
<bib>
<comment>
This file was created by the TYPO3 extension publications
--- Timezone: CEST
Creation date: 2026-04-05
Creation time: 00:37:37
--- Number of references
249
</comment>
<reference>
<bibtype>misc</bibtype>
<citeid>prinz2026highperformanceparallelalgorithmmultiobjective</citeid>
<title>A High-Performance Parallel Algorithm for Multi-Objective Integer Optimization</title>
<year>2026</year>
<keywords>DAAD-Port2425</keywords>
<file_url>https://arxiv.org/abs/2602.11872</file_url>
<annotation>submitted</annotation>
<authors>
<person>
<fn>Kathrin</fn>
<sn>Prinz</sn>
</person>
<person>
<fn>Levin</fn>
<sn>Nemesch</sn>
</person>
<person>
<fn>Stefan</fn>
<sn>Ruzika</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>koenen26output</citeid>
<title>Output-sensitive Complexity of Multi-Objective Integer Network Flow Problems</title>
<year>2026</year>
<DOI>10.1007/s10878-025-01376-2</DOI>
<journal>Journal of Combinatorial Optimization</journal>
<volume>51</volume>
<number>14</number>
<authors>
<person>
<fn>David</fn>
<sn>Könen</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>misc</bibtype>
<citeid>yuden26parametric</citeid>
<title>Parametric Biobjective Linear Programming</title>
<status>2</status>
<year>2026</year>
<keywords>DAAD-Port2425</keywords>
<note>submitted to JMCDA</note>
<authors>
<person>
<fn>Kezang</fn>
<sn>Yuden</sn>
</person>
<person>
<fn>Levin</fn>
<sn>Nemesch</sn>
</person>
<person>
<fn>Stefan</fn>
<sn>Ruzika</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>techreport</bibtype>
<citeid>lopes26solving</citeid>
<title>Solving hypervolume scalarizations for MOCO problems</title>
<year>2026</year>
<keywords>DAAD-Port2425</keywords>
<authors>
<person>
<fn>Gonçalo</fn>
<sn>Lopes</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>koenen25supportedness</citeid>
<title>On Supportedness in Multi‐Objective Integer Linear Programming</title>
<year>2025</year>
<month>11</month>
<issn>1099-1360</issn>
<DOI>10.1002/mcda.70024</DOI>
<journal>Journal of Multi-Criteria Decision Analysis</journal>
<volume>32</volume>
<publisher>Wiley</publisher>
<number>3</number>
<authors>
<person>
<fn>David</fn>
<sn>Könen</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>LOPES2025107140</citeid>
<title>A greedy hypervolume polychotomic scheme for multiobjective combinatorial optimization</title>
<abstract>The usual goal in multiobjective combinatorial optimization is to find the complete set of nondominated points. However, in general, the nondominated set may be too large to be enumerated under a tight time budget. In these cases, it is preferable to rapidly obtain a concise representation of the nondominated set that satisfies a given property of interest. This work describes a generic greedy approach to compute a representation of the nondominated set for multiobjective combinatorial optimization problems that approximately maximizes the dominated hypervolume. The representation is built iteratively by solving a sequence of hypervolume scalarized problems, each of which with respect to k reference points, which is a parameter of our approach. We present a mixed-integer formulation of the hypervolume scalarization function for k reference points as well as a combinatorial branch-and-bound for the m-objective knapsack problem. We empirically analyse the functional relationship between k and its running-time and representation quality. Our results indicate that the branch-and-bound is a much more efficient approach and that increasing k does not directly translate into much better representation quality.</abstract>
<year>2025</year>
<issn>0305-0548</issn>
<DOI>https://doi.org/10.1016/j.cor.2025.107140</DOI>
<journal>Computers & Operations Research</journal>
<volume>183</volume>
<pages>107140</pages>
<keywords>DAAD-Port2425</keywords>
<file_url>https://www.sciencedirect.com/science/article/pii/S0305054825001686</file_url>
