Pareto Optimization or Cascaded Weighted Sum: A Comparison of Concepts

Looking at articles or conference papers published since the turn of the century, Pareto optimization is the dominating assessment method for multi-objective nonlinear optimization problems. However, is it always the method of choice for real-world applications, where either more than four objectives have to be considered, or the same type of task is repeated again and again with only minor modifications, in an automated optimization or planning process? This paper presents a classification of application scenarios and compares the Pareto approach with an extended version of the weighted sum, called cascaded weighted sum, for the different scenarios. Its range of application within the field of multi-objective optimization is discussed as well as its strengths and weaknesses.

[1]  C. Blume,et al.  Automatic generation of collision free moves for the ABB industrial robot control , 1997, Proceedings of 1st International Conference on Conventional and Knowledge Based Intelligent Electronic Systems. KES '97.

[2]  Natalio Krasnogor,et al.  Adaptive Cellular Memetic Algorithms , 2009, Evolutionary Computation.

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

[4]  Andrzej Osyczka,et al.  Multicriterion optimization in engineering with FORTRAN programs , 1984 .

[5]  Wilfried Jakob,et al.  Fast Rescheduling of Multiple Workflows to Constrained Heterogeneous Resources Using Multi-Criteria Memetic Computing , 2013, Algorithms.

[6]  Christian Blume,et al.  GLEAM - General Learning Evolutionary Algorithm and Method : ein Evolutionärer Algorithmus und seine Anwendungen , 2009 .

[7]  J. Marchal Cours d'economie politique , 1950 .

[8]  Kalyanmoy Deb,et al.  Introduction to Evolutionary Multiobjective Optimization , 2008, Multiobjective Optimization.

[9]  Kenneth A. De Jong,et al.  An Analysis of the Effects of Neighborhood Size and Shape on Local Selection Algorithms , 1996, PPSN.

[10]  Kaisa Miettinen,et al.  Introduction to Multiobjective Optimization: Noninteractive Approaches , 2008, Multiobjective Optimization.

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

[12]  Wilfried Jakob,et al.  A general cost-benefit-based adaptation framework for multimeme algorithms , 2010, Memetic Comput..

[13]  Anahí Gallardo Velázquez,et al.  Conference , 1969, Journal of Neuroscience Methods.

[14]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[15]  Thomas Bäck,et al.  Genetic Algorithms and Evolution Strategies - Similarities and Differences , 1990, PPSN.

[16]  Christian Blume GLEAM - A System for Simulated 'Intuitive Learning' , 1990, PPSN.

[17]  P. Gács,et al.  Algorithms , 1992 .

[18]  Christian Blume Optimized Collision Free Robot Move Statement Generation by the Evolutionary Software GLEAM , 2000, EvoWorkshops.

[19]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[20]  Charles Gide,et al.  Cours d'économie politique , 1911 .

[21]  Kathrin Klamroth,et al.  Unbiased approximation in multicriteria optimization , 2003, Math. Methods Oper. Res..

[22]  L. Lasdon,et al.  On a bicriterion formation of the problems of integrated system identification and system optimization , 1971 .

[23]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[24]  Theodor J. Stewart,et al.  Real-World Applications of Multiobjective Optimization , 2008, Multiobjective Optimization.

[25]  Kaisa Miettinen,et al.  Visualizing the Pareto Frontier , 2008, Multiobjective Optimization.

[26]  Martina Gorges-Schleuter,et al.  Explicit Parallelism of Genetic Algorithms through Population Structures , 1990, PPSN.