HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization

By Johannes Bader, Eckart Zitzler. Evolutionary Computation, 2011

1,992 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/7b163dc13dc64db8e6f088f766adf0545d9d21ad

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In Artificial Intelligence

1. Yaochu Jin
2. Ran Cheng
3. Xing-yi Zhang
4. Ye Tian
5. Gary G. Yen
6. Yanan Sun
7. Hisao Ishibuchi
8. Handing Wang

In Computational Theory and Mathematics

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

In Management Science and Operations Research

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

Citations in the corpus

• Improved Regularity Model-Based EDA for Many-Objective Optimization (2018, methodology): “(NSGA-III [14], MOEA/D [11], GrEA [13], and HypE [12]) and 2) EDA-based evolutionary algorithm (MBN-EDA [21] and RM-MEDA [20]) are considered as the peer competitors to”
• A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization (2016, methodology): “Since the exact calculation of hypervolume is avoided in HypE, it renders the hypervolume-based search possible in highdimensional objective space to some extent.”
• Consistencies and Contradictions of Performance Metrics in Multiobjective Optimization (2014, methodology): “experiments, we used HV [4], [5], [16], [60], which is the most widely accepted metric in the MOO community, as the baseline to study the relationships among metrics on different geometrical shapes of PFs.”
• 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 tutorial on multiobjective optimization: fundamentals and evolutionary methods (2018, methodology): “The Hypervolume Estimation Algorithm (HypE) (Bader and Zitzler 2011) uses a Monte Carlo Estimation for the hypervolume in high dimensions and thus it can be used for optimization with a high number of objectives (so-called many-objective optimization problems).”
• Stable Matching-Based Selection in Evolutionary Multiobjective Optimization (2014, methodology): “, [7]–[9]); and 3) decompositionbased MOEAs (e.”
• An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions (2017, methodology): “Representative methods include IBEA (Zitzler and Künzli (2004)), SMS-EMOA (Beume et al (2007)), HypE (Bader and Zitzler (2011)), FV-MOEA (Jiang et al (2015)) and so on.”
• Many-Objective Evolutionary Algorithms (2015, background): “The hypervolume indicator is the only metric known to be strictly monotonic to the Pareto dominance [Bader and Zitzler 2011]. This property gives rise to a series of hypervolume-based algorithms, as shown in Table VIII. To maximize the hypervolume value of the solution set, Emmerich et al. [2005] pr”
• Multi-objective training of Generative Adversarial Networks with multiple discriminators (2019, background): “H ( S ) can be understood as the size of the space covered by { F ( x ) | x ∈ S } (Bader & Zitzler, 2011).”
• An easy-to-use real-world multi-objective optimization problem suite (2020, methodology): “We used the performance score [56] to rank EMOAs on each RE problem.”
• An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints (2014, methodology): “Bader and Zitzler [43] have suggested a fast procedure for computing sample-based hyper-volume and devised an algorithm to find a set of trade-off solutions for maximizing the hyper-volume.”
• A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization (2017, methodology): “In other words, HypE, PICEA-g, and SPEA2+SDE use the same population size settings as NSGA-III and SPEA/R. 3) Stopping Criterion and the Number of Executions: Each algorithm was terminated after a prespecified number of generations.”
• Two_Arch2: An Improved Two-Archive Algorithm for Many-Objective Optimization (2015, background): “Therefore, some researchers focus on hypervolume-based MOEAs [20], [21] for ManyOPs, because hypervolume is a metric to evaluate both convergence and diversity [22].”
• A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization (2016, background): “, the indicator based evolutionary a lgorithm (IBEA) [42], the S-metric selection based evolutio nary multi-objective algorithm (SMS-EMOA) [43], a dynamic neighborhood multi-objective evolutionary algorithm bas ed on hypervolume indicator (DNMOEA/HI) [44], and the fast hypervolume based evolutionary”
• Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization (2013, methodology): “There is evidence that the approach can be effective for many-objective problems [27].”