The concept of environmental sustainable development is in fact a response to the environmental and social damaging effects. Urban sustainable development is one of the foundations for achieving environmental sustainable development and social justice; thus, the location allocation of urban facilities has to be optimized. Location allocation models are among the most widely used methods in GIS spatial analysis. Owing to their importance in recent decades, many unified models have been developed that can solve diverse types of location allocation problems. Recently, several methods have been developed to solve different location allocation problems within the unified vector assignment ordered median problem (VAOMP) model. These methods combine P-Median and Coverage models, based on the tabu search metaheuristic algorithm. The present study uses the unified VAOMP model, integrated GIS, and both tabu search (TS) and simulated annealing (SA) metaheuristic algorithms to solve location allocation problems. The study assesses its findings in two different scenarios for fire stations. The results of applying the two algorithms in terms of time, the number of covered demands, and the quality of the solutions were examined. Comparisons showed that the TS algorithm was faster in solving P-Median problems and generated more qualitative solutions than SA. However, the SA algorithm had less runtime in Coverage and P-Center problems. The results also showed that the VAOMP model is a qualified model in the field of location allocation, which can be used in various fields, in particular, to examine the status of urban facilities in achieving social justice and urban sustainable development.

中文翻译：

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使用矢量分配有序中值问题综合GIS优化环境设施的可持续发展

实际上，环境可持续发展的概念是对环境和社会破坏影响的回应。城市可持续发展是实现环境可持续发展和社会正义的基础之一；因此，必须优化城市设施的位置分配。位置分配模型是GIS空间分析中使用最广泛的方法之一。由于近几十年来它们的重要性，已经开发了许多统一的模型，可以解决各种类型的位置分配问题。最近，已经开发了几种方法来解决统一矢量分配有序中值问题（VAOMP）模型内的不同位置分配问题。这些方法基于禁忌搜索元启发式算法，结合了P中值和Coverage模型。本研究使用统一的VAOMP模型，集成的GIS，禁忌搜索（TS）和模拟退火（SA）元启发式算法来解决位置分配问题。该研究评估了消防局在两种不同情况下的发现。研究了在时间，覆盖需求数量和解决方案质量方面应用这两种算法的结果。比较表明，与SA算法相比，TS算法解决P-Median问题的速度更快，并且产生了更多的定性解决方案。但是，SA算法在Coverage和P-Center问题中的运行时间较少。结果还表明，VAOMP模型在位置分配领域是一种合格的模型，可用于各种领域，特别是在