<authors>
<person>
<fn>Gonçalo</fn>
<sn>Lopes</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<title>A Space Mapping approach for the calibration of financial models with the application to the Heston model</title>
<year>2025</year>
<DOI>10.48550/arXiv.2501.14521</DOI>
<web_url>arXiv:2501.14521</web_url>
<authors>
<person>
<fn>A.</fn>
<sn>Clevenhaus</sn>
</person>
<person>
<fn>C.</fn>
<sn>Totzeck</sn>
</person>
<person>
<fn>M.</fn>
<sn>Ehrhardt</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>gaul25tight</citeid>
<title>A Tight Formulation for the Dial-a-Ride Problem</title>
<year>2025</year>
<issn>0377-2217</issn>
<DOI>10.1016/j.ejor.2024.09.028</DOI>
<journal>European Journal of Operational Research</journal>
<volume>321</volume>
<pages>363-382</pages>
<number>2</number>
<keywords>Optimization and Control (math.OC), Discrete Mathematics (cs.DM), FOS: Mathematics, FOS: Mathematics, FOS: Computer and information sciences, FOS: Computer and information sciences</keywords>
<authors>
<person>
<fn>Daniela</fn>
<sn>Gaul</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Christian</fn>
<sn>Pfeiffer</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
<person>
<fn>Arne</fn>
<sn>Schulz</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>inproceedings</bibtype>
<citeid>bauss23adapting</citeid>
<title>Adapting Branching and Queuing for Multi-objective Branch and Bound</title>
<year>2025</year>
<DOI>10.1007/978-3-031-58405-3_68</DOI>
<booktitle>Operations Research Proceedings 2023. OR 2023. Lecture Notes in Operations Research</booktitle>
<publisher>Springer, Cham</publisher>
<editor>Voigt, G., Fliedner, M., Haase, K., Brüggemann, W., Hoberg, K., Meissner, J.</editor>
<note>accepted</note>
<authors>
<person>
<fn>Julius</fn>
<sn>Bauß</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>koenen25output</citeid>
<title>An output-polynomial time algorithm to determine all supported efficient solutions for multi-objective integer network flow problems</title>
<type>Article</type>
<year>2025</year>
<issn>0166-218X</issn>
<DOI>10.1016/j.dam.2025.06.001</DOI>
<journal>Discrete Applied Mathematics</journal>
<volume>376</volume>
<publisher>Elsevier BV</publisher>
<pages>1-14</pages>
<authors>
<person>
<fn>David</fn>
<sn>Könen</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>inproceedings</bibtype>
<citeid>hoff:asse:2025</citeid>
<title>Assessing the effectiveness and efficiency of selected solution approaches for two-dimensional stock cutting problems (Part III): Hybrid Approach For Printed Circuit Boards</title>
<status>3</status>
<year>2025</year>
<booktitle>AUTOMATION 2025: Conference on Automation — Innovations and Future Perspectives</booktitle>
<note>To appear</note>
<authors>
<person>
<fn>Leon</fn>
<sn>Hoffe</sn>
</person>
<person>
<fn>Berna</fn>
<sn>Ulutas</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Stefan</fn>
<sn>Bracke</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>AAHR1</citeid>
<title>Asymptotic expansions for generalized Bernstein-Durrmeyer and genuine Bernstein-Durrmeyer operators</title>
<year>2025</year>
<note>submitted</note>
<authors>
<person>
<fn>Ulrich</fn>
<sn>Abel</sn>
</person>
<person>
<fn>Ana Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>clement25con</citeid>
<title>Constructing Optimal Star Discrepancy Sets</title>
<year>2025</year>
<DOI>10.48550/arXiv.2311.17463</DOI>
<journal>accepted in Proceedings of the AMS</journal>
<note>accepted in \textitProceedings of the AMS</note>
<authors>
<person>
<fn>François</fn>
<sn>Clément</sn>
</person>
<person>
<fn>Carola</fn>
<sn>Doerr</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>AAHR2</citeid>
<title>Kernels for composition of positive linear operators</title>
<year>2025</year>
<file_url>https:// doi.org/10.1016/j.jmaa.2025.130052</file_url>
<note>accepted</note>
<authors>
<person>
<fn>Ulrich</fn>
<sn>Abel</sn>
