This document illustrates the data used in the paper [1] which was published by EJOR. - Folder "RadiotherapyMOLP" contains three multi-objective linear programmes associated with beam intensity optimisation problem arising in the planning of radiotherapy treatment of cancer, as described in [1,2]. These three MOLPs (data_AC.mat, data_PR.mat, data_PL.mat) correspond to three clinical cases, an acoustic neuroma (AC), a prostate tumour (PR) and a pancreatic lesion (PL), respectively. The problem description is as follows. min Cx, s.t. Ux <= u, lb <= X <= ub Using the RNBI method to solve these three MOLPs, one can get the following results (see [1]). -------------------------------------- RP IP NP ds CPU -------------------------------------- AC 378 92 92 0.89 27.562 PR 378 148 117 4.64 31.437 PL 378 154 137 3.17 110.736 -------------------------------------- AC 153 42 42 1.36 12.351 PR 153 62 48 7.09 20.684 PL 153 62 56 4.84 52.153 -------------------------------------- - Folder "RandomMOLP" contains sixty randomly generated multi-objective linear programmes with three to eight objectives, as described in [1]. The name "Dim*Points*0Ex#.mat" represents the example # for * objectives. The problem description is as follows. min Px, s.t. Bx <= bb Using the RNBI method to solve these MOLPs, one can get the following results (see [1]). ------------------------------------------------------------- p=n l m RP IP NP ds CPU ------------------------------------------------------------- 3 30 56 78 42.7 40.4 0.1851 0.7811 153 74.8 70.9 0.1364 1.3024 ------------------------------------------------------------- 4 40 195 286 82.4 74.2 0.2613 2.1546 816 202.8 180.9 0.1926 5.9825 ------------------------------------------------------------- 5 50 748 727 85.3 71.4 0.3511 7.3551 3080 293.8 237.5 0.2587 25.1582 ------------------------------------------------------------- 6 60 3041 1378 83.5 63.0 0.4339 16.9257 8723 355.9 251.8 0.3197 131.4911 ------------------------------------------------------------- 7 70 12678 2003 57.3 46.0 0.4988 93.5675 19292 350.3 240.8 0.3675 810.3551 ------------------------------------------------------------- 8 80 53239 2281 41.1 28.7 0.5687 445.2241 34122 259.4 146.7 0.4191 6140.5817 ------------------------------------------------------------- Relevant Papers: [1] L. Shao and M. Ehrgott, "Discrete Representation of Non-dominated Sets in Multi-objective Linear Programming", European Journal of Operational Research. [2] Shao, L. and Ehrgott, M. (2008). Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning. Mathematical Methods of Operations Research, 68(2), 257–276. Citation Request: Use of this dataset in publications must be acknowledged by referencing the following publication: L. Shao and M. Ehrgott, "Discrete Representation of Non-dominated Sets in Multi-objective Linear Programming", European Journal of Operational Research.DOI:10.1016/j.ejor.2016.05.001 For info about this dataset contact: Lizhen Shao: lshao@ustb.edu.cn Matthias Ehrgott: m.ehrgott@lancaster.ac.uk