# Professor Rhydian Lewis

BSc, PhD, FHEA

Mathematician

- LewisR9@cardiff.ac.uk
- +44 29208 74856
- Abacws, Room 4.55, Senghennydd Road, Cathays, Cardiff, CF24 4AG

- Media commentator
- Available for postgraduate supervision

## Overview

Rhyd Lewis is a professor at the School of Mathematics, Cardiff University. His research interests are operational research, combinatorial optimisation and algorithmic graph theory. He is the author of the book *A Guide to Graph Colouring: Algorithms and Applications* (2021),

### Administrative duties

- Director of Internationals
- Member of Operational Research Group and the Planning and Optimisation Group

### Personal website

## Publication

### 2024

- Lewis, R. and Corcoran, P. 2024. Fast algorithms for computing fixed-length round trips in real-world street networks. SN Computer Science 5(7), article number: 868. (10.1007/s42979-024-03223-3)
- Dijkstra, L., Gagarin, A., Corcoran, P. and Lewis, R. 2024. Digraphs and k-domination models for facility location problems in road networks: Greedy heuristics. Presented at: International Network Optimization Conference 2024, Dublin, Ireland, 11-13 March 2024Proceedings of the 11th International Network Optimization Conference (INOC). OpenProceedings pp. 22-27., (10.48786/inoc.2024.05)
- Hambly, D., Lewis, R. and Corcoran, P. 2024. Determining fixed-length paths in directed and undirected edge-weighted graphs. Presented at: Symposium on Experimental Algorithms (SEA) 2024, Vienna, Austria, 24-26 July 2024.
- Corcoran, P. and Lewis, R. 2024. Optimisation of livestock routing on farms. Computers & Industrial Engineering 188, article number: 109882. (10.1016/j.cie.2024.109882)
- Bonnet, L. and Lewis, R. 2024. Exact bar nesting with industrial symmetry considerations. Presented at: 25e Congres Annuel de la Societe Francaise de Recherche Operationnelle et d'Aide a la Decision, Amiens, France, 4-7 March, 2024.

### 2023

- Lewis, R., Corcoran, P. and Gagarin, A. 2023. Methods for determining cycles of a specific length in undirected graphs with edge weights. Journal of Combinatorial Optimization 46, article number: 29. (10.1007/s10878-023-01091-w)
- Corcoran, P. and Lewis, R. 2023. A navigability entropy model for street networks. Environment and Planning B: Urban Analytics and City Science 50(8), pp. 2171-2186. (10.1177/23998083231170191)
- Lewis, R. 2023. A comparison of Dijkstra's Algorithm using fibonacci heaps, binary heaps, and self-balancing binary trees. [Online]. Preprint repository: ArXiv. Available at: https://arxiv.org/abs/2303.10034

### 2022

- Thiruvady, D. and Lewis, R. 2022. Recombinative approaches for the maximum happy vertices problem. Swarm and Evolutionary Computation 75, article number: 101188. (10.1016/j.swevo.2022.101188)
- Monique, S., Lewis, R. and Thompson, J. 2022. A school bus routing heuristic algorithm allowing heterogeneous fleets and bus stop selection. SN Computer Science 4, article number: 74. (10.1007/s42979-022-01466-6)
- Hawa, A., Lewis, R. and Thompson, J. 2022. Exact and approximate methods for the score-constrained packing problem. European Journal of Operational Research 302(3), pp. 847-859. (10.1016/j.ejor.2022.01.028)
- Carroll, F. and Lewis, R. 2022. Internet security aesthetics: can internet transparency afford social trust?. Presented at: 2022 International Conference on Computer Communications and Networks (ICCCN), 25-28 July 20222022 International Conference on Computer Communications and Networks (ICCCN). IEEE, (10.1109/ICCCN54977.2022.9868880)
- Lewis, R. and Carroll, F. 2022. Exact algorithms for finding fixed-length cycles in edge-weighted graphs. Presented at: 2022 International Conference on Computer Communications and Networks (ICCCN), 25-28 July 20222022 International Conference on Computer Communications and Networks (ICCCN). IEEE, (10.1109/ICCCN54977.2022.9868939)
- Lewis, R. and Corcoran, P. 2022. Finding fixed-length circuits and cycles in undirected edge-weighted graphs: an application with street networks. Journal of Heuristics 28, pp. 259-285. (10.1007/s10732-022-09493-5)

### 2021

- Lewis, R. 2021. DSatur algorithm for graph coloring. [Online]. https://www.geeksforgeeks.org: Geeks for Geeks. Available at: https://www.geeksforgeeks.org/dsatur-algorithm-for-graph-coloring/
- Lewis, R. M. R. 2021. Guide to graph colouring. Texts in Computer Science. Springer, Cham. (10.1007/978-3-030-81054-2)
- Lewis, R. 2021. Finding attractive exercise circuits in street maps. Presented at: 29th Annual GIS Research UK Conference (GISRUK 2021), Cardiff, Wales, 14-16 April 2021. , (10.5281/zenodo.4665508)
- Lewis, R., Thiruvady, D. and Morgan, K. 2021. The maximum happy induced subgraph problem: bounds and algorithms. Computers and Operations Research 126, article number: 105114. (10.1016/j.cor.2020.105114)
- Kheiri, A., Lewis, R., Thompson, J. and Harper, P. 2021. Constructing operating theatre schedules using partitioned graph colouring techniques. Health Systems 10(4), pp. 286-297. (10.1080/20476965.2020.1796530)
- Sciortino, M., Lewis, R. and Thompson, J. 2021. A heuristic algorithm for school bus routing with bus stop selection. Presented at: EvoCOP 2021, Seville, Spain, Apr 2021 Presented at Zarges, C. and Verel, S. eds.Evolutionary Computation in Combinatorial Optimization, Vol. 12692. Lecture Notes in Computer Science/Theoretical Computer Science and General Issues Springer Verlag, (10.1007/978-3-030-72904-2_13)

