A benchmark test suite for evolutionary many-objective optimization

In the real world, it is not uncommon to face an optimization problem with more than three objectives. Such problems, called many-objective optimization problems (MaOPs), pose great challenges to the area of evolutionary computation. The failure of conventional Pareto-based multi-objective evolutionary algorithms in dealing with MaOPs motivates various new approaches. However, in contrast to the rapid development of algorithm design, performance investigation and comparison of algorithms have received little attention. Several test problem suites which were designed for multi-objective optimization have still been dominantly used in many-objective optimization. In this paper, we carefully select (or modify) 15 test problems with diverse properties to construct a benchmark test suite, aiming to promote the research of evolutionary many-objective optimization (EMaO) via suggesting a set of test problems with a good representation of various real-world scenarios. Also, an open-source software platform with a user-friendly GUI is provided to facilitate the experimental execution and data observation.

[1]  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.

[2]  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.

[3]  Markus Olhofer,et al.  Test Problems for Large-Scale Multiobjective and Many-Objective Optimization , 2017, IEEE Transactions on Cybernetics.

[4]  Shengxiang Yang,et al.  The Supplement of the Paper “ Multi-Line Distance Minimization : A Visualized Many-Objective Test Problem Suite ” , 2017 .

[5]  Hisao Ishibuchi,et al.  Pareto Fronts of Many-Objective Degenerate Test Problems , 2016, IEEE Transactions on Evolutionary Computation.

[6]  Xin Yao,et al.  Many-Objective Evolutionary Algorithms , 2015, ACM Comput. Surv..

[7]  Ye Tian,et al.  PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.

[8]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.

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

[10]  Ye Tian,et al.  A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

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

[12]  Xin Yao,et al.  Two_Arch2: An Improved Two-Archive Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

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

[14]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

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

[16]  Shengxiang Yang,et al.  A test problem for visual investigation of high-dimensional multi-objective search , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[17]  Qingfu Zhang,et al.  Framework for Many-Objective Test Problems with Both Simple and Complicated Pareto-Set Shapes , 2011, EMO.

[18]  Hisao Ishibuchi,et al.  Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space , 2010, PPSN.

[19]  Shengxiang Yang,et al.  Pareto or Non-Pareto: Bi-Criterion Evolution in Multiobjective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[20]  Kaname Narukawa,et al.  Adaptive Reference Vector Generation for Inverse Model Based Evolutionary Multiobjective Optimization with Degenerate and Disconnected Pareto Fronts , 2015, EMO.

[21]  Shengxiang Yang,et al.  A Grid-Based Evolutionary Algorithm for Many-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

[22]  Hisao Ishibuchi,et al.  Common properties of scalable multiobjective problems and a new framework of test problems , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[23]  Yiu-ming Cheung,et al.  Objective Extraction for Many-Objective Optimization Problems: Algorithm and Test Problems , 2016, IEEE Transactions on Evolutionary Computation.

[24]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[25]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

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