In recent years, China’s population is aging rapidly due to the one-child policy and a reduced mortality rate. Shanghai, one of the largest cities in China, is facing a severe challenge with regard to the aging population. During the past few decades, Shanghai has gone through a dramatic demographic transition from high fertility and high mortality to low fertility and low mortality, inevitably leading to rapid aging of the population. The registered elderly population (aged 60 and over) accounted for 35.2% of the total population of Shanghai in 2019, which is a 56.5% increase over the proportion of the elderly population in 2010 [1
]. Residential care facilities (RCFs) play an important role in caring for the elderly. The Special Plan for the Layout of RCFs in Shanghai [2
] issued by the Shanghai local government proposed the planning goal that the number of beds in RCFs in each district of the central urban areas should be no lower than 2.5% of the registered elderly population. However, at present, the total beds offered by RCFs in Shanghai are still insufficient, and the spatial layouts of RCFs in some districts are unreasonable [3
]—directly reducing the efficiency and quality of its services and affecting the improvement of urban elderly care services. Therefore, it is necessary to optimize the configuration of RCFs to provide more efficient and equitable public services.
The existing research on RCFs has mainly focused on two aspects: One aimed at analyzing the demands on RCFs from the perspective of the willingness, preference, economic conditions, and living conditions of the elderly [5
]. The other has concentrated on the development status of RCFs, including accessibility, satisfaction, and influence factors [9
]. However, little attention has been paid to the optimization of RCF configuration. Existing research on the configuration of RCFs has been primarily conducted from three aspects. Firstly, some studied the configuration status by using proportional indicators such as the number of beds per 100 elderly people and geographical area each covered per bed and then put forward some suggestions for the configuration of RCFs from the perspective of urban planning [14
]. Although the proportional indicators are easy to calculate, they do not reflect some of the other crucial factors affecting the configuration of RCFs, such as the quantity, scale, or layout of RCFs. These factors also greatly impact the effectiveness of the supply of elderly care services. Secondly, some studies were conducted from the perspective of sociology. Questionnaires or interviews were used to analyze the care demands of the elderly on RCFs [16
]. These kinds of studies focused on the rationality of the quantity of RCFs and the quality of services, but less on the spatial layouts of RCFs. The third group used GIS-based technology to analyze the rationality of RCF locations of RCFs and make suggestions for optimization from the perspective of geography [18
]. This type of study was more concerned with the spatial analysis of RCFs than their quantity. To sum up, the existing research still has some limitations. On the one hand, they only considered the demands of the elderly without involving other stakeholders. On the other hand, they only analyzed locations or the quantity of RCFs separately and independently without combining the two and other aspects. In fact, the configuration of RCFs involves multiple stakeholders, such as the elderly, the government, and the investor. When configuring RCFs, it is necessary to comprehensively consider the demands of various stakeholders and the impact of multiple factors. Therefore, it is essentially a multi-objective nonlinear dynamic decision-making problem with complex constraints. Multi-objective optimization problems are commonly solved by intelligent algorithms such as a genetic algorithm (GA), particle swarm optimization (PSO), and immune algorithm (IA), etc. Although GA can quickly perform a global search, it requires complex coding and has the disadvantages of slow convergence rate, easy to premature convergence, and low accuracy when dealing with complex problems [21
]. For PSO, it has deficiencies in premature convergence, weak local searchability, and low accuracy of solutions in the early stage [22
]. IA, a new computational method inspired by the biological immune system, was first proposed by Jerne [23
]. As a heuristic method, it can learn new information, recall previously learned information in a highly decentralized fashion, and can tackle complex real-world problems. Many studies have demonstrated that IA possesses certain attractive immune properties that allow it to escape from local optima and avoid premature convergence [24
]. However, the IA still has the disadvantages of a slow convergence rate in the late search stage and low accuracy. Therefore, it is necessary to make modifications to improve the performance of IA [26
