Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

By Miqing Li, Shengxiang Yang, Xiaohui Liu. IEEE Transactions on Evolutionary Computation, 2014

658 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3ed79f273ccc1f8622299cdbfd7f2b0f922ff2a7

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In Computational Theory and Mathematics

1. Yaochu Jin
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3. Ran Cheng
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5. Gary G. Yen
6. Yanan Sun
7. Markus Olhofer
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In Management Science and Operations Research

1. Yaochu Jin
2. Xing-yi Zhang
3. Ye Tian
4. Ran Cheng
5. Gary G. Yen
6. Yanan Sun
7. Markus Olhofer
8. Zhang Yi

In Statistics and Probability

1. Yaochu Jin
2. Hisao Ishibuchi
3. Ye Tian
4. Xing-yi Zhang
5. Xin Yao
6. Bernhard Sendhoff
7. Ran Cheng
8. Markus Olhofer

Citations in the corpus

• A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization (2017, background): “It has been shown that Pareto-based MOEAs, such as nondominated sorting genetic algorithm II (NSGA-II) [17], the improved strength Pareto evolutionary algorithm (SPEA2) [19], the Pareto archived evolution strategy [20], and Pareto envelope-based selection algorithm II (PESAII) [21] encountered diffi”
• A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization (2018, background): “Despite that NSGA-II/SDR performs fairly well on MaOPs, it is known that the crowding distance is ineffective in solving MaOPs [55].”
• Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers (2016, methodology): “For SDE, the version SPEA2 + SDE is used here as it achieves the best overall performance among the three considered versions (NSGA-II + SDE, SPEA2 + SDE, and PESA-II + SDE) in [25].”
• Evolutionary Multi-Objective Workflow Scheduling in Cloud (2016, neutral): “The goals of the scheduling problem (W,S) are given as follows. minimize F = (makespan, cost)T , makespan = FT(Texit), cost = ∑ Ii∈I∗ charge(M0,Type(Ii), Ii), (8) where I∗ = {Ii | ∃Tk ∈ T : Ins(Tk) = Ii}, (9) and FT(Ti) is the finish time of task Ti.”
• An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition (2015, background): “In [52], a shift-based density estimation strategy is proposed to assign high density values to the poorly converged solutions by putting them into crowded areas.”
• Localized Weighted Sum Method for Many-Objective Optimization (2018, background): “, -dominancebased algorithm (DEA) [6] shift-density-based evolutionary algorithm (SDEA) [7], grid-based evolutionary algorithm (GrEA) [8] and 2) Performance indicator based, e.”
• Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization (2020, methodology): “There are also methods which do not belong to the above three categories, such as the objective reduction [24], the shift-based density estimation [25], the two-archive strategy [26], the boundary elimination selection [27] and the knee-point driven MOEAs [28].”
• A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization (2016, methodology): “In fact, numerous of studies [23], [29], [60] relating to many-objective optimization, where IGD is used as the quality indicator, failed to indicate how they sampled those points along the PF.”
• IGD Indicator-Based Evolutionary Algorithm for Many-Objective Optimization Problems (2018, methodology): “In [28], a modification of density estimation, termed as shift-based density estimation, was proposed to make the dominance comparison better suited for solving MaOPs.”
• A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization (2016, methodology): “In [25], a shift-based density estimation strategy is proposed to penalize poorly converged solution s by assigning them a high density value in addition to dominance comparison.”
• Many-Objective Evolutionary Algorithms (2015, methodology): “The goal of optimizing a MaOP, descriptively defined as follows, is the same as that of optimizing a general MOP [Li et al. 2014]: Definition 2.5 ( Goal of optimizing an MaOP ) .”
• PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] (2017, methodology): “MOEA/IGD-NS [36] 2016 Multi-objective evolutionary algorithm based on an enhanced inverted generational distance metric Many-Objective Genetic Algorithms HypE [37] 2011 Hypervolume-based estimation algorithm PICEA-g [38] 2013 Preference-inspired coevolutionary algorithm with goals GrEA [39] 2013 Gri”
• A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization (2017, methodology): “3) SPEA2+SDE6 [32]: This method introduces a density estimator that considers both distribution and convergence information of individuals to increase the selection pressure in many-objective optimization.”
• Efficient Large-Scale Multiobjective Optimization Based on a Competitive Swarm Optimizer (2020, methodology): “To begin with, the fitness of each particle in the current population P is calculated, which adopts the shift based density estimation (SDE) strategy [50].”