An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach

By Himanshu Jain, Kalyanmoy Deb. IEEE Transactions on Evolutionary Computation, 2014

1,967 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/20041765de0014194d9d76dd26f86f2b8bacaa6a

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Citations in the corpus

• Handling Constrained Multiobjective Optimization Problems With Constraints in Both the Decision and Objective Spaces (2019, methodology): “Most of current arti-ficial CMOPs belong to this category, including CTPs [8], C-DTLZ [14], DAS-CMOPs [16], and NCTPs [15].”
• Pymoo: Multi-Objective Optimization in Python (2020, background): “For instance, a Steady-State NSGA-II [34] can be initialized by setting the number of offspring NSGA-II [12] RNSGA-II [14] NSGA-III [10, 26, 4] UNSGA-III [43] RNSGA-III [47] MOEAD [52] to 1 .”
• From evolutionary computation to the evolution of things (2015, background): “Having proven highly successful for finding solutions to problems with multiple objectives (typically up to ten) 76 , the community is now making rapid advances in the field of many objectives – moving way beyond the capabilities of other algorithms 77,78,79 .”
• A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization (2016, methodology): “To begin with, the constraint violation function suggested in [81] is adopted to evaluate the degree of violation of a candidate solution:”
• Two-Archive Evolutionary Algorithm for Constrained Multiobjective Optimization (2017, methodology): “Let us first consider a test problem C1-DTLZ3 defined in [15], where the objective functions are the same as the”
• Evolutionary Constrained Multiobjective Optimization: Test Suite Construction and Performance Comparisons (2019, background): “Remark 2: To the best of our knowledge, over 80 research papers have focused on solving current artificial test problems (e.g., CTPs, CFs, and C-DTLZs) during the past two decades.”
• PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] (2017, methodology): “UF1–UF12 [81] 2008 Unconstrained multi-objective test problems for the CEC 2009 special session and competition F1–F9 for MOEA/D-DE [18] 2009 The test problems extended from [82] designed for MOEA/D-DE C1 DTLZ1, C2 DTLL2, C3 DTLZ4 2014 Constrained DTLZ and IDTLZ1, IDTLZ2 [41] inverted DTLZ F1–F7 for”
• Many-Objective Evolutionary Algorithms (2015, methodology): “Some adaptive variants of NSGA-III are also proposed and obtain better distributions of solutions [Jain and Deb 2013, 2014].”
• Test Problems for Large-Scale Multiobjective and Many-Objective Optimization (2017, background): “In [24], som e constrained DTLZ problems have been suggested to verify the constraint handling capability of MOEAs.”
• Localized Weighted Sum Method for Many-Objective Optimization (2018, neutral): “adaptive weights [38]–[42].”
• An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility (2018, methodology): “IDTLZ1, IDTLZ2 [45], WFG1–WFG9 [52], MaF2, MaF4, MaF13 [57], and Pareto-Box problem [58], where the relevant settings are given in Table I.”
• A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization (2017, background): “frequently used to evaluate the performance of MOEAs for MaOPs [7], [8], [23], [56], etc.”
• A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling (2015, background): “Actually, such MOPs may cause general difficulties for all MOEAs relying on predefined reference vectors or reference points in the objective space [77].”
• Multiobjective Multifactorial Optimization in Evolutionary Multitasking (2017, background): “Some popular examples of multiobjective evolutionary algorithms (MOEAs) commonly in use today include nondominated sorting genetic algorithm (NSGA-II) [11], NSGA-III [12], [13], SPEA2 [14], MOEA/D [15]–[17], and indicator-based MOEAs [18].”
• A Decomposition-Based Evolutionary Algorithm for Many Objective Optimization (2015, methodology): “DBEA-Eps relied on the use of an adaptive epsilon level comparison to avoid aggregation, whereas a scaling based on axis intercepts similar to the scheme introduced in [37] was used to deal with objectives in different orders of magnitude.”
• Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes (2017, methodology): “This was demonstrated by Jain & Deb [44] for NSGA-III on the three-objective and fiveobjective inverted DTLZ1 problems.”