Navigation in multiobjective optimization methods

Building on previous work of the authors, this paper formally defines and reviews the first approach, referred to as navigation, towards a common understanding of search and decision making strategies to identify the most preferred solution among the Pareto set for a multiobjective optimization problem. In navigation methods, the decision maker interactively learns about the problem, while the decision support system learns about the preferences of the decision maker. This work introduces a detailed view on navigation leading to the identification of integral components and features. A number of different existing navigation methods are reviewed and characterized. Finally, an overview of applications involving navigation is given, and promising future research directions are discussed.

[1]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[2]  Fernando Alonso,et al.  Intensity-modulated radiotherapy – a large scale multi-criteria programming problem , 2003, OR Spectr..

[3]  Stacey L. Faulkenberg,et al.  On the quality of discrete representations in multiple objective programming , 2010 .

[4]  J. Gower,et al.  Methods for statistical data analysis of multivariate observations , 1977, A Wiley publication in applied statistics.

[5]  P. Kall.  STOCHASTIC LINEAR PROGRAMMING Models , Theory , and Computation , 2013 .

[6]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[7]  Martin Josef Geiger,et al.  On the Interactive Resolution of Multi-objective Vehicle Routing Problems , 2006, EMO.

[8]  Matthias Ehrgott,et al.  Interactive decision support in radiation therapy treatment planning , 2011, OR Spectr..

[9]  Garrison W. Greenwood,et al.  Fitness Functions for Multiple Objective Optimization Problems: Combining Preferences with Pareto Rankings , 1996, FOGA.

[10]  Fernando Alonso,et al.  A new concept for interactive radiotherapy planning with multicriteria optimization: first clinical evaluation. , 2007, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[11]  Li Chen,et al.  Survey of Preference Elicitation Methods , 2004 .

[12]  Tolio. Tullio,et al.  Design of Flexible Production Systems , 2009 .

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

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

[15]  Joshua D. Knowles,et al.  Efficient discovery of anti-inflammatory small molecule combinations using evolutionary computing , 2011, Nature chemical biology.

[16]  Nicolas Jozefowiez,et al.  Multi-objective vehicle routing problems , 2008, Eur. J. Oper. Res..

[17]  Evangelos Triantaphyllou,et al.  Multi-criteria Decision Making Methods: A Comparative Study , 2000 .

[18]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[19]  Jürgen Branke,et al.  Using Choquet integral as preference model in interactive evolutionary multiobjective optimization , 2016, Eur. J. Oper. Res..

[20]  Martin Josef Geiger,et al.  Interactive Utility Maximization in Multi-Objective Vehicle Routing Problems: A "Decision Maker in the Loop"-Approach , 2007, 2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making.

[21]  Peter J. Fleming,et al.  Many-Objective Optimization: An Engineering Design Perspective , 2005, EMO.

[22]  Pekka Korhonen,et al.  A pareto race , 1988 .

[23]  Kaisa Miettinen,et al.  Optimal control of cooling process in continuous casting of steel using a visualization-based multi-criteria approach , 2005 .

[24]  Joshua D. Knowles,et al.  On Handling Ephemeral Resource Constraints in Evolutionary Search , 2013, Evolutionary Computation.

[25]  Kathrin Klamroth,et al.  Pareto navigator for interactive nonlinear multiobjective optimization , 2010, OR Spectr..

[26]  Kaisa Miettinen,et al.  Survey of methods to visualize alternatives in multiple criteria decision making problems , 2012, OR Spectrum.

[27]  Pekka Korhonen,et al.  Solving generalized goal programming problems using a visual interactive approach , 1986 .

[28]  Daniel M. Johnson,et al.  Effective affective user interface design in games , 2003, Ergonomics.

[29]  Roman Neruda,et al.  Aggregate meta-models for evolutionary multiobjective and many-objective optimization , 2013, Neurocomputing.

[30]  Jürgen Branke,et al.  Consideration of Partial User Preferences in Evolutionary Multiobjective Optimization , 2008, Multiobjective Optimization.

[31]  Jürgen Branke,et al.  Learning Value Functions in Interactive Evolutionary Multiobjective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[32]  Kaisa Miettinen,et al.  E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method , 2015, Eur. J. Oper. Res..

[33]  Kaisa Miettinen,et al.  PAINT: Pareto front interpolation for nonlinear multiobjective optimization , 2012, Comput. Optim. Appl..

[34]  Adrian Thompson,et al.  Hardware evolution - automatic design of electronic circuits in reconfigurable hardware by artificial evolution , 1999, CPHC/BCS distinguished dissertations.

