On decomposition methods in interactive user-preference based optimization

Graphical abstractDisplay Omitted HighlightsA model how to combine preference information and the framework of MOEA/D.A new way of generating weight vectors with preference information.Use the ASF function into MOEA/D to reflect preference information.The proposed approaches could deal with many-objective problems well.The desired solutions can be found in different ROIs interactively. Evolutionary multi-objective optimization (EMO) methodologies have been widely applied to find a well-distributed trade-off solutions approximating to the Pareto-optimal front in the past decades. However, integrating the user-preference into the optimization to find the region of interest (ROI) [1] or preferred Pareto-optimal solutions could be more efficient and effective for the decision maker (DM) straightforwardly. In this paper, we propose several methods by combining preference-based strategy (like the reference points) with the decomposition-based multi-objective evolutionary algorithm (MOEA/D) [2], and demonstrate how preferred sets or ROIs near the different reference points specified by the DM can be found simultaneously and interactively. The study is based on the experiments conducted on a set of test problems with objectives ranging from two to fifteen objectives. Experiments have proved that the proposed approaches are more efficient and effective especially on many-objective problems to provide a set of solutions to the DM's preference, so that a better and a more reliable decision can be made.

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

[2]  Kalyanmoy Deb,et al.  Integrating User Preferences into Evolutionary Multi-Objective Optimization , 2005 .

[3]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.

[4]  Kalyanmoy Deb,et al.  Towards estimating nadir objective vector using evolutionary approaches , 2006, GECCO.

[5]  Mario Köppen,et al.  Fuzzy-Pareto-Dominance and its Application in Evolutionary Multi-objective Optimization , 2005, EMO.

[6]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[7]  Kaisa Miettinen,et al.  A Preference Based Interactive Evolutionary Algorithm for Multi-objective Optimization: PIE , 2011, EMO.

[8]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[9]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[10]  Andrzej Jaszkiewicz,et al.  The 'Light Beam Search' approach - an overview of methodology and applications , 1999, Eur. J. Oper. Res..

[11]  Laetitia Vermeulen-Jourdan,et al.  Synergies between operations research and data mining: The emerging use of multi-objective approaches , 2012, Eur. J. Oper. Res..

[12]  Radu Prodan,et al.  A Multi-objective Approach for Workflow Scheduling in Heterogeneous Environments , 2012, 2012 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (ccgrid 2012).

[13]  Carlos A. Coello Coello,et al.  g-dominance: Reference point based dominance for multiobjective metaheuristics , 2009, Eur. J. Oper. Res..

[14]  E. Hughes.  Multiple single objective Pareto sampling , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[15]  Jinhua Zheng,et al.  Decomposing the user-preference in multiobjective optimization , 2016, Soft Comput..

[16]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[17]  A. Tamhane.  Multiple comparisons in model i one-way anova with unequal variances , 1977 .

[18]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[19]  Kalyanmoy Deb,et al.  Multi-objective optimal path planning using elitist non-dominated sorting genetic algorithms , 2012, Soft Computing.

[20]  Qingfu Zhang,et al.  Interactive MOEA/D for multi-objective decision making , 2011, GECCO '11.

[21]  Shengxiang Yang,et al.  Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[22]  M. Farina,et al.  On the optimal solution definition for many-criteria optimization problems , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[23]  A. Wierzbicki.  On the completeness and constructiveness of parametric characterizations to vector optimization problems , 1986 .

[24]  M. Koppen,et al.  A fuzzy scheme for the ranking of multivariate data and its application , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

[25]  Khaled Ghédira,et al.  The r-Dominance: A New Dominance Relation for Interactive Evolutionary Multicriteria Decision Making , 2010, IEEE Transactions on Evolutionary Computation.

[26]  J. Branke,et al.  Guidance in evolutionary multi-objective optimization , 2001 .

[27]  Ian Griffin,et al.  A Comparative Study of Progressive Preference Articulation Techniques for Multiobjective Optimisation , 2007, EMO.

[28]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[29]  Kiyoshi Tanaka,et al.  Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs , 2007, EMO.

[30]  Xiaodong Li,et al.  Reference point based multi-objective optimization through decomposition , 2012, 2012 IEEE Congress on Evolutionary Computation.

[31]  Kalyanmoy Deb,et al.  Light beam search based multi-objective optimization using evolutionary algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

[33]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[34]  Peter J. Fleming,et al.  A Diversity Management Operator for Evolutionary Many-Objective Optimisation , 2009, EMO.

[35]  Gary B. Lamont,et al.  Applications Of Multi-Objective Evolutionary Algorithms , 2004 .

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

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

[38]  Xiaodong Li,et al.  Designing airfoils using a reference point based evolutionary many-objective particle swarm optimization algorithm , 2010, IEEE Congress on Evolutionary Computation.

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

[40]  Kalyanmoy Deb,et al.  Evaluating the -Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions , 2005, Evolutionary Computation.

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

[42]  Jeffrey T. Scruggs,et al.  Multi-objective optimal control of vibratory energy harvesting systems , 2012 .