An adaptive decomposition-based evolutionary algorithm for many-objective optimization

Abstract Penalty boundary intersection (PBI) is one popular method in decomposition based evolutionary multi-objective algorithms, where the penalty factor is crucial for striking a balance between convergence and diversity in a high-dimensional objective space. Meanwhile, the distribution of the obtained solutions highly depends on the setting of the weight vectors. This paper proposes an adaptive decomposition-based evolutionary algorithm for many-objective optimization, which introduces one adaptation mechanism for PBI-based decomposition and the other for adjusting the weight vector. The former assigns a specific penalty factor for each subproblem by using the distribution information of both population and the weight vectors, while the latter adjusts the weight vectors based on the objective ranges to handle problems with different scales on the objectives. We have compared the proposed algorithm with seven state-of-the-art many-objective evolutionary algorithms on a number of benchmark problems. The empirical results demonstrate the superiority of the proposed algorithm.

[1]  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.

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

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

[4]  José M. Molina López,et al.  Effective Evolutionary Algorithms for Many-Specifications Attainment: Application to Air Traffic Control Tracking Filters , 2009, IEEE Transactions on Evolutionary Computation.

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

[6]  Hisao Ishibuchi,et al.  Simultaneous use of different scalarizing functions in MOEA/D , 2010, GECCO '10.

[7]  J. Dennis,et al.  A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems , 1997 .

[8]  Michael G. Epitropakis,et al.  Progressive preference articulation for decision making in multi-objective optimisation problems , 2017, Integr. Comput. Aided Eng..

[9]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[10]  Hisao Ishibuchi,et al.  Adaptation of Scalarizing Functions in MOEA/D: An Adaptive Scalarizing Function-Based Multiobjective Evolutionary Algorithm , 2009, EMO.

[11]  Fang Liu,et al.  MOEA/D with Adaptive Weight Adjustment , 2014, Evolutionary Computation.

[12]  Hisao Ishibuchi,et al.  Use of Piecewise Linear and Nonlinear Scalarizing Functions in MOEA/D , 2016, PPSN.

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

[14]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

[15]  Ye Tian,et al.  A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

[16]  H. Scheffé.  Experiments with Mixtures , 1958 .

[17]  Hiroyuki Sato,et al.  Inverted PBI in MOEA/D and its impact on the search performance on multi and many-objective optimization , 2014, GECCO.

[18]  Jun Zhang,et al.  Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algorithms , 2014, IEEE Transactions on Evolutionary Computation.

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

[20]  Xin Yao,et al.  Nadir point estimation for many-objective optimization problems based on emphasized critical regions , 2017, Soft Comput..

[21]  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.

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

[23]  Li Li,et al.  An improved decomposition-based multiobjective evolutionary algorithm with a better balance of convergence and diversity , 2017, Appl. Soft Comput..

[24]  Shengxiang Yang,et al.  Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes , 2017, Soft Comput..

[25]  Markus Olhofer,et al.  A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges , 2017, Complex & Intelligent Systems.

[26]  Qingfu Zhang,et al.  Decomposition-Based Algorithms Using Pareto Adaptive Scalarizing Methods , 2016, IEEE Transactions on Evolutionary Computation.

[27]  Mark Fleischer,et al.  The measure of pareto optima: Applications to multi-objective metaheuristics , 2003 .

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

[29]  Ferrante Neri,et al.  Covariance matrix adaptation pareto archived evolution strategy with hypervolume-sorted adaptive grid algorithm , 2016, Integr. Comput. Aided Eng..

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

[31]  Ye Tian,et al.  An Efficient Approach to Nondominated Sorting for Evolutionary Multiobjective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[32]  Carlos A. Coello Coello,et al.  MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator , 2013, 2013 IEEE Congress on Evolutionary Computation.

[33]  Peter J. Fleming,et al.  Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

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

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

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

[37]  Frederico G. Guimarães,et al.  A comparison of dominance criteria in many-objective optimization problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[38]  Ferrante Neri,et al.  A fast hypervolume driven selection mechanism for many-objective optimisation problems , 2017, Swarm Evol. Comput..

[39]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

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

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

[42]  Peter J. Fleming,et al.  Generalized decomposition and cross entropy methods for many-objective optimization , 2014, Inf. Sci..

[43]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[44]  Min Wei,et al.  Integrated Dual-Production Mode Modeling and Multiobjective Optimization of an Industrial Continuous Catalytic Naphtha Reforming Process , 2016 .

[45]  Xin Yao,et al.  A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[46]  Ye Tian,et al.  An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility , 2018, IEEE Transactions on Evolutionary Computation.

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

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

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