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3 objective problem test cases
Version 3 2018-09-28, 10:03
Version 2 2017-04-25, 12:28
Version 1 2017-04-04, 10:11
dataset
posted on 2018-09-28, 10:03 authored by William PetterssonWilliam PetterssonA set of randomly generated 3 objective knapsack, assignment and travelling salesman problems used to test optimisation algorithms.
These are generated using similar techniques to those of Laumanns et al. (2006) (for knapsack problems), Przybylski et al. (2010) (for assignment problems), and Özpeynirci and Köksalan (2010) (for traveling salesman problems). A knapsack instance is generated by randomly assigned an integer weight (uniformly at random in the range {60, ... , 100}) to each of n items. The upper bound on the total weight of the selected items is set to be half of the total weight of all items. Each objective function is chosen in a similar manner, with the coefficients for each item drawn uniformly
at random from the range {[60, ... , 100}.
Assignment problems are generated in the manner of Przybylski et al. (2010), with objective function coefficients drawn uniformly at random from {0, ... , 20}. We also generate instances of the traveling salesman problem as per Özpeynirci and Köksalan (2010). We place cities on a 1000 × 1000 plane by assigning integer coordinates to cities, and round the Euclidean distance between any two cities to an integer value.
Finally some non-Euclidean traveling salesman problems are generated by assigning distances between towns uniformly at random from {20, ..., 180}. Note that these distances will not satisfy common properties of distances or norms (such as the triangle inequality).
Laumanns M, Thiele L, Zitzler E (2006) An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169(3):932 – 942, ISSN 0377-2217, URL http://dx.doi.org/http://dx.doi.org/10.1016/j.ejor.2004.08.029.
Przybylski A, Gandibleux X, Ehrgott M (2010) A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discrete Optimization 7(3):149 – 165, ISSN 1572-5286, URL http://dx.doi.org/https://doi.org/10.1016/j.disopt.2010.03.005.
Özpeynirci O, Köksalan M (2010) An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs. Management Science 56(12):2302–2315, URL http://dx.doi.org/10.1287/mnsc.1100.1248.
These use an extended LP file format where multiple objectives are defined as additional constraints after the original problem's constraints. The right-hand-side value of the last constraint defines the number of objectives.
These are generated using similar techniques to those of Laumanns et al. (2006) (for knapsack problems), Przybylski et al. (2010) (for assignment problems), and Özpeynirci and Köksalan (2010) (for traveling salesman problems). A knapsack instance is generated by randomly assigned an integer weight (uniformly at random in the range {60, ... , 100}) to each of n items. The upper bound on the total weight of the selected items is set to be half of the total weight of all items. Each objective function is chosen in a similar manner, with the coefficients for each item drawn uniformly
at random from the range {[60, ... , 100}.
Assignment problems are generated in the manner of Przybylski et al. (2010), with objective function coefficients drawn uniformly at random from {0, ... , 20}. We also generate instances of the traveling salesman problem as per Özpeynirci and Köksalan (2010). We place cities on a 1000 × 1000 plane by assigning integer coordinates to cities, and round the Euclidean distance between any two cities to an integer value.
Finally some non-Euclidean traveling salesman problems are generated by assigning distances between towns uniformly at random from {20, ..., 180}. Note that these distances will not satisfy common properties of distances or norms (such as the triangle inequality).
Laumanns M, Thiele L, Zitzler E (2006) An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169(3):932 – 942, ISSN 0377-2217, URL http://dx.doi.org/http://dx.doi.org/10.1016/j.ejor.2004.08.029.
Przybylski A, Gandibleux X, Ehrgott M (2010) A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discrete Optimization 7(3):149 – 165, ISSN 1572-5286, URL http://dx.doi.org/https://doi.org/10.1016/j.disopt.2010.03.005.
Özpeynirci O, Köksalan M (2010) An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs. Management Science 56(12):2302–2315, URL http://dx.doi.org/10.1287/mnsc.1100.1248.
These use an extended LP file format where multiple objectives are defined as additional constraints after the original problem's constraints. The right-hand-side value of the last constraint defines the number of objectives.
