Effects of Noisy Multiobjective Test Functions Applied to Evolutionary Optimization Algorithms

In this paper we study the effects of noise in multiobjective optimization problems. We consider a test function, which may be affected by noise with different strength and frequency of occurrence. To simplify the analysis, the noise is applied to only one of the objective functions, i.e. one of the objective functions is affected by additional random influences. Three different evolutionary algorithms for multiobjective problems are analyzed in this way: the Covariance Matrix Adaption Evolution Strategy (CMA-ES), the Non-dominated Sorting Genetic AlgorithmII (NSGA-II), and the Particle Swarm Optimization (PSO). The results are presented and analyzed with respect to the resulting Pareto fronts and with respect to the distribution of variable values during the algorithm run. It can be observed that all three algorithms are basically able to derive suitable results. However, only PSO leads to a sparse Pareto front in case of noisy and non-noisy situations while CMA and NSGA-II perform similarly well. In some situations for NSGA-II and more clearly for CMA-ES specific patterns for the variable values (denoted as striae in this paper) can be observed which appear to be partly caused by the noise.

[1]  Pratyusha Rakshit,et al.  Uncertainty Management in Differential Evolution Induced Multiobjective Optimization in Presence of Measurement Noise , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[2]  Fang Liu,et al.  MOEA/D with Adaptive Weight Adjustment , 2014, Evolutionary Computation.

[3]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[4]  H. Beyer.  Evolutionary algorithms in noisy environments : theoretical issues and guidelines for practice , 2000 .

[5]  Pratyusha Rakshit,et al.  Artificial Bee Colony induced multi-objective optimization in presence of noise , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[6]  Andrew M. Sutton,et al.  Robustness of Ant Colony Optimization to Noise , 2015, Evolutionary Computation.

[7]  Kay Chen Tan,et al.  An Investigation on Noisy Environments in Evolutionary Multiobjective Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[8]  Hans-Georg Beyer,et al.  A Comparison of Evolution Strategies with Other Direct Search Methods in the Presence of Noise , 2003, Comput. Optim. Appl..

[9]  W. Premchaiswadi,et al.  Applying Fuzzy-Genetic mining in conformance and dependency relations , 2012, 2012 Tenth International Conference on ICT and Knowledge Engineering.

[10]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[11]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[12]  Hans-Georg Beyer,et al.  A general noise model and its effects on evolution strategy performance , 2006, IEEE Transactions on Evolutionary Computation.

[13]  Hussein A. Abbass,et al.  Fitness inheritance for noisy evolutionary multi-objective optimization , 2005, GECCO '05.

[14]  Hamidreza Eskandari,et al.  Evolutionary multiobjective optimization in noisy problem environments , 2009, J. Heuristics.

[15]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

[16]  Xavier Llorà,et al.  Bounding the Effect of Noise in Multiobjective Learning Classifier Systems , 2003, Evolutionary Computation.

[17]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[18]  Konstantinos E. Parsopoulos,et al.  PARTICLE SWARM OPTIMIZER IN NOISY AND CONTINUOUSLY CHANGING ENVIRONMENTS , 2001 .

[19]  Stefan Roth,et al.  Covariance Matrix Adaptation for Multi-objective Optimization , 2007, Evolutionary Computation.

[20]  Kay Chen Tan,et al.  An investigation on noise-induced features in robust evolutionary multi-objective optimization , 2010, Expert Syst. Appl..