### 2020

- Thiruvady, D., Lewis, R. and Morgan, K. 2020. Tackling the maximum happy vertices problem in large networks. 4OR: A Quarterly Journal of Operations Research 18, pp. 507-527. (10.1007/s10288-020-00431-4)
- Padungwech, W., Thompson, J. and Lewis, R. 2020. Effects of update frequencies in a dynamic capacitated arc routing problem. Networks 76(4), pp. 522-538. (10.1002/net.21990)
- Lewis, R. 2020. Cite or be damned: some thoughts on reviewer-coerced citation. [Online]. https://scientistsarehumans.com/: Scientists are Humans. Available at: http://rhydlewis.eu/papers/ReviewerCoercedCitation.pdf
- Lewis, R. 2020. Editorial for the special issue on “Algorithms for graphs and networks”. Algorithms 13(11), pp. 292. (10.3390/a13110292)
- Lewis, R. 2020. Algorithms for finding shortest paths in networks with vertex transfer penalties. Algorithms 13(11), article number: 269. (10.3390/a13110269)
- Lewis, R. 2020. A heuristic algorithm for finding attractive fixed-length circuits in street maps. Presented at: International Conference on Computational Logistics, Enschede, The Netherlands, 28–30 Sept 2020Computational Logistics, Vol. 12433. Springer Verlag pp. 384-395., (10.1007/978-3-030-59747-4_25)
- Lewis, R. 2020. A shortest path algorithm for graphs featuring transfer costs at their vertices. Presented at: International Conference on Computational Logistics, Enschede, The Netherlands, 28–30 Sept 2020Computational Logistics, Vol. 12433. Springer Verlag pp. 539-552., (10.1007/978-3-030-59747-4_35)
- Lewis, R., Anderson, T. and Carroll, F. 2020. Can school enrolment and performance be improved by maximizing students' sense of choice in elective subjects?. Journal of Learning Analytics 7(1), pp. 75-87. (10.18608/jla.2020.71.6)
- Lewis, R. 2020. Five degrees of separation from De Niro - charting the social networks of movie stars. The Conversation
- Lewis, R. 2020. Who is the centre of the movie universe? Using python and networkX to analyse the social network of movie stars. [Online]. arXiv. Available at: https://arxiv.org/abs/2002.11103
- Neis, P. and Lewis, R. 2020. Evaluating the influence of parameter setup on the performance of heuristics for the graph colouring problem. International Journal of Metaheuristics 7(4), pp. 352-378.

### 2019

- Lewis, R., Thiruvady, D. and Morgan, K. 2019. Finding happiness: an analysis of the maximum happy vertices problem. Computers and Operations Research 103 (10.1016/j.cor.2018.11.015)
- Lewis, R. 2019. Want to mislead and confuse? use statistics!. [Online]. Scientists are Humans. Available at: http://rhydlewis.eu/papers/statsArticle.pdf

### 2018

- Hawa, A. L., Lewis, R. and Thompson, J. M. 2018. Heuristics for the score-constrained strip-packing problem. Presented at: COCOA 2018: International Conference on Combinatorial Optimization and Applications, Atlanta, GA, USA, 15-17 December 2018 Presented at Kim, D., Uma, R. N. and Zelikovsky, A. eds.Combinatorial Optimization and Applications: 12th International Conference, COCOA 2018, Atlanta, GA, USA, December 15-17, 2018, Proceedings, Vol. 11346. Lecture Notes in Computer Science Springer Verlag pp. 449., (10.1007/978-3-030-04651-4_30)
- Lewis, R. 2018. Two example optimisation problems from the world of education. Presented at: OR Society Annual Conference (OR60), Lancaster, UK, 11-13 Sep 2018.
- Lewis, R. and Smith-Miles, K. 2018. A heuristic algorithm for finding cost-effective solutions to real-world school bus routing problems. Journal of Discrete Algorithms 52-53, pp. 2-17. (10.1016/j.jda.2018.11.001)
- Hardy, B., Lewis, R. and Thompson, J. 2018. Tackling the edge dynamic graph colouring problem with and without future adjacency information. Journal of Heuristics 24, pp. 321-343. (10.1007/s10732-017-9327-z)
- Lewis, R., Smith-Miles, K. and Phillips, K. 2018. The school bus routing problem: An analysis and algorithm. Presented at: IWOCA 2017: 28th International Workshop on Combinatorial Algorithms, Newcastle, NSW, Australia, 17-21 July 2017 Presented at Brankovic, L., Ryan, J. and Smyth, W. F. eds.Combinatorial Algorithms: 28th International Workshop, IWOCA 2017, Newcastle, NSW, Australia, July 17-21, 2017, Revised Selected Papers. Lecture Notes in Computer Science Springer pp. 287-298., (10.1007/978-3-319-78825-8_24)

### 2017

- Lewis, R. and Holborn, P. 2017. How to pack trapezoids: exact and evolutionary algorithms. IEEE Transactions on Evolutionary Computation 21(3), pp. 463-476. (10.1109/TEVC.2016.2609000)

