A note on the exact solution of the minimum squared load assignment problem
The problem of finding a fair assignment of tasks to agents that minimizes the total sum of squared workloads was introduced by Karsu and Azizoglu (2019) as the Minimum Squared Load Assignment Problem (MSLAP). To solve this problem, the authors developed a tailored branch-and-bound algorithm. While...
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| Vydané v: | Computers & operations research Ročník 159; s. 106309 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
01.11.2023
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| ISSN: | 0305-0548 |
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| Abstract | The problem of finding a fair assignment of tasks to agents that minimizes the total sum of squared workloads was introduced by Karsu and Azizoglu (2019) as the Minimum Squared Load Assignment Problem (MSLAP). To solve this problem, the authors developed a tailored branch-and-bound algorithm. While this algorithm was shown to produce better results than CPLEX on a mixed binary linear programming formulation of the MSLAP, about 71% of the 1200 benchmark instances yet remained unsolved. In this note, we test two state-of-the-art solvers on different mathematical programming formulations of the MSLAP. Our computational results show that the performance of the solvers is heavily dependent on the type of mathematical optimization model. The best results are obtained when the MSLAP is expressed as a quadratically-constrained program. Such a formulation allows one of the solvers to find and verify an optimal solution for every problem in the existing benchmark data sets within just a few seconds per problem, on average. Additional experiments on large-sized instances demonstrate that the solvers’ performances remain at a high level.
•The minimum squared load assignment problem is analyzed.•(Mixed) binary linear and nonlinear mathematical programming formulations are presented.•Comprehensive computer experiments with different solvers are conducted.•Optimal solutions for all 1200 problems in the benchmark data sets of Karsu and Azizoglu are found.•New sets of large-sized test problems are generated. |
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| AbstractList | The problem of finding a fair assignment of tasks to agents that minimizes the total sum of squared workloads was introduced by Karsu and Azizoglu (2019) as the Minimum Squared Load Assignment Problem (MSLAP). To solve this problem, the authors developed a tailored branch-and-bound algorithm. While this algorithm was shown to produce better results than CPLEX on a mixed binary linear programming formulation of the MSLAP, about 71% of the 1200 benchmark instances yet remained unsolved. In this note, we test two state-of-the-art solvers on different mathematical programming formulations of the MSLAP. Our computational results show that the performance of the solvers is heavily dependent on the type of mathematical optimization model. The best results are obtained when the MSLAP is expressed as a quadratically-constrained program. Such a formulation allows one of the solvers to find and verify an optimal solution for every problem in the existing benchmark data sets within just a few seconds per problem, on average. Additional experiments on large-sized instances demonstrate that the solvers’ performances remain at a high level.
•The minimum squared load assignment problem is analyzed.•(Mixed) binary linear and nonlinear mathematical programming formulations are presented.•Comprehensive computer experiments with different solvers are conducted.•Optimal solutions for all 1200 problems in the benchmark data sets of Karsu and Azizoglu are found.•New sets of large-sized test problems are generated. |
| ArticleNumber | 106309 |
| Author | Schulze, Philipp Walter, Rico |
| Author_xml | – sequence: 1 givenname: Philipp surname: Schulze fullname: Schulze, Philipp email: philipp.schulze@uni-jena.de – sequence: 2 givenname: Rico surname: Walter fullname: Walter, Rico email: rico.walter@uni-jena.de |
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| Cites_doi | 10.1016/j.ejor.2005.09.014 10.1016/j.cor.2019.02.011 10.1080/00207543.2021.1934589 10.1016/j.ejor.2015.02.035 10.1016/j.ejor.2005.09.032 10.1016/j.cor.2020.104975 |
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| References | Gurobi (b3) 2021 Pentico (b7) 2007; 176 Karsu, Azizoglu (b4) 2019; 106 Bektaş, Letchford (b1) 2020; 120 CPLEX (b2) 2022 Loiola, de Abreu, Boaventura-Netto, Hahn, Querido (b6) 2007; 176 Karsu, Morton (b5) 2015; 245 Walter, Schulze (b8) 2022; 60 Karsu (10.1016/j.cor.2023.106309_b4) 2019; 106 CPLEX (10.1016/j.cor.2023.106309_b2) 2022 Pentico (10.1016/j.cor.2023.106309_b7) 2007; 176 Walter (10.1016/j.cor.2023.106309_b8) 2022; 60 Bektaş (10.1016/j.cor.2023.106309_b1) 2020; 120 Gurobi (10.1016/j.cor.2023.106309_b3) 2021 Loiola (10.1016/j.cor.2023.106309_b6) 2007; 176 Karsu (10.1016/j.cor.2023.106309_b5) 2015; 245 |
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