</person>
<person>
<fn>Ana Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>bolt:nonc:2025</citeid>
<title>Non-convex shape optimization by dissipative Hamiltonian flows</title>
<year>2025</year>
<DOI>10.1080/0305215X.2024.2304135</DOI>
<journal>Engineering Optimization</journal>
<volume>57</volume>
<pages>384--403</pages>
<authors>
<person>
<fn>Matthias</fn>
<sn>Bolten</sn>
</person>
<person>
<fn>Onur Tanil</fn>
<sn>Doganay</sn>
</person>
<person>
<fn>Hanno</fn>
<sn>Gottschalk</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>figueira25computational</citeid>
<title>On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial Optimization</title>
<year>2025</year>
<DOI>10.1016/j.orl.2025.107302</DOI>
<journal>Operations Research Letters</journal>
<pages>107302</pages>
<authors>
<person>
<fn>José Rui</fn>
<sn>Figueira</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
<person>
<fn>Julia</fn>
<sn>Sudhoff Santos</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>loehken25multiobjective</citeid>
<title>On the multiobjective cable-trench problem</title>
<year>2025</year>
<DOI>10.1007/s10878-025-01289-0</DOI>
<journal>Journal of Combinatorial Optimization</journal>
<volume>49</volume>
<number>55</number>
<authors>
<person>
<fn>Lara</fn>
<sn>Löhken</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>clem:sear:2025</citeid>
<title>Searching Permutations for Constructing Uniformly Distributed Point Sets</title>
<year>2025</year>
<DOI>10.1073/pnas.2424464122</DOI>
<journal>Proceedings of the National Academy of Sciences</journal>
<volume>122</volume>
<pages>e2424464122</pages>
<number>14</number>
<note>To appear</note>
<authors>
<person>
<fn>François</fn>
<sn>Clément</sn>
</person>
<person>
<fn>Carola</fn>
<sn>Doerr</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>doss:solv:2024</citeid>
<title>Solving the Multiobejctive Quasi-Clique Problem</title>
<year>2025</year>
<DOI>10.1016/j.ejor.2024.12.018</DOI>
<journal>European Journal of Operational Research</journal>
<volume>323</volume>
<pages>409—424</pages>
<authors>
<person>
<fn>Daniela Dos</fn>
<sn>Santos</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Pedro</fn>
<sn>Martins</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>antunes24special</citeid>
<title>Special issue on exact and approximation methods for mixed-integer multi-objective optimization</title>
<year>2024</year>
<month>8</month>
<issn>1432-5217</issn>
<DOI>10.1007/s00186-024-00874-z</DOI>
<journal>Mathematical Methods of Operations Research</journal>
<publisher>Springer Science and Business Media LLC</publisher>
<authors>
<person>
<fn>Carlos Henggeler</fn>
<sn>Antunes</sn>
</person>
<person>
<fn>Carlos M.</fn>
<sn>Fonseca</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>daec:asim:2024</citeid>
<title>A simple,  efficient and versatile objective space algorithm for multiobjective integer programming</title>
<year>2024</year>
<DOI>10.1007/s00186-023-00841-0</DOI>
<journal>Mathematical Methods of Operations Research</journal>
<volume>100</volume>
<pages>351—384</pages>
<tags>DFG-higher</tags>
<note>accepted</note>
<authors>
<person>
<fn>Kerstin</fn>
<sn>Dächert</sn>
</person>
<person>
<fn>Tino</fn>
<sn>Fleuren</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>Abelasymptotic2024</citeid>
<title>Asymptotic expansions for variants of the gamma and Post–Widder operators preserving 1 and x^j</title>
<year>2024</year>
<DOI>10.1002/mma.10217</DOI>
<journal>Mathematical Methods in the Applied Sciences</journal>
<volume>47</volume>
<pages>13718-13733</pages>
<number>18</number>
<authors>
<person>
<fn>Ulrich</fn>
<sn>Abel</sn>
</person>
<person>
<fn>Ana Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>abel2024asymptoticpropertiesgeneralclass</citeid>
<title>Asymptotic properties for a general class of Szász-Mirakjan-Durrmeyer operators</title>
<year>2024</year>
