodology
Scalability and speed
Discussion
Parameterization and methodology
Parameterization
1 Aimed at fairly comparing the algorithms (e.g. using the same population
size)
2 They all are implemented using jMetal
(http://neo.lcc.uma.es/metal)
Methodology
1 The stopping condition is either
1 500,000 function evaluation, or
2 Convergence criterium reached → the Hypervolume indicator
2 The convergence criterium in-depth
1 Reach 95% of the HV value of the true Pareto front of the problem
2 Every 100 function evaluations
Nondominated solutions at each generation of NSGA-II and SPEA2
2
The external archive of PESA-II, PAES, and MOCell
The leaders archive of OMOPSO
1
3
J. J. Durillo, A.J. Nebro, C. A. Coello, F. Luna, E. AlbaParameter Scalability in MO Metaheuristics5/13