[35]  George E. P. Box,et al.  Evolutionary Operation: a Method for Increasing Industrial Productivity , 1957 .

[36]  Kaisa Miettinen,et al.  NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point , 2010, Eur. J. Oper. Res..

[37]  Joshua D. Knowles,et al.  Multiobjective optimization: When objectives exhibit non-uniform latencies , 2015, Eur. J. Oper. Res..

[38]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[39]  Horst W. Hamacher,et al.  Mathematical optimization in intensity modulated radiation therapy , 2008, 4OR.

[40]  Xavier Gandibleux,et al.  RECIFE: A MCDSS for Railway Capacity Evaluation , 2008, MCDM.

[41]  Kalyanmoy Deb,et al.  A review of hybrid evolutionary multiple criteria decision making methods , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[42]  Aurelien Merel.  Evaluation biobjectif de la capacité d'infrastructures ferroviaires par génération de colonnes hybride. (Biobjective evaluation of railway infrastructure's capacity with hybrid column generation) , 2012 .

[43]  Kaisa Miettinen,et al.  An Interactive Evolutionary Multiobjective Optimization Method: Interactive WASF-GA , 2015, EMO.

[44]  Margaret M. Wiecek,et al.  Generating equidistant representations in biobjective programming , 2012, Comput. Optim. Appl..

[45]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[46]  Xavier Delorme.  Modélisation et résolution de problèmes liés à l'exploitation d'infrastructures ferroviaires , 2003 .

[47]  Daniel A. Keim,et al.  Visual Analytics , 2009, Encyclopedia of Database Systems.

[48]  Ben Shneiderman,et al.  Designing the User Interface: Strategies for Effective Human-Computer Interaction , 1998 .

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

[50]  Pekka Korhonen,et al.  A Visual Interactive Method for Solving the Multiple-Criteria Problem , 1986 .

[51]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[52]  Xavier Gandibleux,et al.  Stability evaluation of a railway timetable at station level , 2009, Eur. J. Oper. Res..

[53]  Joshua D. Knowles.  Closed-loop evolutionary multiobjective optimization , 2009, IEEE Computational Intelligence Magazine.

[54]  Yaochu Jin,et al.  Surrogate-assisted evolutionary computation: Recent advances and future challenges , 2011, Swarm Evol. Comput..

[55]  Joshua D. Knowles,et al.  An Evolutionary Approach to Multiobjective Clustering , 2007, IEEE Transactions on Evolutionary Computation.

[56]  Vincent T'Kindt,et al.  An Ant Colony Optimisation Algorithm for the Set Packing Problem , 2004, ANTS Workshop.

[57]  Ingo Rechenberg,et al.  Case studies in evolutionary experimentation and computation , 2000 .

[58]  Behnam Malakooti,et al.  Clustering and selection of multiple criteria alternatives using unsupervised and supervised neural networks , 2000, J. Intell. Manuf..

[59]  Markku Kuula,et al.  Selecting a flexible manufacturing system using multiple criteria analysis , 1991 .

[60]  F. B. Vernadat,et al.  Decisions with Multiple Objectives: Preferences and Value Tradeoffs , 1994 .

[61]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[62]  Hisao Ishibuchi,et al.  Behavior of Evolutionary Many-Objective Optimization , 2008, Tenth International Conference on Computer Modeling and Simulation (uksim 2008).

[63]  Joshua D. Knowles,et al.  Closed-loop, multiobjective optimization of analytical instrumentation: gas chromatography/time-of-flight mass spectrometry of the metabolomes of human serum and of yeast fermentations. , 2005, Analytical chemistry.

[64]  Serpil Sayin,et al.  Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming , 2000, Math. Program..

[65]  O. M. Shir.  Niching in derandomized evolution strategies and its applications in quantum control , 2008 .

[66]  Pekka Korhonen,et al.  Quadratic Pareto Race , 1997 .

[67]  Suzanne S Farid,et al.  Process economics of industrial monoclonal antibody manufacture. , 2007, Journal of chromatography. B, Analytical technologies in the biomedical and life sciences.

[68]  Inman Harvey,et al.  Evolutionary robotics: the Sussex approach , 1997, Robotics Auton. Syst..

[69]  K. Miettinen,et al.  Interactive bundle-based method for nondifferentiable multiobjeective optimization: nimbus § , 1995 .

[70]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

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

[72]  J. Branke,et al.  Interactive evolutionary multiobjective optimization driven by robust ordinal regression , 2010 .