### 2016

- Lewis, R. and Carroll, F. 2016. Creating seating plans: a practical application. Journal of the Operational Research Society 67(11), pp. 1353-1362. (10.1057/jors.2016.34)
- Padungwech, W., Thompson, J. and Lewis, R. 2016. Investigating edge-reordering procedures in a tabu search algorithm for the capacitated arc routing problem. Presented at: HM 2016: International Workshop on Hybrid Metaheuristics, Plymouth, UK, 8-10 June 2016 Presented at Blesa, M. J., Blum, C. and Cangelosi, A. eds.Hybrid Metaheuristics: 10th International Workshop, HM 2016, Plymouth, UK, June 8-10, 2016, Proceedings, Vol. 9668. Lecture Notes in Computer Science Cham: Springer pp. 62-74., (10.1007/978-3-319-39636-1_5)
- Hardy, B., Lewis, R. and Thompson, J. M. 2016. Modifying colourings between time-steps to tackle changes in dynamic random graphs. Presented at: EvoCOP 2016: European Conference on Evolutionary Computation in Combinatorial Optimization, Porto, Portugal, 30 March - 1 April 2016 Presented at Chicano, F., Hu, B. and Garcia-Sanchez, P. eds.Evolutionary Computation in Combinatorial Optimization: 16th European Conference, EvoCOP 2016, Porto, Portugal, March 30 – April 1, 2016, Proceedings, Vol. 9595. Springer pp. 186-201., (10.1007/978-3-319-30698-8_13)
- Lewis, R. 2016. Graph colouring: an ancient problem with modern applications. Impact 3(1), pp. 47-50. (10.1080/2058802X.2016.11963998)
- Kheiri, A., Özcan, E., Lewis, R. and Thompson, J. 2016. A Sequence-based selection hyper-heuristic: a case study in nurse rostering. Presented at: PATAT 2016: 11th International Conference on the Practice and Theory of Automated Timetabling, Udine, Italy, 23-26 August 2016 Presented at Burke, E. K. et al. eds.PATAT 2016: Proceedings of the 11th International Conference of the Practice and Theory of Automated Timetabling. pp. 503-505.

### 2015

- Lewis, R. M. R. 2015. A guide to graph colouring: algorithms and applications. Springer. (10.1007/978-3-319-25730-3)
- Lewis, R. and Thompson, J. 2015. Analysing the effects of solution space connectivity with an effective metaheuristic for the course timetabling problem. European Journal of Operational Research 240(3), pp. 637-648. (10.1016/j.ejor.2014.07.041)
- Lewis, R. 2015. Graph coloring and recombination. In: Kacprzyk, J. and Pedrycz, W. eds. Springer Handbook of Computational Intelligence. Springer, pp. 1239-1254.
- Rowse, E. L., Lewis, R., Harper, P. R. and Thompson, J. M. 2015. Applying set partitioning methods in the construction of operating theatre schedules. Presented at: International Conference on Theory and Practice in Modern Computing 2015, Las Palmas de Gran Canaria, Spain, 22-24 July 2015.

### 2014

- Smith-Miles, K., Baatar, D., Wreford, B. and Lewis, R. 2014. Towards objective measures of algorithm performance across instance space. Computers & Operations Research 45, pp. 12-24. (10.1016/j.cor.2013.11.015)
- John, M. P., Mumford, C. L. and Lewis, R. 2014. An improved multi-objective algorithm for the urban transit routing problem. Presented at: EvoCOP 2014: 14th European Conference on Evolutionary Computation in Combinatorial Optimization, Granada, Spain, 23-25 April 2014 Presented at Blum, C. and Ochoa, G. eds.Evolutionary Computation in Combinatorial Optimisation: 14th European Conference, EvoCOP 2014, Granada, Spain, April 23-25, 2014, Revised Selected Papers, Vol. 8600. Lecture Notes in Computer Science Springer pp. 49-60., (10.1007/978-3-662-44320-0_5)
- Cooper, I., John, M. P., Lewis, R., Mumford, C. L. and Olden, A. 2014. Optimising large scale public transport network design problems using mixed-mode parallel multi-objective evolutionary algorithms. Presented at: IEEE Congress on Evolutionary Computation, Beijing, China, 6 - 11 July 2014Evolutionary Computation (CEC). IEEE pp. 2841-2848., (10.1109/CEC.2014.6900362)

### 2013

- Lewis, R. and Carroll, F. 2013. The "engaged" interaction: important considerations for the HCI design and development of a web application for solving a complex combinatorial optimization problem. World Journal of Computer Application and Technology 1(3), pp. 75-82.

### 2012

- Lewis, R., Thompson, J. M., Mumford, C. L. and Gillard, J. W. 2012. A wide-ranging computational comparison of high-performance graph colouring algorithms. Computers & Operations Research 39(9), pp. 1933-1950. (10.1016/j.cor.2011.08.010)
- Song, X., Lewis, R., Thompson, J. M. and Wu, Y. 2012. An incomplete m-exchange algorithm for solving the large-scale multi-scenario knapsack problem. Computers & Operations Research 39(9), pp. 1988-2000. (10.1016/j.cor.2011.09.012)
- Lewis, R. 2012. A time-dependent metaheuristic algorithm for post enrolment-based course timetabling. Annals of Operations Research 194(1), pp. 273-289. (10.1007/s10479-010-0696-z)
- Holborn, P. L., Thompson, J. M. and Lewis, R. 2012. Combining heuristic and exact methods to solve the vehicle routing problem with pickups, deliveries and time windows. Presented at: EvoCOP 2012: 12th European Conference on Evolutionary Computation in Combinatorial Optimization, Malaga, Spain, 11-13 April 2012 Presented at Hao, J. K. and Middendorf, M. eds.Evolutionary Computation in Combinatorial Optimization: 12th European Conference, EvoCOP 2012, Málaga, Spain, April 11-13, 2012. Proceedings, Vol. 7245. Lecture Notes in Computer Science Springer Verlag pp. 63-74., (10.1007/978-3-642-29124-1_6)