<web_url>https://arxiv.org/abs/2407.16474</web_url>
<authors>
<person>
<fn>Ulrich</fn>
<sn>Abel</sn>
</person>
<person>
<fn>Ana Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>bauss24augmenting</citeid>
<title>Augmenting Biobjective Branch & Bound with Scalarization-Based Information</title>
<year>2024</year>
<DOI>10.1007/s00186-024-00854-3</DOI>
<journal>Mathematical Methods of Operations Research</journal>
<keywords>Optimization and Control (math.OC), FOS: Mathematics</keywords>
<tags>DFG-higher</tags>
<authors>
<person>
<fn>Julius</fn>
<sn>Bauß</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>Bailo2024</citeid>
<title>CBX: Python and Julia Packages for Consensus-Based Interacting Particle Methods</title>
<year>2024</year>
<DOI>10.21105/joss.06611</DOI>
<journal>Journal of Open Source Software</journal>
<volume>9</volume>
<publisher>The Open Journal</publisher>
<pages>6611</pages>
<number>98</number>
<file_url>https://doi.org/10.21105/joss.06611</file_url>
<authors>
<person>
<fn>Rafael</fn>
<sn>Bailo</sn>
</person>
<person>
<fn>Alethea</fn>
<sn>Barbaro</sn>
</person>
<person>
<fn>Susana N.</fn>
<sn>Gomes</sn>
</person>
<person>
<fn>Konstantin</fn>
<sn>Riedl</sn>
</person>
<person>
<fn>Tim</fn>
<sn>Roith</sn>
</person>
<person>
<fn>Claudia</fn>
<sn>Totzeck</sn>
</person>
<person>
<fn>Urbain</fn>
<sn>Vaes</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>abel2024commutativityspectralpropertiesgeneral</citeid>
<title>Commutativity and spectral properties for a general class of Szász-Mirakjan-Durrmeyer operators</title>
<year>2024</year>
<DOI>10.1007/s43036-024-00403-z</DOI>
<journal>Advances in Operator Theory</journal>
<volume>10</volume>
<pages>14</pages>
<number>1</number>
<file_url>https://arxiv.org/abs/2407.21722</file_url>
<authors>
<person>
<fn>Ulrich</fn>
<sn>Abel</sn>
</person>
<person>
<fn>Ana Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>MO-CBO</citeid>
<title>Consensus-Based Optimization for Multi-Objective Problems: A Multi-Swarm Approach</title>
<year>2024</year>
<DOI>10.1007/s10898-024-01369-1</DOI>
<journal>Journal of Global Optimization</journal>
<authors>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
<person>
<fn>Claudia</fn>
<sn>Totzeck</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>Guenther2024</citeid>
<title>Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain</title>
<year>2024</year>
<DOI>https://doi.org/10.1007/s00498-024-00389-2</DOI>
<journal>Math. Control Signals Syst.</journal>
<volume>36</volume>
<pages>957–977</pages>
<authors>
<person>
<fn>M.</fn>
<sn>Günther</sn>
</person>
<person>
<fn>B.</fn>
<sn>Jacob</sn>
</person>
<person>
<fn>C.</fn>
<sn>Totzeck</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>stiglmayr24determining</citeid>
<title>Determining Cost-Efficient Controls of Electrical Energy Storages Using Dynamic Programming</title>
<year>2024</year>
<DOI>10.1186/s13362-024-00140-1</DOI>
<journal>Journal of Mathematics in Industry</journal>
<authors>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
<person>
<fn>Svenja</fn>
<sn>Uhlemeyer</sn>
</person>
<person>
<fn>Björn</fn>
<sn>Uhlemeyer</sn>
</person>
<person>
<fn>Markus</fn>
<sn>Zdrallek</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>techreport</bibtype>
<citeid>Santos24b</citeid>
<title>Ensuring connectedness for the Maximum Quasi-clique and Densest $k$-subgraph problems</title>
<year>2024</year>
<DOI>10.48550/arXiv.2403.08534</DOI>
<school>arXiv</school>
<authors>
<person>
<fn>Daniela Scherer</fn>
<sn>Santos</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Pedro</fn>
<sn>Martins</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>phdthesis</bibtype>
<citeid>gaul24exact</citeid>
<title>Exact and Heuristic Methods for Dial-a-Ride Problems</title>
<type>Dissertation</type>
<year>2024</year>
<DOI>10.25926/BUW/0-303</DOI>
<school>Bergische Universität Wuppertal</school>
