Weighted Hypervolume Indicator: Implementation of hypervolume indicators for different weight distribution functions. Using the hypervolume of the dominated portion of the objective space as a measure for the quality of Pareto set approximations has received more and more attention in recent years. So far, the hypervolume indicator is the only measure known in the literature on evolutionary multiobjective optimization that possesses the following two properties. On the one hand, it is sensitive to any type of improvements, i.e., whenever an approximation set A dominates another approximation set B, then the measure yields a strictly better quality value for the former than for the latter set. On the other hand, the hypervolume measure guarantees that any approximation set A that achieves the maximally possible quality value for a particular problem contains all Pareto-optimal objective vectors. With the recently proposed approach of a weighted hypervolume indicator, these properties are not removed by simultaneously be able to incorporate various user preferences. According to [zbt2007a], three different hypervolume based indicators have been developed incorporating the following preferences: Focus on extreme points, Focus on the extremes of the second objective plus one additional extreme point for the first objective, Focus on a given reference point.

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  1. Audet, Charles; Bigeon, Jean; Cartier, Dominique; Le Digabel, Sébastien; Salomon, Ludovic: Performance indicators in multiobjective optimization (2021)
  2. Diaz, Juan Esteban; López-Ibáñez, Manuel: Incorporating decision-maker’s preferences into the automatic configuration of bi-objective optimisation algorithms (2021)
  3. Guerreiro, Andreia P.; Manquinho, Vasco; Figueira, José Rui: Exact hypervolume subset selection through incremental computations (2021)
  4. Araya, Ignacio; Moyano, Mauricio; Sanchez, Cristobal: A beam search algorithm for the biobjective container loading problem (2020)
  5. Guerreiro, Andreia P.; Fonseca, Carlos M.: An analysis of the hypervolume Sharpe-ratio indicator (2020)
  6. Hale, Joshua Q.; Zhu, Helin; Zhou, Enlu: Domination measure: a new metric for solving multiobjective optimization (2020)
  7. Liu, Ruochen; Zhou, Runan; Ren, Rui; Liu, Jiangdi; Jiao, Licheng: Multi-layer interaction preference based multi-objective evolutionary algorithm through decomposition (2020)
  8. Rojas-Gonzalez, Sebastian; van Nieuwenhuyse, Inneke: A survey on kriging-based infill algorithms for multiobjective simulation optimization (2020)
  9. Tang, Weisen; Liu, Hai-Lin; Chen, Lei; Tan, Kay Chen; Cheung, Yiu-ming: Fast hypervolume approximation scheme based on a segmentation strategy (2020)
  10. García-León, Andrés Alberto; Dauzère-Pérès, Stéphane; Mati, Yazid: An efficient Pareto approach for solving the multi-objective flexible job-shop scheduling problem with regular criteria (2019)
  11. Kaucic, Massimiliano: Equity portfolio management with cardinality constraints and risk parity control using multi-objective particle swarm optimization (2019)
  12. Pal, Aritra; Charkhgard, Hadi: A feasibility pump and local search based heuristic for bi-objective pure integer linear programming (2019)
  13. Pal, Aritra; Charkhgard, Hadi: FPBH: a feasibility pump based heuristic for multi-objective mixed integer linear programming (2019)
  14. Dai, Rui; Charkhgard, Hadi: Bi-objective mixed integer linear programming for managing building clusters with a shared electrical energy storage (2018)
  15. Dolgui, A. B.; Eremeev, A. V.; Sigaev, V. S.: Analysis of a multicriterial buffer capacity optimization problem for a production line (2017)
  16. Steponavičė, Ingrida; Hyndman, Rob J.; Smith-Miles, Kate; Villanova, Laura: Dynamic algorithm selection for Pareto optimal set approximation (2017)
  17. Boland, Natashia; Charkhgard, Hadi; Savelsbergh, Martin: The (L)-shape search method for triobjective integer programming (2016)
  18. Martí, Luis; García, Jesús; Berlanga, Antonio; Molina, José M.: MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm (2016)
  19. Steponavičė, Ingrida; Shirazi-Manesh, Mojdeh; Hyndman, Rob J.; Smith-Miles, Kate; Villanova, Laura: On sampling methods for costly multi-objective black-box optimization (2016)
  20. Cao, Yongtao; Smucker, Byran J.; Robinson, Timothy J.: On using the hypervolume indicator to compare Pareto fronts: applications to multi-criteria optimal experimental design (2015)

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