@inproceedings{48857,
  abstract     = {{While finding minimum-cost spanning trees (MST) in undirected graphs is solvable in polynomial time, the multi-criteria minimum spanning tree problem (mcMST) is NP-hard. Interestingly, the mcMST problem has not been in focus of evolutionary computation research for a long period of time, although, its relevance for real world problems is easy to see. The available and most notable approaches by Zhou and Gen as well as by Knowles and Corne concentrate on solution encoding and on fairly dated selection mechanisms. In this work, we revisit the mcMST and focus on the mutation operators as exploratory components of evolutionary algorithms neglected so far. We investigate optimal solution characteristics to discuss current mutation strategies, identify shortcomings of these operators, and propose a sub-tree based operator which offers what we term Pareto-beneficial behavior: ensuring convergence and diversity at the same time. The operator is empirically evaluated inside modern standard evolutionary meta-heuristics for multi-criteria optimization and compared to hitherto applied mutation operators in the context of mcMST.}},
  author       = {{Bossek, Jakob and Grimme, Christian}},
  booktitle    = {{2017 IEEE Symposium Series on Computational Intelligence (SSCI)}},
  keywords     = {{Convergence, Encoding, Euclidean distance, Evolutionary computation, Heating systems, Optimization, Standards}},
  pages        = {{1–8}},
  title        = {{{A Pareto-Beneficial Sub-Tree Mutation for the Multi-Criteria Minimum Spanning Tree Problem}}},
  doi          = {{10.1109/SSCI.2017.8285183}},
  year         = {{2017}},
}

@article{11870,
  abstract     = {{We derive a class of computationally inexpensive linear dimension reduction criteria by introducing a weighted variant of the well-known K-class Fisher criterion associated with linear discriminant analysis (LDA). It can be seen that LDA weights contributions of individual class pairs according to the Euclidean distance of the respective class means. We generalize upon LDA by introducing a different weighting function}},
  author       = {{Loog, M. and Duin, R.P.W. and Haeb-Umbach, Reinhold}},
  journal      = {{IEEE Transactions on Pattern Analysis and Machine Intelligence}},
  keywords     = {{approximate pairwise accuracy, Bayes error, Bayes methods, error statistics, Euclidean distance, Fisher criterion, linear dimension reduction, linear discriminant analysis, pattern classification, statistical analysis, statistical pattern classification, weighting function}},
  number       = {{7}},
  pages        = {{762--766}},
  title        = {{{Multiclass linear dimension reduction by weighted pairwise Fisher criteria}}},
  doi          = {{10.1109/34.935849}},
  volume       = {{23}},
  year         = {{2001}},
}