论文标题

在澳门食品节上,最佳的布局平面图通过将静电势能量降至最低,以有效的收费为看台

Optimal Layout Plan of Stands at the Macao Food Festival via Minimizing the Electrostatic Potential Energy with the Effective Charge as Popularity of Stands

论文作者

Im, Ka Ian, Choi, In Kio, Lei, Pak Kio, Chan, Hou Fai, Ian, U In, Lee, Wei Shan

论文摘要

我们提出了一个数学模型,用于在澳门美食节上设计展台位置的布局图。最佳布局图可以以这样的方式定义,尽管需要每对架子之间的距离彼此之间的距离不远,但人群控制得到了良好的管理,以便人们可以更有效地光顾摊位。更受欢迎的看台可能会有更大的光顾,从而导致附近的行人流动较高。因此,为了避免客户在越受欢迎的看台周围的肩膀上挤压,我们可能会将每个摊位视为带有有效费用的充电粒子:支架越受欢迎,其携带的有效费用就越高。在此假设下,该问题随后将其转换为库仑静电势能在电荷位置的特定配置上的最小化问题,通过模拟退火和大都市算法可以发现全局最小值。静电能量密度被解释为客户的密度,而电场反向人群流动。因此,在某个位置,我们能够通过计算电场线的能量密度和净人群来预测客户密度。我们还得出结论,即使获得的计算时间以获得支架位置的配置,其能量值接近全球最小值,并且可容忍的差异可能与随机生成的站立位置的初始配置无关,但设置适当的初始配置可能是关键问题之一,以找出实际的全球最低最小值。

We proposed a mathematical model for designing the layout diagram of stand locations at the Macao Food Festival. The optimal layout diagram may be defined in such a way that, while requiring the distance between every pair of stands should not be too far away from each other, the crowd control is well managed so that people may patronize stands more effectively. More popular stands may have larger patronage, resulting in higher pedestrian flow nearby. Therefore, to avoid customers from packing shoulder to shoulder around more popular stands, we may treat every stand as a charged particle carrying an effective charge: the more popular a stand is, the higher the effective charge it carries. Under this assumption, the problem is then converted to the minimization problem of Coulomb electrostatic potential energy on a specific configuration of charge locations, with which the global minimum may be found by the Simulated Annealing and Metropolis Algorithm. Electrostatic energy density is interpreted as density of customers, while electric field the reversed crowd flow. Therefore, at a certain location we are able to predict the customer density by calculating the energy density and the net crowd flow with electric field lines. We also concluded that even though the required computation time to obtain a configuration of stand locations with the energy value close to the global minimum with a tolerable difference may be irrelevant to the randomly generated initial configuration of stand locations, setting up an appropriate initial configuration could be one of the key issues to find out the actual global minimum.

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