### 2011

- Lewis, R., Song, X., Dowsland, K. A. and Thompson, J. M. 2011. An investigation into two bin packing problems with ordering and orientation implications. European Journal of Operational Research 213(1), pp. 52-65. (10.1016/j.ejor.2011.03.016)
- Lewis, R. and Thompson, J. M. 2011. On the application of graph colouring techniques in round-robin sports scheduling. Computers & Operations Research 38(1), pp. 190-204. (10.1016/j.cor.2010.04.012)
- Lewis, R. and Pullin, E. J. 2011. Revisiting the restricted growth function genetic algorithm for grouping problems. Evolutionary Computation 19(4), pp. 693-704. (10.1162/EVCO_a_00040)

### 2010

- Song, X., Chu, C. B., Lewis, R., Nie, Y. Y. and Thompson, J. M. 2010. A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting. European Journal of Operational Research 202(2), pp. 368-378. (10.1016/j.ejor.2009.05.047)

### 2009

- McCollum, B. et al. 2009. Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition. INFORMS Journal on Computing 22(1), pp. 120-130. (10.1287/ijoc.1090.0320)
- Lewis, R. 2009. A general-purpose hill-climbing method for order independent minimum grouping problems: A case study in graph colouring and bin packing. Computers & Operations Research 36(7), pp. 2295-2310. (10.1016/j.cor.2008.09.004)

### 2007

- Lewis, R., Paechter, B. and McCollum, B. 2007. Post enrolment based course timetabling: a description of the problem model used for track two of the second International Timetabling Competition. Working paper. Cardiff: Cardiff University.
- Lewis, R. and Paechter, B. 2007. Finding feasible timetables using group-based operators. IEEE Transactions on Evolutionary Computation 11(3), pp. 397-413. (10.1109/TEVC.2006.885162)
- Lewis, R. 2007. A survey of metaheuristic-based techniques for university timetabling problems. OR Spectrum 30(1), pp. 167-190. (10.1007/s00291-007-0097-0)
- Lewis, R. 2007. Metaheuristics can solve sudoku puzzles. Journal of Heuristics 13(4), pp. 387-401. (10.1007/s10732-007-9012-8)
- Lewis, R. 2007. On the combination of constraint programming and stochastic search: the Sudoku case. In: Hybrid Metaheuristics. Lecture Notes in Computer Science Vol. 4771. Springer, pp. 96-107., (10.1007/978-3-540-75514-2_8)
- Lewis, R., Paechter, B. and Rossi-Doria, O. 2007. Metaheuristics for university course timetabling. In: Dahal, K. P., Tan, K. C. and Cowling, P. I. eds. Evolutionary Scheduling. Studies in Computational Intelligence Vol. 49. Springer, pp. 237-272., (10.1007/978-3-540-48584-1_9)

### 2005

- Lewis, R. and Paechter, B. 2005. Application of the grouping genetic algorithm to university course timetabling. Lecture Notes in Computer Science 3448, pp. 144-153. (10.1007/978-3-540-31996-2_14)

