The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed "directional gradual cover". Contrary to all gradual cover models, the joint cover depends on the facilities' directions. In order to calculate the joint cover, existing models apply the partial cover by each facility disregarding their direction. We develop a genetic algorithm to solve the facilities location problem and also solve the problem for facilities that can be located anywhere in the plane. The proposed modifications were extensively tested on a case study of covering Orange County, California.

中文翻译：

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逐步覆盖的定向方法：连续情况

覆盖位置模型的目标是覆盖给定距离内设施的需求。逐渐（或部分）覆盖通过定义覆盖的逐渐下降来代替从完全覆盖到无覆盖的突然下降。在本文中，我们使用最近提出的规则来计算多个设施点对请求点的联合覆盖，称为“定向渐变覆盖”。与所有渐变覆盖模型相反，联合覆盖取决于设施的方向。为了计算联合覆盖，现有模型通过每个设施应用部分覆盖，而不管它们的方向。我们开发了一种遗传算法来解决设施位置问题，也解决了可以位于平面上任何位置的设施的问题。提议的修改在覆盖奥兰治县的案例研究中进行了广泛测试，