<file_url>https://elekpub.bib.uni-wuppertal.de/ubwhs/download/pdf/7539417</file_url>
<authors>
<person>
<fn>Daniela</fn>
<sn>Gaul</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>conference</bibtype>
<citeid>AAHR0</citeid>
<title>Genuine Bernstein-Durrmeyer operators preserving 1 and x^j (II)</title>
<year>2024</year>
<event_name>ATSF 2024</event_name>
<event_place>Ankara, Turkey</event_place>
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<person>
<fn>Carlos M.</fn>
<sn>Fonseca</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<title>A Bernstein-Schnabl type operator</title>
<year>2022</year>
<DOI>10.2298/AADM210714011A</DOI>
<journal>Applicable Analysis and Discrete Mathematics</journal>
<volume>16(2)</volume>
<pages>495-507</pages>
<authors>
<person>
<fn>Ana-Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Madalina</fn>
<sn>Dancs</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
</person>
<person>
<fn>Vlad</fn>
<sn>Paşca</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<title>Branch-and-bound and objective branching with three or more objectives</title>
<abstract>The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the efficient computation of upper and lower bound sets. These bound sets are used as a supplement to the classical dominance test to improve the computational time by imposing inequalities derived from (partial) dominance in the objective space. This process is called objective branching since it is mostly applied when generating child nodes. In this paper, we extend the concept of objective branching to multi-objective integer optimization problems with three or more objective functions. Several difficulties arise in this case, as there is no longer a lexicographic order among non-dominated outcome vectors when there are three or more objectives. We discuss the general concept of objective branching in any number of dimensions and suggest a merging operation of local upper bounds to avoid the generation of redundant sub-problems. Finally, results from extensive experimental studies on several classes of multi-objective optimization problems is reported.</abstract>
<year>2022</year>
<issn>0305-0548</issn>
<DOI>10.1016/j.cor.2022.106012</DOI>
<journal>Computers & Operations Research</journal>
<edition>148</edition>
<volume>148</volume>
<keywords>Multi-objective combinatorial optimization, Multi-objective integer programming, Branch & bound, Objective branching, Bound sets</keywords>
<authors>
<person>
<fn>Nicolas</fn>
<sn>Forget</sn>
</person>
<person>
<fn>Sune Lauth</fn>
<sn>Gadegaard</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Lars Relund</fn>
<sn>Nielsen</sn>
</person>
<person>
<fn>Anthony</fn>
<sn>Przybylski</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>paquete21computing</citeid>
<title>Computing Representations using Hypervolume Scalarizations</title>
<year>2022</year>
<DOI>10.1016/j.cor.2021.105349</DOI>
<journal>Computers and Operations Research</journal>
<volume>137</volume>
<pages>105349</pages>
<authors>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
<person>
<fn>Britta</fn>
<sn>Schulze</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
<person>
<fn>Ana Catarina</fn>
<sn>Lourenço</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>stiglmayr22decision</citeid>
<title>Decision Space Robustness for Multiobjective Integer Linear Programming</title>
<year>2022</year>
<DOI>10.1007/s10479-021-04462-w</DOI>
<journal>Annals of Operations Research</journal>
<volume>319</volume>
<pages>1769--1791</pages>
<file_url>https://www.imacm.uni-wuppertal.de/fileadmin/imacm/preprints/2020/imacm_20_37.pdf</file_url>
<authors>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
<person>
<fn>José Rui</fn>
<sn>Figueira</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Luís</fn>
<sn>Paquete</sn>
</person>
<person>
<fn>Britta</fn>