### Articles

- Lewis, R. and Corcoran, P. 2024. Fast algorithms for computing fixed-length round trips in real-world street networks. SN Computer Science 5(7), article number: 868. (10.1007/s42979-024-03223-3)
- Corcoran, P. and Lewis, R. 2024. Optimisation of livestock routing on farms. Computers & Industrial Engineering 188, article number: 109882. (10.1016/j.cie.2024.109882)
- Lewis, R., Corcoran, P. and Gagarin, A. 2023. Methods for determining cycles of a specific length in undirected graphs with edge weights. Journal of Combinatorial Optimization 46, article number: 29. (10.1007/s10878-023-01091-w)
- Corcoran, P. and Lewis, R. 2023. A navigability entropy model for street networks. Environment and Planning B: Urban Analytics and City Science 50(8), pp. 2171-2186. (10.1177/23998083231170191)
- Thiruvady, D. and Lewis, R. 2022. Recombinative approaches for the maximum happy vertices problem. Swarm and Evolutionary Computation 75, article number: 101188. (10.1016/j.swevo.2022.101188)
- Monique, S., Lewis, R. and Thompson, J. 2022. A school bus routing heuristic algorithm allowing heterogeneous fleets and bus stop selection. SN Computer Science 4, article number: 74. (10.1007/s42979-022-01466-6)
- Hawa, A., Lewis, R. and Thompson, J. 2022. Exact and approximate methods for the score-constrained packing problem. European Journal of Operational Research 302(3), pp. 847-859. (10.1016/j.ejor.2022.01.028)
- Lewis, R. and Corcoran, P. 2022. Finding fixed-length circuits and cycles in undirected edge-weighted graphs: an application with street networks. Journal of Heuristics 28, pp. 259-285. (10.1007/s10732-022-09493-5)
- Lewis, R., Thiruvady, D. and Morgan, K. 2021. The maximum happy induced subgraph problem: bounds and algorithms. Computers and Operations Research 126, article number: 105114. (10.1016/j.cor.2020.105114)
- Kheiri, A., Lewis, R., Thompson, J. and Harper, P. 2021. Constructing operating theatre schedules using partitioned graph colouring techniques. Health Systems 10(4), pp. 286-297. (10.1080/20476965.2020.1796530)
- Thiruvady, D., Lewis, R. and Morgan, K. 2020. Tackling the maximum happy vertices problem in large networks. 4OR: A Quarterly Journal of Operations Research 18, pp. 507-527. (10.1007/s10288-020-00431-4)
- Padungwech, W., Thompson, J. and Lewis, R. 2020. Effects of update frequencies in a dynamic capacitated arc routing problem. Networks 76(4), pp. 522-538. (10.1002/net.21990)
- Lewis, R. 2020. Editorial for the special issue on “Algorithms for graphs and networks”. Algorithms 13(11), pp. 292. (10.3390/a13110292)
- Lewis, R. 2020. Algorithms for finding shortest paths in networks with vertex transfer penalties. Algorithms 13(11), article number: 269. (10.3390/a13110269)
- Lewis, R., Anderson, T. and Carroll, F. 2020. Can school enrolment and performance be improved by maximizing students' sense of choice in elective subjects?. Journal of Learning Analytics 7(1), pp. 75-87. (10.18608/jla.2020.71.6)
- Lewis, R. 2020. Five degrees of separation from De Niro - charting the social networks of movie stars. The Conversation
- Neis, P. and Lewis, R. 2020. Evaluating the influence of parameter setup on the performance of heuristics for the graph colouring problem. International Journal of Metaheuristics 7(4), pp. 352-378.
- Lewis, R., Thiruvady, D. and Morgan, K. 2019. Finding happiness: an analysis of the maximum happy vertices problem. Computers and Operations Research 103 (10.1016/j.cor.2018.11.015)
- Lewis, R. and Smith-Miles, K. 2018. A heuristic algorithm for finding cost-effective solutions to real-world school bus routing problems. Journal of Discrete Algorithms 52-53, pp. 2-17. (10.1016/j.jda.2018.11.001)
- Hardy, B., Lewis, R. and Thompson, J. 2018. Tackling the edge dynamic graph colouring problem with and without future adjacency information. Journal of Heuristics 24, pp. 321-343. (10.1007/s10732-017-9327-z)
- Lewis, R. and Holborn, P. 2017. How to pack trapezoids: exact and evolutionary algorithms. IEEE Transactions on Evolutionary Computation 21(3), pp. 463-476. (10.1109/TEVC.2016.2609000)
- Lewis, R. and Carroll, F. 2016. Creating seating plans: a practical application. Journal of the Operational Research Society 67(11), pp. 1353-1362. (10.1057/jors.2016.34)
- Lewis, R. 2016. Graph colouring: an ancient problem with modern applications. Impact 3(1), pp. 47-50. (10.1080/2058802X.2016.11963998)
- Lewis, R. and Thompson, J. 2015. Analysing the effects of solution space connectivity with an effective metaheuristic for the course timetabling problem. European Journal of Operational Research 240(3), pp. 637-648. (10.1016/j.ejor.2014.07.041)
- Smith-Miles, K., Baatar, D., Wreford, B. and Lewis, R. 2014. Towards objective measures of algorithm performance across instance space. Computers & Operations Research 45, pp. 12-24. (10.1016/j.cor.2013.11.015)
- Lewis, R. and Carroll, F. 2013. The "engaged" interaction: important considerations for the HCI design and development of a web application for solving a complex combinatorial optimization problem. World Journal of Computer Application and Technology 1(3), pp. 75-82.
- Lewis, R., Thompson, J. M., Mumford, C. L. and Gillard, J. W. 2012. A wide-ranging computational comparison of high-performance graph colouring algorithms. Computers & Operations Research 39(9), pp. 1933-1950. (10.1016/j.cor.2011.08.010)
- Song, X., Lewis, R., Thompson, J. M. and Wu, Y. 2012. An incomplete m-exchange algorithm for solving the large-scale multi-scenario knapsack problem. Computers & Operations Research 39(9), pp. 1988-2000. (10.1016/j.cor.2011.09.012)
- Lewis, R. 2012. A time-dependent metaheuristic algorithm for post enrolment-based course timetabling. Annals of Operations Research 194(1), pp. 273-289. (10.1007/s10479-010-0696-z)
- Lewis, R., Song, X., Dowsland, K. A. and Thompson, J. M. 2011. An investigation into two bin packing problems with ordering and orientation implications. European Journal of Operational Research 213(1), pp. 52-65. (10.1016/j.ejor.2011.03.016)
- Lewis, R. and Thompson, J. M. 2011. On the application of graph colouring techniques in round-robin sports scheduling. Computers & Operations Research 38(1), pp. 190-204. (10.1016/j.cor.2010.04.012)
- Lewis, R. and Pullin, E. J. 2011. Revisiting the restricted growth function genetic algorithm for grouping problems. Evolutionary Computation 19(4), pp. 693-704. (10.1162/EVCO_a_00040)
- Song, X., Chu, C. B., Lewis, R., Nie, Y. Y. and Thompson, J. M. 2010. A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting. European Journal of Operational Research 202(2), pp. 368-378. (10.1016/j.ejor.2009.05.047)
- McCollum, B. et al. 2009. Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition. INFORMS Journal on Computing 22(1), pp. 120-130. (10.1287/ijoc.1090.0320)
- Lewis, R. 2009. A general-purpose hill-climbing method for order independent minimum grouping problems: A case study in graph colouring and bin packing. Computers & Operations Research 36(7), pp. 2295-2310. (10.1016/j.cor.2008.09.004)
- Lewis, R. and Paechter, B. 2007. Finding feasible timetables using group-based operators. IEEE Transactions on Evolutionary Computation 11(3), pp. 397-413. (10.1109/TEVC.2006.885162)
- Lewis, R. 2007. A survey of metaheuristic-based techniques for university timetabling problems. OR Spectrum 30(1), pp. 167-190. (10.1007/s00291-007-0097-0)
- Lewis, R. 2007. Metaheuristics can solve sudoku puzzles. Journal of Heuristics 13(4), pp. 387-401. (10.1007/s10732-007-9012-8)
- Lewis, R. and Paechter, B. 2005. Application of the grouping genetic algorithm to university course timetabling. Lecture Notes in Computer Science 3448, pp. 144-153. (10.1007/978-3-540-31996-2_14)

