A stopping criterion based on Kalman estimation techniques with several progress indicators

The need for a stopping criterion in MOEA's is a repeatedly mentioned matter in the domain of MOOP's, even though it is usually left aside as secondary, while stopping criteria are still usually based on an a-priori chosen number of maximum iterations. In this paper we want to present a stopping criterion for MOEA's based on three different indicators already present in the community. These indicators, some of which were originally designed for solution quality measuring (as a function of the distance to the optimal Pareto front), will be processed so they can be applied as part of a global criterion, based on estimation theory to achieve a cumulative evidence measure to be used in the stopping decision (by means of a Kalman filter). The implications of this cumulative evidence are analyzed, to get a problem and algorithm independent stopping criterion (for each individual indicator). Finally, the stopping criterion is presented from a data fusion perspective, using the different individual indicators' stopping criteria together, in order to get a final global stopping criterion.

[1]  Jesús García,et al.  An approach to stopping criteria for multi-objective optimization evolutionary algorithms: The MGBM criterion , 2009, 2009 IEEE Congress on Evolutionary Computation.

[2]  J. Periaux,et al.  Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems , 2001 .

[3]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[4]  Carlos A. Coello Coello,et al.  An updated survey of GA-based multiobjective optimization techniques , 2000, CSUR.

[5]  Marc Schoenauer,et al.  A Steady Performance Stopping Criterion for Pareto-based Evolutionary Algorithms , 2004 .

[6]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[7]  Jesús García,et al.  A cumulative evidential stopping criterion for multiobjective optimization evolutionary algorithms , 2007, GECCO.

[8]  Gary B. Lamont,et al.  Evolutionary algorithms for solving multi-objective problems, Second Edition , 2007, Genetic and evolutionary computation series.

[9]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[10]  Marco Laumanns,et al.  Why Quality Assessment Of Multiobjective Optimizers Is Difficult , 2002, GECCO.

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

[12]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[13]  Matthias Ehrgott,et al.  Multicriteria Optimization (2. ed.) , 2005 .

[14]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[15]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[16]  P. Groves.  Principles of GNSS, Inertial, and Multi-Sensor Integrated Navigation Systems , 2007 .

[17]  Jesús García,et al.  Domain Transformation for Uniform Motion Identification in Air Traffic Trajectories , 2008, DCAI.

[18]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[19]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[20]  Pau Klein,et al.  San Francisco, California , 2007 .

[21]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[22]  Lothar Thiele,et al.  The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration , 2007, EMO.

[23]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[24]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization: Theoretical Advances and Applications (Advanced Information and Knowledge Processing) , 2005 .