<sn>Schulze</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>reiners22efficient</citeid>
<title>Efficient and sparse neural networks by pruning weights in a multiobjective learning approach</title>
<year>2022</year>
<DOI>10.1016/j.cor.2021.105676</DOI>
<journal>Computers & Operations Research</journal>
<edition>141</edition>
<pages>105676</pages>
<authors>
<person>
<fn>Malena</fn>
<sn>Reiners</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Fabian</fn>
<sn>Heldmann</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>InfGradCBO</citeid>
<title>Ensemble-based gradient inference for particle methods in optimization and sampling</title>
<year>2022</year>
<DOI>10.48550/arXiv.2209.15420</DOI>
<note>arXiv:2209.15420</note>
<authors>
<person>
<fn>Claudia</fn>
<sn>Schillings</sn>
</person>
<person>
<fn>Claudia</fn>
<sn>Totzeck</sn>
</person>
<person>
<fn>Philipp</fn>
<sn>Wacker</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>gaul21event</citeid>
<title>Event-based MILP models for ridepooling applications</title>
<year>2022</year>
<DOI>10.1016/j.ejor.2021.11.053</DOI>
<journal>European Journal of Operational Research</journal>
<edition>3</edition>
<volume>301</volume>
<pages>1048-1063</pages>
<authors>
<person>
<fn>Daniela</fn>
<sn>Gaul</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>halffmann22MOILPsurvey</citeid>
<title>Exact algorithms for multiobjective linear optimization problems with integer variables - a state of the art survey</title>
<year>2022</year>
<DOI>10.1002/mcda.1780</DOI>
<journal>Journal of Multicriteria Decision Analysis</journal>
<volume>29</volume>
<pages>343–363</pages>
<authors>
<person>
<fn>Pascal</fn>
<sn>Halffmann</sn>
</person>
<person>
<fn>Luca E.</fn>
<sn>Schäfer</sn>
</person>
<person>
<fn>Kerstin</fn>
<sn>Dächert</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Stefan</fn>
<sn>Ruzika</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>KONEN2022333</citeid>
<title>Finding all minimum cost flows and a faster algorithm for the K best flow problem</title>
<abstract>This paper addresses the problem of determining all optimal integer solutions of a linear integer network flow problem, which we call the all optimal integer flow (AOF) problem. We derive an O(F(m+n)+mn+M) time algorithm to determine all F many optimal integer flows in a directed network with n nodes and m arcs, where M is the best time needed to find one minimum cost flow. We remark that stopping Hamacher’s well-known method for the determination of the K best integer flows (Hamacher, 1995) at the first sub-optimal flow results in an algorithm with a running time of O(Fm(nlogn+m)+M) for solving the AOF problem. Our improvement is essentially made possible by replacing the shortest path sub-problem with a more efficient way to determine a so-called proper zero cost cycle using a modified depth-first search technique. As a byproduct, our analysis yields an enhanced algorithm to determine the K best integer flows that runs in O(Kn3+M). Besides, we give lower and upper bounds for the number of all optimal integer and feasible integer solutions. Our bounds are based on the fact that any optimal solution can be obtained by an initial optimal tree solution plus a conical combination of incidence vectors of all induced cycles with bounded coefficients.</abstract>
<year>2022</year>
<issn>0166-218X</issn>
<DOI>10.1016/j.dam.2022.07.007</DOI>
<journal>Discrete Applied Mathematics</journal>
<volume>321</volume>
<pages>333-349</pages>
<keywords>Minimum cost flow, K best network flow, Integer network flow algorithm, All optimal solutions, Combinatorial optimization</keywords>
<authors>
<person>
<fn>David</fn>
<sn>Könen</sn>
</person>
<person>
<fn>Daniel</fn>
<sn>Schmidt</sn>
</person>
<person>
<fn>Christiane</fn>
<sn>Spisla</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>PAMM_2022</citeid>
<title>Modeling Minimum Cost Network Flows With Port-Hamiltonian Systems</title>
