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Giving formal roles to elevators for breaking symmetry in static elevator operation problems

机译:在静态电梯运行问题中为电梯提供正式作用

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In this paper, we propose a technique to decrease computational times in solving an integer linear programming (ILP) model for the static elevator operation problem (SEOP). The SEOP is a problem to optimally operate elevators on such assumption that all information on passengers who use an elevator system is known beforehand. In planning, there is a symmetry on elevators that exchanging 2 elevators does not affect the value of the objective function, if initial states of those elevators are identical. Such symmetry requires much computational times for problems to be solved, since there are at least 2 optimal solutions which differ only in allocations of elevators and partial solutions for those solutions can not be bound. That symmetry is resolved by giving different roles to elevators, and those roles are assignment pattern numbers (APNs) in the proposed technique. An APN of an elevator is a decimal number which is calculated from a binary vector which represents assignments of passengers to that elevator. The proposed technique deploys such a straightforward fact that all elevators have different APNs, and enfoces an elevator with a smaller index to have a smaller APN than other elevators with larger indexes. The effectiveness of that technique is numerically examined by applying a mathematical solver to ILP equations generated from some problem instances.
机译:在本文中,我们提出了一种技术来减少求解静态电梯操作问题的整数线性编程(ILP)模型的计算时间(SEOP)。 SEOP是最佳地操作电梯的问题,即在使用电梯系统的乘客的所有信息是事先已知的。在规划中,如果这些电梯的初始状态相同,则在电梯上交换2个电梯的对称性不会影响目标函数的值。这种对称需要很多计算时间来解决问题,因为至少有2个最佳解决方案,其仅在电梯的分配中不同,而这些解决方案的部分解决方案则不能绑定。通过向电梯提供不同的角色来解决这种对称性,并且这些角色是所提出的技术中的分配模式编号(APNS)。电梯的APN是由二进制向量计算的十进制数,其代表乘客的分配给该电梯。所提出的技术部署了这种直接的事实,即所有电梯都具有不同的APN,并且将具有较小索引的电梯剥离,以具有比具有较大指标更大索引的其他电梯更小的APN。通过将数学求解器应用于从一些问题实例生成的ILP方程来进行数值检查该技术的有效性。

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