In addition, the configuration of RCFs is a complex issue of decision-making and spatial optimization, in which both the optimization of quantity and layout should be considered simultaneously. Although the intelligent algorithms can be utilized to study the complex systems and dynamic behavior, they still have some shortcomings in spatial optimization. Fortunately, geographic information system (GIS) can provide a variety of spatial data for spatial decision and has the advantage of spatial visualization. As a result, the modified immune algorithm (MIA) and GIS are integrated to analyze and solve the optimization problems in spatial decision-making in this study, allowing their respective advantages to work in complement with each other and help to simultaneously optimize the quantity, locations, and scales of RCFs. Moreover, this approach can give rise to better solutions for multi-objective optimization configuration of RCFs compared with application of IA alone, while there are as yet no published studies on the integration of both techniques as an assistant decision-making tool for public service facility optimization. The optimization problem of RCF configuration belongs to an interdisciplinary field involving computer science, operations research, geography, and planning. We introduce complex spatial decision theory and swarm intelligence optimization theory as the theoretical framework, and planning control theory, location theory, and spatial structure theory as the research foundations. The specific research question, research methods, and procedures are described as follows: To optimize the configuration of RCFs, considering the demands of the three stakeholders of the government, the elderly, and the investor, an optimization model for RCF configuration is constructed. By taking the Jing’an District of Shanghai as an example, the configuration rationality of the existing RCFs is analyzed firstly, and then the optimization model is solved and analyzed by integrating MIA and GIS. According to the results, some optimization suggestions are further proposed to provide references for the planning of RCFs. The approach combining GIS and optimization techniques proposed in this study can also be used for the optimization of the configuration of other public service facilities in practice and can enrich the method of public service facility planning systems in theory. The remaining part of this study is organized as follows. In the following section, the optimization model for RCF configuration is developed, and the MIA is proposed. Followed by that, by taking the Jing’an District of Shanghai in China as an example, the MIA is used to solve the developed optimization model, and GIS is integrated with MIA for the spatial optimization analysis of the RCFs. The last two sections discuss the calculation results and conclude the study, respectively.
4. Optimization and Results
The optimization process is as follows:
Step 1: Identify Existing RCFs with Unreasonable Locations and Adjust the Scale of Other RCFs
According to the above analysis, most of the existing RCFs deviate from the best locations, however, it is unrealistic to adjust the locations of all RCFs. Hence, we only appropriately adjusted a few RCFs with seriously unreasonable locations along the number of beds in some other RCFs. The specific approaches are as follows. By using MIA and GIS to solve and analyze the constructed optimization model, it can be found that there are 2 among the existing 41 RCFs with unreasonable locations requiring adjustment, whose locations are shown in Figure 4
a. Next, the numbers of beds in the remaining 39 RCFs are adjusted within the maximum number of beds proposed in the Special Plan for the Layout of RCFs in Shanghai. The difference values of the number of beds between the optimized RCFs and existing RCFs are shown in Figure 4
a. After the above optimization and adjustment, the RCFs can only meet the care demands of 6970 elderly people, leaving 1193 elderly people whose demands cannot be met. Therefore, it is necessary to build up some RCFs to meet the demands. The locations of the population centers whose care demands are met and unmet after the preliminary optimization of this step are shown in Figure 4
From Figure 4
, we can draw the following conclusions. Firstly, RCFs in which the number of beds need to be reduced or whose locations need to be adjusted are mainly located in the northern and southwest marginal areas of Jing’an District, namely Linfen Road Subdistrict, Caojiadu Subdistrict, and the northern of Pengpu Xincun Subdistrict and Pengpu Town. Although population centers are relatively dense in these areas, they are almost small-sized communities, thus the density of the elderly is not as big as other subdistricts. At the same time, the RCFs here are so densely distributed that supply exceeds demand. With regard to the two RCFs requiring adjustment mentioned above, because other RCFs near them are closer to the population center and able to fully meet the demands of the elderly in the vicinity, there are many redundant beds in these two RCFs, causing waste of public resources. Secondly, the number of beds for most RCFs in the central areas of Jing’an District needs to be increased. For some subdistricts in the central of Jing’an District, such as Zhijiang West Road Subdistrict, Baoshan Road Subdistrict, and Beizhan Subdistrict, population centers are densely distributed, and the number of elderly people is large and increasing. Although there are many RCFs here, due to high land prices and the urban planning restrictions, the scales of these RCFs are not large enough to meet the increasing demands of the elderly. Thirdly, after adjusting the number of beds in some RCFs in the south of Pengpu Town, south of Daning Road, and west of Nanjing West Road, the demands of nearby population centers still have not been met. This is mainly because there are few RCFs there, and it is still difficult to meet the huge care demands of elderly people nearby by simply adding beds to existing RCFs. Therefore, it is necessary to establish some new RCFs here to bridge the gap between supply and demand.