<year>2022</year>
<DOI>10.48550/arXiv.2303.13196</DOI>
<journal>PAMM</journal>
<publisher>Wiley</publisher>
<authors>
<person>
<fn>Onur Tanil</fn>
<sn>Doganay</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Bruno</fn>
<sn>Lang</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
<person>
<fn>Claudia</fn>
<sn>Totzeck</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>article</bibtype>
<citeid>PHS-pedestrians</citeid>
<title>Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems</title>
<year>2022</year>
<DOI>10.48550/arXiv.2211.06503</DOI>
<note>arXiv:2211.06503</note>
<authors>
<person>
<fn>Antoine</fn>
<sn>Tordeux</sn>
</person>
<person>
<fn>Claudia</fn>
<sn>Totzeck</sn>
</person>
</authors>
</reference>
<reference>
<bibtype>phdthesis</bibtype>
<citeid>sudhoff22ordinal</citeid>
<title>Ordinal costs in multi-objective combinatorial optimization</title>
<type>Dissertation</type>
<year>2022</year>
<DOI>10.25926/BUW/0-50</DOI>
<school>Bergische Universität Wuppertal</school>
<file_url>https://elekpub.bib.uni-wuppertal.de/ubwhs/download/pdf/7085087</file_url>
<authors>
<person>
<fn>Julia</fn>
<sn>Sudhoff</sn>
</person>
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<reference>
<bibtype>article</bibtype>
<citeid>bolten22tracing</citeid>
<title>Tracing locally Pareto optimal points by numerical integration</title>
<year>2022</year>
<DOI>10.1137/20M1341106</DOI>
<journal>SIAM Journal on Control and Optimization</journal>
<volume>59</volume>
<pages>3302-3328</pages>
<number>5</number>
<authors>
<person>
<fn>Matthias</fn>
<sn>Bolten</sn>
</person>
<person>
<fn>Onur Tanil</fn>
<sn>Doganay</sn>
</person>
<person>
<fn>Hanno</fn>
<sn>Gottschalk</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
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<reference>
<bibtype>article</bibtype>
<citeid>AcuHR2021</citeid>
<title>Voronovskaya type results for special sequences of operators</title>
<year>2022</year>
<DOI>10.1007/s13398-021-01157-6</DOI>
<journal>RACSAM</journal>
<volume>116,19</volume>
<authors>
<person>
<fn>Ana-Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Madalina</fn>
<sn>Dancs</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
</person>
<person>
<fn>Vlad</fn>
<sn>Paşca</sn>
</person>
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<reference>
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<citeid>schnepper20local</citeid>
<title>A Local Analysis to Determine All Optimal Solutions of p-k-max Location Problems on Networks
</title>
<year>2021</year>
<DOI>10.1016/j.dam.2020.05.013</DOI>
<journal>Discrete Applied Mathematics</journal>
<volume>296</volume>
<pages>217-234</pages>
<authors>
<person>
<fn>Teresa</fn>
<sn>Schnepper</sn>
</person>
<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
</person>
<person>
<fn>Justo</fn>
<sn>Puerto</sn>
</person>
<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
</person>
</authors>
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<reference>
<bibtype>phdthesis</bibtype>
<citeid>doganay21biobjective</citeid>
<title>Biobjective shape optimization algorithms enhanced by derivative information</title>
<type>Dissertation</type>
<year>2021</year>
<DOI>10.25926/pfta-7236</DOI>
<school>Bergische Universität Wuppertal</school>
<file_url>https://elekpub.bib.uni-wuppertal.de/ubwhsmig/download/pdf/6249554</file_url>
<authors>
<person>
<fn>Onur Tanil</fn>
<sn>Doganay</sn>
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<reference>
<bibtype>article</bibtype>
<citeid>GAUL2021188</citeid>
<title>Chvátal-Gomory cuts for the Steiner tree problem</title>
<year>2021</year>
<issn>0166-218X</issn>
<DOI>10.1016/j.dam.2020.12.016</DOI>
<journal>Discrete Applied Mathematics</journal>
<volume>291</volume>
<pages>188-200</pages>
<authors>
<person>
<fn>Daniela</fn>
<sn>Gaul</sn>
</person>
<person>
<fn>Daniel R.</fn>
<sn>Schmidt</sn>
