$I_{\rm SDE}$ +—An Indicator for Multi and Many-Objective Optimization

In this letter, an efficient indicator for multi and many-objective optimization is proposed. The proposed indicator (<inline-formula> <tex-math notation="LaTeX">$I_{{SDE}}$ </tex-math></inline-formula><sup>+</sup>) is a combination of sum of objectives and shift-based density estimation and benefits from their ability to promote convergence and diversity, respectively. An evolutionary multiobjective optimization framework based on the proposed indicator is shown to perform comparably or better than the state-of-the-art on a variety of scalable benchmark problems.

[1]  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.

[2]  Xin Yao,et al.  Stochastic Ranking Algorithm for Many-Objective Optimization Based on Multiple Indicators , 2016, IEEE Transactions on Evolutionary Computation.

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

[4]  Rammohan Mallipeddi,et al.  Pareto Dominance-Based Algorithms With Ranking Methods for Many-Objective Optimization , 2017, IEEE Access.

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

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

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

[8]  Carlos A. Coello Coello,et al.  Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization , 2015, GECCO.

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

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

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

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

[13]  Shengxiang Yang,et al.  Bi-goal evolution for many-objective optimization problems , 2015, Artif. Intell..

[14]  Tobias Friedrich,et al.  Approximation quality of the hypervolume indicator , 2013, Artif. Intell..

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

[16]  Markus Wagner,et al.  A fast approximation-guided evolutionary multi-objective algorithm , 2013, GECCO '13.

[17]  Ponnuthurai N. Suganthan,et al.  Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection , 2010, Inf. Sci..

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

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

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