The Measure of Pareto Optima

By Mark A. Fleischer. International Conference on Evolutionary Multi-Criterion Optimization, 2003

495 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d2e2a4f8e64aeb9405f647e69218933d2ec97645

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Yaochu Jin
2. Xing-yi Zhang
3. Ran Cheng
4. Ye Tian
5. Xin Yao
6. Gary G. Yen
7. Shengxiang Yang
8. Hisao Ishibuchi

In Control and Systems Engineering

1. Anne Auger
2. Xin Yao
3. Lothar Thiele
4. Eckart Zitzler
5. Simon Huband
6. Johannes Bader
7. Philip Hingston
8. L. Barone

In Statistics and Probability

1. Johannes Bader
2. Eckart Zitzler
3. Xin Yao
4. Lothar Thiele
5. Simon Huband
6. Bo Zhang
7. Philip Hingston
8. L. Barone

Citations in the corpus

• A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization (2016, background): “It has been indicated that maximizing the hypervolume indicator is equivalent to finding the PF [40].”
• A faster algorithm for calculating hypervolume (2006, methodology): “A survey of papers from the proceedings of the CEC 2003 reveals that the great majority of authors who considered more than two objectives studied problems with only three or four objectives, and none studied problems with more than 12 objectives.”
• The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration (2007, background): “On the one hand, the hypervolume indicator is meanwhile among the most popular measures for the performance assessment of multiobjective optimizers and in this context it has been subject to several theoretical investigations [8, 5, 23, 15].”
• HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization (2011, unknown): “However, this changed with the advent of theoretical studies that provided evidence for a unique property of this indicator [23], [46], [17]: it is the only indicator known to be strictly monotonic with respect to Pareto dominance and thereby guaranteeing that the Paretooptimal front achieves the ma”
• Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers (2016, background): “The hypervolume (HV) [1] may be the most popular performance indicator ever adopted due to its nice theoretical properties [29].”
• Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point (2009, background): “They overcome the problems arising with density-based multiobjective evolutionary algorithms [21], since the hyper-volume indicator guarantees strict monotonicity regarding Pareto dominance [11, 28].”
• A Fast Way of Calculating Exact Hypervolumes (2012, background): “Hypervolume captures in one scalar both the closeness of the solutions to the optimal set and their spread across objective space.”