Step 2: Determine the Quantity and Locations of RCFs that Need to be Newly Added
We select some new RCFs from the 810 candidate sites to serve the population centers whose care demands have not been met after the preliminary optimization of Step 1. According to the Special Plan for the Layout of RCFs in Shanghai, the number of beds in each newly-added RCF should not exceed 300. Since there are 1193 elderly people in Jing’an District whose care demands have not been met, at least 4 new RCFs are required. Next MIA and GIS are used to obtain the optimal objective function values for different numbers of RCFs (see Table 2
). In this study, the lower the objective function value is, the better the optimization results are. As shown in Table 2
, when the number of RCFs is 6, the objective function value is the lowest. It indicates that 6 RCFs should be added to Jing’an District. The locations of the newly-added RCFs are shown in Figure 5
It can be seen from Figure 5
that the newly-added RCFs are roughly distributed in a densely populated area, which greatly reduces the travel costs of the elderly and improves the equity of residents’ access to public resources. In addition, most of the new RCFs are far away from main roads and highways, close to branch roads, and the transportation is convenient. At the same time, they are located far from noise and pollution sources and close to public facilities such as hospitals, parks, and green spaces, making them suitable for living. This demonstrates that the locations of the new-added RCFs are in line with the planning requirements.
Step 3: Determine the Number of Beds for Each Newly-Added RCF
Since it is assumed that each population center is served by its nearest RCF, the number of beds required for each newly-added RCF is the total number of elderly people in the corresponding population centers who have service demands for RCFs. The service relationship between the newly-added RCFs and population centers is shown in Figure 5
. The numbers of beds in newly-added RCFs can be found in Table 3
The rational configuration of RCFs helps to improve the ability of urban old-age service. Considering the impact of three stakeholders including the government, the elderly, and the investor on the configuration of RCFs, a multi-objective spatial optimization model with complex constraints for RCF configuration is developed based on the goals of maximizing configuration equity and efficiency of government-configured service facilities, minimizing travel costs of the elderly and maximizing profits of investors. An MIA method that improves the performance of standard IA from three aspects, including the selection operator, the mutation operator, and the global optima, is proposed to solve the model. Taking Jing’an District in Shanghai as an example, the rationality of existing RCF configuration in terms of the quantity, scale, and spatial location is analyzed firstly. Then, an optimization scheme is proposed by integrating MIA and GIS to solve and analyze the proposed optimization model. By comparing the optimization results with the current situation, the rationality of the optimization scheme is illustrated. In addition, the superiority of MIA in this optimization conundrum is discussed by comparing the performance of GA, PSO, IA, and MIA.
The results show that the configuration of existing RCFs is irrational in terms of quantity, scale, and location. The number of existing RCFs of Jing’an District is insufficient, and two of them with unreasonable locations require adjustment. There is a significant gap between the service supply of existing RCFs and the care demands of the elderly. There are six new RCFs required to be added to meet the demands of the elderly. The optimization scheme has improved the equity and efficiency of RCF configuration, increased the profits of investors, and reduced the travel costs of the elderly. Compared with conventional algorithms such as the GA, PSO, and IA, the MIA performs better in calculating efficiency and accuracy for solving RCF optimization problems.
The novelty of this paper is that an effective method to optimize the RCF configuration under complex constraints by integrating intelligent algorithms and GIS is proposed. The MIA is an effective algorithm for solving complex optimization problems, while GIS is used to overlay spatial variables to make a composite map. The integration allows the two techniques to mutually benefit from each other and can optimize the quantity, scales, and locations of RCFs simultaneously. We make some contributions in four aspects: Firstly, a multi-objective spatial optimization model is developed for RCF configuration by considering the demands of multiple stakeholders, which enriches the connotation of multi-objective constraints. Secondly, a modified immune algorithm is proposed by improving the standard IA, thus that it can solve optimization problems more efficiently. Thirdly, by integrating the intelligent algorithm and GIS, dynamic optimization, and spatial visualization for RCF configuration is realized. This method also can be used for the configuration optimization of other public service facilities, which broadens the application research of complex spatial decision theory and swarm intelligence optimization theory in the optimization of public service facilities. Finally, the conclusions drawn from this study provide a basis for the planning and configuration decision-making of RCFs in Shanghai and also have reference value for the configuration of RCFs in other cities in China and other developing countries, which develops the theory and method of public service facility planning system. Nevertheless, there are still several limitations in this study. On the one hand, the spatial optimization of the RCF configuration is an intricate multi-objective decision-making problem. Although the objectives of equity, efficiency, cost, and profits have been taken into account in this study, more complex objectives such as policy and resource constraints are possible ones in need of consideration, thus that the spatial optimization model is more realistic. On the other hand, China’s aging process is accelerating and the elderly population is growing rapidly. It is necessary to scientifically predict the elderly populations in the future and their spatial distribution, and propose an optimal configuration plan for RCFs based on the population prediction.