Post-Pareto Optimality Analysis With Sum of Ranking Differences

In multiobjective optimization, objectives are typically conflicting, i.e., they cannot reach their individual optima simultaneously. Identifying the best one among Pareto-optimal solutions is not a simple task for the decision maker (DM), since the Pareto-optimal set can potentially contain a very large number of solutions. To ease this task, it is possible to resort to aggregate objective functions that should take into consideration the DM’s preferences and objectives; however, accurately specifying meaningful weights can be a challenge for many practitioners. Moreover, for the same DM’s preferences, different criteria give different results. A new post-Pareto analysis methodology, based on sum of ranking differences, is proposed to rank and detect the possible groupings of similar solutions of the Pareto front that match the DM’s preferences. This way the proposed technique provides the DM a smaller set of optimal solutions. The proposed method was tested in two practical benchmark problems, in the design of a brushless dc motor and in the optimization of a die press model (TEAM Workshop Problem 25).

[1]  S.L. Ho,et al.  Incorporating A Priori Preferences in a Vector PSO Algorithm to Find Arbitrary Fractions of the Pareto Front of Multiobjective Design Problems , 2008, IEEE Transactions on Magnetics.

[2]  J.-L. Coulomb,et al.  TEAM workshop problem 25: a multiobjective analysis , 2004, IEEE Transactions on Magnetics.

[3]  Jean Pierre Brans,et al.  HOW TO SELECT AND HOW TO RANK PROJECTS: THE PROMETHEE METHOD , 1986 .

[4]  P. Ekel.  Fuzzy sets and models of decision making , 2002 .

[5]  Kwang-Jae Kim,et al.  Simultaneous optimization of mechanical properties of steel by maximizing exponential desirability functions , 2000 .

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

[7]  Joseph J. Pignatiello,et al.  STRATEGIES FOR ROBUST MULTIRESPONSE QUALITY ENGINEERING , 1993 .

[8]  R.H.C. Takahashi,et al.  A multiobjective proposal for the TEAM benchmark problem 22 , 2006, IEEE Transactions on Magnetics.

[9]  E. Zavadskas,et al.  Multi‐objective contractor's ranking by applying the Moora method , 2008 .

[10]  R.H.C. Takahashi,et al.  Sensitivity analysis applied to decision making in multiobjective evolutionary optimization , 2006, IEEE Transactions on Magnetics.

[11]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[12]  S. Noguchi,et al.  Selection of an Optimal Solution for Multiobjective Electromagnetic Apparatus Design Based on Game Theory , 2008, IEEE Transactions on Magnetics.

[13]  Dennis K. J. Lin,et al.  Optimization of multiple responses considering both location and dispersion effects , 2006, Eur. J. Oper. Res..

[14]  D.A. Lowther,et al.  Selection of approximation models for electromagnetic device optimization , 2006, IEEE Transactions on Magnetics.

[15]  Nuno Ricardo Costa,et al.  Desirability function approach: A review and performance evaluation in adverse conditions , 2011 .

[16]  Edmundas Kazimieras Zavadskas,et al.  The MOORA method and its application to privatization in a transition economy , 2006 .

[17]  G. Geoffrey Vining,et al.  A Compromise Approach to Multiresponse Optimization , 1998 .

[18]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[19]  K. Héberger,et al.  Consistency of QSAR models: Correct split of training and test sets, ranking of models and performance parameters† , 2015, SAR and QSAR in environmental research.

[20]  K. Héberger.  Sum of ranking differences compares methods or models fairly , 2010 .

[21]  K. Héberger,et al.  Method and model comparison by sum of ranking differences in cases of repeated observations (ties) , 2013 .

[22]  K. Héberger,et al.  Sum of ranking differences for method discrimination and its validation: comparison of ranks with random numbers , 2011 .

[23]  Károly Héberger,et al.  Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods. , 2015, Analytica chimica acta.

[24]  Shankar Chakraborty,et al.  Applications of the MOORA method for decision making in manufacturing environment , 2011 .

[25]  Maria Evelina Mognaschi,et al.  Sorting Pareto solutions: a principle of optimal design for electrical machines , 2009 .

[26]  William T. Scherer,et al.  "The desirability function: underlying assumptions and application implications" , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[27]  Reza Baradaran Kazemzadeh,et al.  PROMETHEE: A comprehensive literature review on methodologies and applications , 2010, Eur. J. Oper. Res..

[28]  David J. Weiss,et al.  SMARTS and SMARTER: Improved Simple Methods for Multiattribute Utility Measurement , 2008 .

[29]  J. Vasconcelos,et al.  The a posteriori decision in multiobjective optimization problems with smarts, promethee II, and a fuzzy algorithm , 2006, IEEE Transactions on Magnetics.

[30]  Stephane Brisset,et al.  Analytical model for the optimal design of a brushless DC wheel motor , 2005 .