### Book sections

- Lewis, R. 2015. Graph coloring and recombination. In: Kacprzyk, J. and Pedrycz, W. eds. Springer Handbook of Computational Intelligence. Springer, pp. 1239-1254.
- Lewis, R. 2007. On the combination of constraint programming and stochastic search: the Sudoku case. In: Hybrid Metaheuristics. Lecture Notes in Computer Science Vol. 4771. Springer, pp. 96-107., (10.1007/978-3-540-75514-2_8)
- Lewis, R., Paechter, B. and Rossi-Doria, O. 2007. Metaheuristics for university course timetabling. In: Dahal, K. P., Tan, K. C. and Cowling, P. I. eds. Evolutionary Scheduling. Studies in Computational Intelligence Vol. 49. Springer, pp. 237-272., (10.1007/978-3-540-48584-1_9)

### Books

- Lewis, R. M. R. 2021. Guide to graph colouring. Texts in Computer Science. Springer, Cham. (10.1007/978-3-030-81054-2)
- Lewis, R. M. R. 2015. A guide to graph colouring: algorithms and applications. Springer. (10.1007/978-3-319-25730-3)

### Conferences

- Dijkstra, L., Gagarin, A., Corcoran, P. and Lewis, R. 2024. Digraphs and k-domination models for facility location problems in road networks: Greedy heuristics. Presented at: International Network Optimization Conference 2024, Dublin, Ireland, 11-13 March 2024Proceedings of the 11th International Network Optimization Conference (INOC). OpenProceedings pp. 22-27., (10.48786/inoc.2024.05)
- Hambly, D., Lewis, R. and Corcoran, P. 2024. Determining fixed-length paths in directed and undirected edge-weighted graphs. Presented at: Symposium on Experimental Algorithms (SEA) 2024, Vienna, Austria, 24-26 July 2024.
- Bonnet, L. and Lewis, R. 2024. Exact bar nesting with industrial symmetry considerations. Presented at: 25e Congres Annuel de la Societe Francaise de Recherche Operationnelle et d'Aide a la Decision, Amiens, France, 4-7 March, 2024.
- Carroll, F. and Lewis, R. 2022. Internet security aesthetics: can internet transparency afford social trust?. Presented at: 2022 International Conference on Computer Communications and Networks (ICCCN), 25-28 July 20222022 International Conference on Computer Communications and Networks (ICCCN). IEEE, (10.1109/ICCCN54977.2022.9868880)
- Lewis, R. and Carroll, F. 2022. Exact algorithms for finding fixed-length cycles in edge-weighted graphs. Presented at: 2022 International Conference on Computer Communications and Networks (ICCCN), 25-28 July 20222022 International Conference on Computer Communications and Networks (ICCCN). IEEE, (10.1109/ICCCN54977.2022.9868939)
- Lewis, R. 2021. Finding attractive exercise circuits in street maps. Presented at: 29th Annual GIS Research UK Conference (GISRUK 2021), Cardiff, Wales, 14-16 April 2021. , (10.5281/zenodo.4665508)
- Sciortino, M., Lewis, R. and Thompson, J. 2021. A heuristic algorithm for school bus routing with bus stop selection. Presented at: EvoCOP 2021, Seville, Spain, Apr 2021 Presented at Zarges, C. and Verel, S. eds.Evolutionary Computation in Combinatorial Optimization, Vol. 12692. Lecture Notes in Computer Science/Theoretical Computer Science and General Issues Springer Verlag, (10.1007/978-3-030-72904-2_13)
- Lewis, R. 2020. A heuristic algorithm for finding attractive fixed-length circuits in street maps. Presented at: International Conference on Computational Logistics, Enschede, The Netherlands, 28–30 Sept 2020Computational Logistics, Vol. 12433. Springer Verlag pp. 384-395., (10.1007/978-3-030-59747-4_25)
- Lewis, R. 2020. A shortest path algorithm for graphs featuring transfer costs at their vertices. Presented at: International Conference on Computational Logistics, Enschede, The Netherlands, 28–30 Sept 2020Computational Logistics, Vol. 12433. Springer Verlag pp. 539-552., (10.1007/978-3-030-59747-4_35)
- Hawa, A. L., Lewis, R. and Thompson, J. M. 2018. Heuristics for the score-constrained strip-packing problem. Presented at: COCOA 2018: International Conference on Combinatorial Optimization and Applications, Atlanta, GA, USA, 15-17 December 2018 Presented at Kim, D., Uma, R. N. and Zelikovsky, A. eds.Combinatorial Optimization and Applications: 12th International Conference, COCOA 2018, Atlanta, GA, USA, December 15-17, 2018, Proceedings, Vol. 11346. Lecture Notes in Computer Science Springer Verlag pp. 449., (10.1007/978-3-030-04651-4_30)