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<title>Eigenstructure and iterates for uniquely ergodic Kantorovich modifications of operators II</title>
<year>2021</year>
<DOI>10.1007/s11117-021-00832-7</DOI>
<journal>Positivity</journal>
<volume>25</volume>
<pages>1585-1599</pages>
<authors>
<person>
<fn>Ana-Maria</fn>
<sn>Acu</sn>
</person>
<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
</person>
<person>
<fn>Ioan</fn>
<sn>Raşa</sn>
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<citeid>backhaus20mathematical</citeid>
<title>GivEn - Shape Optimization for Gas Turbines in Volatile Energy Networks</title>
<year>2021</year>
<DOI>10.1007/978-3-030-62732-4_4</DOI>
<booktitle>Mathematical MSO for Power Engineering and Management</booktitle>
<publisher>Springer Berlin/Heidelberg</publisher>
<series>Mathematics in Industry</series>
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<volume>22</volume>
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<number>2</number>
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<fn>Johanna</fn>
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<person>
<fn>Michael</fn>
<sn>Stiglmayr</sn>
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<person>
<fn>Kathrin</fn>
<sn>Klamroth</sn>
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<year>2021</year>
<DOI>10.1007/s11117-020-00773-7</DOI>
<journal>Positivity</journal>
<volume>25</volume>
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<authors>
<person>
<fn>Ana-Maria</fn>
<sn>Acu</sn>
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<person>
<fn>Margareta</fn>
<sn>Heilmann</sn>
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<person>
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<citeid>BurgerPTT2021</citeid>
<title>Mean-field optimal control and optimality conditions in the space of probability measures</title>
<year>2021</year>
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<journal>SIAM Journal of Control and Optimization</journal>
<volume>59</volume>
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<number>2</number>
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<fn>Martin</fn>
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<fn>Oliver</fn>
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<year>2021</year>
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<journal>ESAIM COCV</journal>
<volume>27</volume>
<number>40</number>
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<person>
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<fn>Lisa Maria</fn>
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<journal>Journal of Global Optimization</journal>
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<person>
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<journal>Mathematics of Control, Signals, and Systems</journal>
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<fn>Simone</fn>
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<citeid>stiglmayr21projekt</citeid>
<title>Projekt Ride-Hailing Wuppertal</title>
<year>2021</year>
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<editor>Matthias Ehrhardt and Michael G</editor>
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<status>2</status>
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<fn>Ana-Maria</fn>
<sn>Acu</sn>
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<citeid>gaul21solving</citeid>
<title>Solving the Dynamic Dial-a-Ride Problem Using a Rolling-Horizon Event-Based Graph</title>
<year>2021</year>
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<booktitle>21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)</booktitle>
<volume>96</volume>
<publisher>Schloss Dagstuhl - Leibniz-Zentrum für Informatik</publisher>
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<fn>Daniela</fn>
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