Finding Knees in Multi-objective Optimization

By J. Branke, Kalyanmoy Deb, Henning Dierolf, Matthias Osswald. Parallel Problem Solving from Nature, 2004

590 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fcf9dacc5ae094b560e36c540c424d0752442179

How researchers see this paper

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

In Artificial Intelligence

1. Yaochu Jin
2. Xing-yi Zhang
3. Ye Tian
4. Ran Cheng
5. Markus Olhofer
6. Kalyanmoy Deb
7. Guo Yu
8. Handing Wang

In Computational Theory and Mathematics

1. Yaochu Jin
2. Xing-yi Zhang
3. Ye Tian
4. Ran Cheng
5. Markus Olhofer
6. Kalyanmoy Deb
7. Guo Yu
8. Gary G. Yen

Citations in the corpus

• Understanding knee points in bicriteria problems and their implications as preferred solution principles (2011, background): “Past studies are reviewed and a couple of new definitions are suggested.”
• Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization (2020, methodology): “Different from [42], [45], here we propose a new structure of the knee combinations and embed them into the stretching Fig.”
• A Method for a Posteriori Identification of Knee Points Based on Solution Density (2018, methodology): “It can be seen that KneeDis completely fails to work on DEB3DK since none of the knee regions have been correctly detected.”
• Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point (2009, background): “Therefore, optimizing the hypervolume indicator stresses so-called knee-points—parts of the Pareto front decision makers believe to be interesting regions [5, 4, 6].”
• A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization (2015, methodology): “[42] proposed two variants of NSGA-II for finding knee regions, where the crowding distance in NSGA-II was substituted by two new measures, an angle based measure and a utility measure.”
• Dynamic multiobjective optimization problems: test cases, approximations, and applications (2004, background): “These approaches not only provide a good idea of the extent (ideal and nadir solutions) of the true POF but also provide information about the shape of the front [1] and existence of any “knee” solution [ 2 ].”
• An Evolutionary Approach to Multiobjective Clustering (2007, background): “1) Motivating Concepts: The identification of promising solutions from Pareto front approximations has been investigated in several recent works [52]–[56].”
• Multiobjective Optimization in Bioinformatics and Computational Biology (2007, background): “Automatic identification of promising solutions from Pareto front approximations has been investigated in several recent works [135], [136], [137], [138], [139].”
• Multi-objective scheduling problems: Determination of pruned Pareto sets (2008, background): “The “knee” (Das, 1999; Branke et al., 2004) region is formed by those solutions of the Pareto-optimal front where a small improvement in one objective would lead to a large deterioration in at least one other objective.”
• Grasshopper optimization algorithm for multi-objective optimization problems (2017, unknown): “In the literature, there are three main approaches for solving multi-objective problems using metaheuristics: a priori [37], a posteriori [38], and interactive [39].”