- Lewis, R. 2018. Two example optimisation problems from the world of education. Presented at: OR Society Annual Conference (OR60), Lancaster, UK, 11-13 Sep 2018.
- Lewis, R., Smith-Miles, K. and Phillips, K. 2018. The school bus routing problem: An analysis and algorithm. Presented at: IWOCA 2017: 28th International Workshop on Combinatorial Algorithms, Newcastle, NSW, Australia, 17-21 July 2017 Presented at Brankovic, L., Ryan, J. and Smyth, W. F. eds.Combinatorial Algorithms: 28th International Workshop, IWOCA 2017, Newcastle, NSW, Australia, July 17-21, 2017, Revised Selected Papers. Lecture Notes in Computer Science Springer pp. 287-298., (10.1007/978-3-319-78825-8_24)
- Padungwech, W., Thompson, J. and Lewis, R. 2016. Investigating edge-reordering procedures in a tabu search algorithm for the capacitated arc routing problem. Presented at: HM 2016: International Workshop on Hybrid Metaheuristics, Plymouth, UK, 8-10 June 2016 Presented at Blesa, M. J., Blum, C. and Cangelosi, A. eds.Hybrid Metaheuristics: 10th International Workshop, HM 2016, Plymouth, UK, June 8-10, 2016, Proceedings, Vol. 9668. Lecture Notes in Computer Science Cham: Springer pp. 62-74., (10.1007/978-3-319-39636-1_5)
- Hardy, B., Lewis, R. and Thompson, J. M. 2016. Modifying colourings between time-steps to tackle changes in dynamic random graphs. Presented at: EvoCOP 2016: European Conference on Evolutionary Computation in Combinatorial Optimization, Porto, Portugal, 30 March - 1 April 2016 Presented at Chicano, F., Hu, B. and Garcia-Sanchez, P. eds.Evolutionary Computation in Combinatorial Optimization: 16th European Conference, EvoCOP 2016, Porto, Portugal, March 30 – April 1, 2016, Proceedings, Vol. 9595. Springer pp. 186-201., (10.1007/978-3-319-30698-8_13)
- Kheiri, A., Özcan, E., Lewis, R. and Thompson, J. 2016. A Sequence-based selection hyper-heuristic: a case study in nurse rostering. Presented at: PATAT 2016: 11th International Conference on the Practice and Theory of Automated Timetabling, Udine, Italy, 23-26 August 2016 Presented at Burke, E. K. et al. eds.PATAT 2016: Proceedings of the 11th International Conference of the Practice and Theory of Automated Timetabling. pp. 503-505.
- Rowse, E. L., Lewis, R., Harper, P. R. and Thompson, J. M. 2015. Applying set partitioning methods in the construction of operating theatre schedules. Presented at: International Conference on Theory and Practice in Modern Computing 2015, Las Palmas de Gran Canaria, Spain, 22-24 July 2015.
- John, M. P., Mumford, C. L. and Lewis, R. 2014. An improved multi-objective algorithm for the urban transit routing problem. Presented at: EvoCOP 2014: 14th European Conference on Evolutionary Computation in Combinatorial Optimization, Granada, Spain, 23-25 April 2014 Presented at Blum, C. and Ochoa, G. eds.Evolutionary Computation in Combinatorial Optimisation: 14th European Conference, EvoCOP 2014, Granada, Spain, April 23-25, 2014, Revised Selected Papers, Vol. 8600. Lecture Notes in Computer Science Springer pp. 49-60., (10.1007/978-3-662-44320-0_5)
- Cooper, I., John, M. P., Lewis, R., Mumford, C. L. and Olden, A. 2014. Optimising large scale public transport network design problems using mixed-mode parallel multi-objective evolutionary algorithms. Presented at: IEEE Congress on Evolutionary Computation, Beijing, China, 6 - 11 July 2014Evolutionary Computation (CEC). IEEE pp. 2841-2848., (10.1109/CEC.2014.6900362)
- Holborn, P. L., Thompson, J. M. and Lewis, R. 2012. Combining heuristic and exact methods to solve the vehicle routing problem with pickups, deliveries and time windows. Presented at: EvoCOP 2012: 12th European Conference on Evolutionary Computation in Combinatorial Optimization, Malaga, Spain, 11-13 April 2012 Presented at Hao, J. K. and Middendorf, M. eds.Evolutionary Computation in Combinatorial Optimization: 12th European Conference, EvoCOP 2012, Málaga, Spain, April 11-13, 2012. Proceedings, Vol. 7245. Lecture Notes in Computer Science Springer Verlag pp. 63-74., (10.1007/978-3-642-29124-1_6)

### Monographs

- Lewis, R., Paechter, B. and McCollum, B. 2007. Post enrolment based course timetabling: a description of the problem model used for track two of the second International Timetabling Competition. Working paper. Cardiff: Cardiff University.

