Teymourifar Aydin
Universidade Católica Portuguesa, Católica Porto Business School, Centro de Estudos em Gestão e Economia Porto, Portugal.
Heliyon. 2023 Jul 29;9(8):e18602. doi: 10.1016/j.heliyon.2023.e18602. eCollection 2023 Aug.
In this study, we compare the performance of optimization software to solve the bi-objective sectorization problem. The used solution method is based on an approach that has not been used before in the literature on sectorization, in which, the bi-objective model is transformed into single-objective ones, whose results are regarded as ideal points for the objective functions in the bi-objective model. Anti-ideal points are also searched similarly. Then, using the ideal and anti-ideal points, the bi-objective model is redefined as a single-objective one and solved. The difficulties of solving the models, which are basically non-linear, are discussed. Furthermore, the models are linearized, in which case how the number of variables and constraints changes is discussed. Mathematical models are implemented in Python's Pulp library, Lingo, IBM ILOG CPLEX Optimization Studio, and GAMS software, and the obtained results are presented. Furthermore, metaheuristics available in Python's Pymoo library are utilized to solve the models' single- and bi-objective versions. In the experimental results section, benchmarks of different sizes are derived for the problem, and the results are presented. It is observed that the solvers do not perform satisfactorily in solving models; of all of them, GAMS achieves the best results. The utilized metaheuristics from the Pymoo library gain feasible results in reasonable times. In the conclusion section, suggestions are given for solving similar problems. Furthermore, this article summarizes the managerial applications of the sectorization problems.
在本研究中，我们比较了优化软件解决双目标分区问题的性能。所采用的求解方法基于一种在分区文献中未曾使用过的方法，即把双目标模型转化为单目标模型，其结果被视为双目标模型中目标函数的理想点。反理想点也以类似方式搜索。然后，利用理想点和反理想点，将双目标模型重新定义为单目标模型并求解。讨论了解决这些基本为非线性模型的困难。此外，对模型进行了线性化，并讨论了变量数量和约束条件在这种情况下如何变化。数学模型在Python的Pulp库、Lingo、IBM ILOG CPLEX Optimization Studio和GAMS软件中实现，并给出了所得结果。此外，利用Python的Pymoo库中的元启发式算法来求解模型的单目标和双目标版本。在实验结果部分，针对该问题得出了不同规模的基准，并展示了结果。可以观察到，求解器在求解模型时表现并不令人满意；在所有求解器中，GAMS取得了最佳结果。从Pymoo库中使用的元启发式算法在合理时间内获得了可行结果。在结论部分，给出了求解类似问题的建议。此外，本文总结了分区问题的管理应用。
