An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints

Having developed multiobjective optimization algorithms using evolutionary optimization methods and demonstrated their niche on various practical problems involving mostly two and three objectives, there is now a growing need for developing evolutionary multiobjective optimization (EMO) algorithms for handling many-objective (having four or more objectives) optimization problems. In this paper, we recognize a few recent efforts and discuss a number of viable directions for developing a potential EMO algorithm for solving many-objective optimization problems. Thereafter, we suggest a reference-point-based many-objective evolutionary algorithm following NSGA-II framework (we call it NSGA-III) that emphasizes population members that are nondominated, yet close to a set of supplied reference points. The proposed NSGA-III is applied to a number of many-objective test problems with three to 15 objectives and compared with two versions of a recently suggested EMO algorithm (MOEA/D). While each of the two MOEA/D methods works well on different classes of problems, the proposed NSGA-III is found to produce satisfactory results on all problems considered in this paper. This paper presents results on unconstrained problems, and the sequel paper considers constrained and other specialties in handling many-objective optimization problems.

[1]  Lishan Kang,et al.  A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

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

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

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

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

[7]  Kalyanmoy Deb,et al.  Handling many-objective problems using an improved NSGA-II procedure , 2012, 2012 IEEE Congress on Evolutionary Computation.

[8]  Eckart Zitzler,et al.  Dimensionality Reduction in Multiobjective Optimization: The Minimum Objective Subset Problem , 2006, OR.

[9]  Hiroyuki Sato,et al.  Pareto Partial Dominance MOEA in Many-Objective Optimization , 2009 .

[10]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO '06.

[11]  Aimin Zhou,et al.  A Multiobjective Evolutionary Algorithm Based on Decomposition and Preselection , 2015, BIC-TA.

[12]  Kalyanmoy Deb,et al.  Toward an Estimation of Nadir Objective Vector Using a Hybrid of Evolutionary and Local Search Approaches , 2010, IEEE Transactions on Evolutionary Computation.

[13]  Carlos A. Coello Coello,et al.  Ranking Methods for Many-Objective Optimization , 2009, MICAI.

[14]  Gabriele Eichfelder,et al.  Optimal Elements in Vector Optimization with a Variable Ordering Structure , 2011, J. Optim. Theory Appl..

[15]  Tapabrata Ray,et al.  A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems , 2011, IEEE Transactions on Evolutionary Computation.

[16]  Qingfu Zhang,et al.  Approximating the Set of Pareto-Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm , 2009, IEEE Transactions on Evolutionary Computation.

[17]  Qingfu Zhang,et al.  Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms , 2013, IEEE Transactions on Evolutionary Computation.

[18]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[19]  Kalyanmoy Deb,et al.  A Hybrid Framework for Evolutionary Multi-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

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

[21]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[22]  Hirotaka Nakayama,et al.  An application of a multi-objective programming technique to construction accuracy control of cable-stayed bridges , 1995 .

[23]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach , 2014, IEEE Transactions on Evolutionary Computation.

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

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

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

[27]  R. Lyndon While,et al.  A faster algorithm for calculating hypervolume , 2006, IEEE Transactions on Evolutionary Computation.

[28]  Andrzej Jaszkiewicz,et al.  Genetic local search for multi-objective combinatorial optimization , 2022 .

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

[30]  Kiyoshi Tanaka,et al.  Pareto partial dominance MOEA and hybrid archiving strategy included CDAS in many-objective optimization , 2010, IEEE Congress on Evolutionary Computation.

[31]  Lucas Bradstreet,et al.  A Fast Incremental Hypervolume Algorithm , 2008, IEEE Transactions on Evolutionary Computation.

[32]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[33]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[34]  Qingfu Zhang,et al.  MOEA/D with NBI-style Tchebycheff approach for portfolio management , 2010, IEEE Congress on Evolutionary Computation.

[35]  Marco Laumanns,et al.  A Spatial Predator-Prey Approach to Multi-objective Optimization: A Preliminary Study , 1998, PPSN.

[36]  Kalyanmoy Deb,et al.  Faster Hypervolume-Based Search Using Monte Carlo Sampling , 2008, MCDM.

[37]  Patrick M. Reed,et al.  Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework , 2013, Evolutionary Computation.

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

[39]  Carlos A. Coello Coello,et al.  Some techniques to deal with many-objective problems , 2009, GECCO '09.

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

[41]  Qing Li,et al.  Multiobjective optimization for crash safety design of vehicles using stepwise regression model , 2008 .

[42]  Kiyoshi Tanaka,et al.  Many-Objective Optimization by Space Partitioning and Adaptive epsilon-Ranking on MNK-Landscapes , 2009, EMO.

[43]  Kalyanmoy Deb,et al.  Reliability-Based Optimization Using Evolutionary Algorithms , 2009, IEEE Transactions on Evolutionary Computation.

[44]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

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

[46]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[47]  Kalyanmoy Deb,et al.  Approximating a multi-dimensional Pareto front for a land use management problem: A modified MOEA with an epigenetic silencing metaphor , 2012, 2012 IEEE Congress on Evolutionary Computation.

[48]  K. Deb,et al.  On Finding Pareto-Optimal Solutions Through Dimensionality Reduction for Certain Large-Dimensional Multi-Objective Optimization Problems , 2022 .

[49]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

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

[51]  Kalyanmoy Deb,et al.  Towards a Quick Computation of Well-Spread Pareto-Optimal Solutions , 2003, EMO.

[52]  Patrick M. Reed,et al.  Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization , 2012, Evolutionary Computation.

[53]  Peter J. Fleming,et al.  Diversity Management in Evolutionary Many-Objective Optimization , 2011, IEEE Transactions on Evolutionary Computation.

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

[55]  Evan J. Hughes,et al.  Evolutionary many-objective optimisation: many once or one many? , 2005, 2005 IEEE Congress on Evolutionary Computation.

[56]  Xiaodong Li,et al.  A Distance Metric for Evolutionary Many-Objective Optimization Algorithms Using User-Preferences , 2009, Australasian Conference on Artificial Intelligence.

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

[58]  David W. Corne,et al.  Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization , 2007, EMO.

[59]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[60]  Marco Farina,et al.  A fuzzy definition of "optimality" for many-criteria optimization problems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[61]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

[62]  Carlos M. Fonseca,et al.  An Improved Dimension-Sweep Algorithm for the Hypervolume Indicator , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[63]  Mario Köppen,et al.  Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems , 2007, EMO.