### Websites

- Lewis, R. 2023. A comparison of Dijkstra's Algorithm using fibonacci heaps, binary heaps, and self-balancing binary trees. [Online]. Preprint repository: ArXiv. Available at: https://arxiv.org/abs/2303.10034
- Lewis, R. 2021. DSatur algorithm for graph coloring. [Online]. https://www.geeksforgeeks.org: Geeks for Geeks. Available at: https://www.geeksforgeeks.org/dsatur-algorithm-for-graph-coloring/
- Lewis, R. 2020. Cite or be damned: some thoughts on reviewer-coerced citation. [Online]. https://scientistsarehumans.com/: Scientists are Humans. Available at: http://rhydlewis.eu/papers/ReviewerCoercedCitation.pdf
- Lewis, R. 2020. Who is the centre of the movie universe? Using python and networkX to analyse the social network of movie stars. [Online]. arXiv. Available at: https://arxiv.org/abs/2002.11103
- Lewis, R. 2019. Want to mislead and confuse? use statistics!. [Online]. Scientists are Humans. Available at: http://rhydlewis.eu/papers/statsArticle.pdf

- Lewis, R., Corcoran, P. and Gagarin, A. 2023. Methods for determining cycles of a specific length in undirected graphs with edge weights. Journal of Combinatorial Optimization 46, article number: 29. (10.1007/s10878-023-01091-w)
- Thiruvady, D. and Lewis, R. 2022. Recombinative approaches for the maximum happy vertices problem. Swarm and Evolutionary Computation 75, article number: 101188. (10.1016/j.swevo.2022.101188)
- Hawa, A., Lewis, R. and Thompson, J. 2022. Exact and approximate methods for the score-constrained packing problem. European Journal of Operational Research 302(3), pp. 847-859. (10.1016/j.ejor.2022.01.028)
- Lewis, R. and Corcoran, P. 2022. Finding fixed-length circuits and cycles in undirected edge-weighted graphs: an application with street networks. Journal of Heuristics 28, pp. 259-285. (10.1007/s10732-022-09493-5)
- Lewis, R. M. R. 2021. Guide to graph colouring. Texts in Computer Science. Springer, Cham. (10.1007/978-3-030-81054-2)
- Lewis, R., Thiruvady, D. and Morgan, K. 2021. The maximum happy induced subgraph problem: bounds and algorithms. Computers and Operations Research 126, article number: 105114. (10.1016/j.cor.2020.105114)
- Lewis, R. 2020. Algorithms for finding shortest paths in networks with vertex transfer penalties. Algorithms 13(11), article number: 269. (10.3390/a13110269)

## Research

Rhyd Lewis's research interests include:

- Algorithmic graph theory;
- Combinatorial optimisation;
- Graph colouring;
- Metaheuristics and integer programming;
- Vehicle routing and arc routing;
- Shortest path algorithms;
- School bus routing;
- Automated timetabling and related problems;
- Grouping and partitioning problems;
- Operating theatre scheduling;
- Sports scheduling;
- Solving Latin square and Sudoku problems;
- Bin-packing, trapezoid (trapezium) packing, and the equal-piles problem.

Find out more about his research and download resources at his personal website.

### Research group

## Teaching

### Undergraduate

- MA2760 Mathematical Investigations in Python
- MA3602 Algorithms and Heuristics

### Postgraduate

- MAT004 Computational Methods

Rhyd Lewis is a fellow of the Higher Education Academy.

## Biography

Rhyd Lewis is a professor in mathematics. He is the author of the book A Guide to Graph Colouring: Algorithms and Applications. He has a PhD from Edinburgh Napier University (2006), and a BSc (hons) in Computer Science from Swansea University (2002).

### Professional memberships

- Fellow of the Higher Education Academy

### Academic positions

- 2023 - Present: Personal Chair, School of Mathematics, Cardiff University
- 2019 - 2023: Reader, School of Mathematics, Cardiff University
- 2015 - 2019: Senior Lecturer, School of Mathematics, Cardiff University
- 2008 - 2015: Lecturer, School of Mathematics, Cardiff University
- 2006 - 2008: Lecturer, Cardiff Business School, Cardiff University
- 2003 - 2006: Postgraduate Demonstrator, School of Computing, Edinburgh Napier University
- 2003 - 2006: Postgraduate Researcher, School of Computing, Edinburgh Napier University

### Committees and reviewing

- Associate Editor, International Journal of Metaheuristics.
- Guest editor, Special Issue on Algorithms for Graphs and Networks,
*Algorithms,*2020. - Programme commitee member for:
- Evolutionary Computation in Combinatorial Optimisation (EVOCOP).
- Practice and Theory of Automated Timetabling conference (PATAT).
- Genetic and Evolutionary Computation Conference (GECCO).

## Supervisions

I am interested in supervising PhD students in the areas of:

- Combinatorial optimisation
- Algorithmic graph theory
- Graph colouring;
- Packing, scheduling, and timetabling problems
- Transportation and navigation problems
- Network analysis

### Current supervision

## Monique Sciortino

Research student

## Daniel Hambly

Graduate Demonstrator

## Lukas Dijkstra

Graduate Tutor

### Past projects

• Hawa, A. (2020) "Exact and evolutionary algorithms for the score-constrained packing problem".

• Hardy, B. (2018) "Heuristic methods for colouring dynamic random graphs".

• Padungwech, W. (2018) "Heuristic algorithms for dynamic capacitated arc routing".

• John, M. (2016) "Metaheuristics for designing efficient routes and schedules for urban transportation networks".

• Rowse, E. (2015) "Robust optimisation of operating theatre schedules".

• Holborn, P. (2013) "Heuristics for dynamic vehicle routing problems with pickups and deliveries and time windows".

• Taylor, L. (2013) "Local search methods for the post enrolment-based course timetabling problem".

## Research themes

## Specialisms

- Combinatorics and discrete mathematics
- Applied statistics
- Programming languages
- graph theory