## 1 Introduction  
Location-allocation is one of the most important analyses in GIS science, identifying optimal facility locations for optimal services to specific demands [1]. Demands can be allocated to facilities based on factors, such as minimum distance, minimum cost, the capacity of facilities, etc. The best location for each facility depends on such criteria as optimal distance, capacity, population density, and optimal cost. An unsuitable location for a facility would adversely affect that facility in providing an effective service. If the location of a facility is far from an appropriate demographic space, then it will not service it well [2]. Similarly, the capacity of facilities is a factor in the effectiveness of their service. The location of the facilities must be well-defined and distributed in such a way that they can respond to the demand, in terms of their capacity. For example, if the capacity of a hospital is 10,000 beds, it means that the hospital is not able to provide more than this number and should not accept more patients than this capacity. As is clear, capacity is a main criterion in location-allocation problems, because each facility in the real world can serve only a specified demand. The location-allocation problem has four main models, namely, the P-Median model, the Simple Plant Location Problem (SPLP), P-Center, and Coverage problem [3]. The Median problem approach introduces the median points into the candidate points, with the objective of minimizing the total cost [4]. The Maximal Covering Location model aims to maximize demand coverage with the predetermined number of facilities [5]. The Center problem covers all the points, its goal being to minimize the maximum distance between demand points and the closest service center [6]. The objective of SPLP is to minimize the combined transportation costs and fixed costs for setting up and operating facilities. Improvements in optimization methods, computer programming, computational theory, algorithms, and computer hardware have resulted in a wide range of well-developed location analysis approaches [7]. Many models have been developed, with various criteria and constraints, to solve the complexity of real-world problems. Although these models are different from each other in their objective and structure, they are, in fact, derived from the same four main models [7]. Many research studies have been undertaken using these models: [PERSON] and [PERSON], for example, have studied min-max cover problems, while [PERSON] and [PERSON] [8,9] applied an algorithm for the facility location problem with the goal of minimizing total cost. [PERSON] and et al. [10] examined the mixed center location problem, developing three heuristics to solve it. Because of the complexity of these models, which belong to the NP-hard problem category [11], employing exact methods to solve them is very time-consuming. Consequently, metaheuristic algorithms are used. Unifying these location-allocation main models would make the problem still more complicated, but this unification is important for two reasons: (1) it helps us to categorize and understand the relationship between different problems; and (2) it can be a tool for introducing and constructing new models that satisfy human needs [1]. In 1984, [PERSON] [12] used the median structure to solve many location problems by changing distance or cost matrix. [PERSON] and [PERSON] also introduced the Vector Assignment P-Median Problem (VAPMP). The VAPMP allows each demand to be assigned several facilities [13]. In 2014, [PERSON] and [PERSON] presented a model called the Vector Assignment Ordered Median Problem (VAOMP), which generalizes both the VAPMP and OMP models. This model is used to solve many problems. They used the Integer Linear Programming method to solve their developed model, which requires expensive software, and its computational time is long [7]. To reduce the computational time of the model, [PERSON] et al. [1] applied the VAOMP unified approach and Tabu Search algorithm in 2016.