Spatial Optimization of Residential Care Facility Configuration Based on the Integration of Modified Immune Algorithm and GIS: A Case Study of Jing’an District in Shanghai, China
Abstract
:1. Introduction
2. Methods
2.1. Optimization Model
2.1.1. Maximizing Equity
2.1.2. Maximizing Efficiency of Configuration
2.1.3. Minimizing Travel Costs
2.1.4. Maximizing Profits
- (1)
- The number of RCFs selected from candidate sites should be equal to a predefined number p, namely:
- (2)
- The elderly in every population center can get the service from a RCF, namely:
- (3)
- For each selected RCF candidate site, it will serve at least one population center, namely:
- (4)
- According to the Special Plan for the Layout of RCFs in Shanghai, RCFs are divided into 3 types: small-sized (the number of beds should be less than 100), medium-sized (the number of beds should be between 100 and 300), and large-sized (the number of beds should be between 300 and 500), and the RCFs of Jing’an District, which is located in the downtown area of Shanghai, should be small-sized or medium-sized, and the number of beds here should be between 0 and 300, namely:
2.2. Modified Immune Algorithm
2.2.1. Variable Threshold for Selection Operator
2.2.2. Guo Elite Mutation Operator
2.2.3. Periodically Varying Mutation Probability
2.2.4. The Perturbations of Global Optima
- Step 1:
- Initialization. The simple decimal encoding is used to initialize an antibody population as a set of randomly generated decision vectors within the predefined feasible solutions. Each antibody represents a candidate solution, which is the sequence of the RCFs selected from the candidate sites.
- Step 2:
- Calculation. In this step, the affinity and the concentration of antibodies are calculated, and some excellent antibodies to store in the memory bank are selected.
- Step 3:
- Memory cell updating. Replace the memory cells whose affinities with antigens are worse with the excellent antibodies. At the same time, for those that have worse affinities with memory cells, their ability is reduced to survive to ensure that the algorithm will not get stuck in local optima.
- Step 4:
- Clonal selection. According to variable threshold for selection operator, a certain number of antibodies with great affinities and low concentrations are selected to be cloned.
- Step 5:
- Mutation. Mutation means random change the permutation of encoding. At this stage, the Guo elite mutation operator is applied to improve the search efficiency, and the periodic varying mutation probability is used to increase the diversity of antibody populations.
- Step 6:
- Perturbation. The global optima is perturbed at set intervals to avoid getting stuck in the local optima.
- Step 7:
- Termination. If , go to step 2; otherwise, terminate the procedure.
2.3. Integration of MIA and GIS
3. Model Implementation and Results
3.1. Study Area
3.2. Data Sources
3.3. Definition of Candidate Sites for RCFs
3.4. Sensitivity Analysis of β
3.5. Rationality Analysis of Existing RCFs
3.5.1. Quantity
3.5.2. Scale
3.5.3. Location
4. Optimization and Results
5. Discussion
5.1. Comparison of Optimization Scheme with the Current Situation of RCF Configuration
- (1)
- For the government: Firstly, the equity of RCF configuration improves. Table 4 shows that the configuration scheme for RCFs after optimization has 64.23% improvement in equity compared with the current situation. The Gini coefficient of potential service resources available to residents has also dropped from 0.5563 to 0.1225. The Gini coefficient was originally used to measure people’s income equity. In recent years, it has been used by some researchers to reflect the equity of public resource allocation [44]. The lower the Gini coefficient is, the better the equity of resource allocation will be. In addition, the ratio of the accessibility from each population center to the RCF and the average value of the accessibility can also reflect the equity of RCF configuration. The closer the value is to 1, the better the equity of RCF configuration. Figure 6a indicates that 72.83% of the population centers have this ratio indicator between 0.9 and 1.1, which indicates that most population centers can obtain services of RCFs evenly after optimization. Secondly, the efficiency of the RCF configuration improves. The 45 RCFs, including 39 existing RCFs and 6 new RCFs, are able to meet the care demands of all the elderly in Jing’an District after optimization. Table 4 shows that the configuration efficiency of RCFs has been improved by 84.24%. As mentioned above, due to the irrational locations and scales, existing RCFs cannot meet the actual demands, resulting in low service capabilities. When the demand-oriented optimization method is used, the configuration of the RCFs is more balanced, which is more conducive to improving configuration efficiency.
- (2)
- For the investors: Table 4 shows that the economic efficiency of investment has been improved by 29.82%. Therefore, with the optimization of the RCF configuration, the care demands of more and more elderly people are met, while the economic efficiency of investors can also be greatly improved.
- (3)
- For the elderly: Residents’ travel becomes more convenient and efficient. Figure 6b shows that the per capita travel cost is significantly reduced after optimization, and travel efficiency in 99% of population centers has been improved to some degree. From the perspective of the spatial layout of RCFs, there is at least one RCF near each population center. The maximum travel distance from population centers to their nearest RCF is reduced from 2150 m to 1374 m, with the average travel distance reduced from 526 m to 373 m. In addition, the average number of beds available for each population center within a one-hour service radius is increased from 1.5624 to 3.3986, indicating that the optimization scheme has achieved the goal of 2.5 beds per 100 elderly people proposed in the Special Plan for the Layout of RCFs in Shanghai. The above results reveal that the convenience of RCF services after optimization has been improved.
5.2. Comparison of the Performance of MIA with Other Algorithms
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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β | Accessibility | ||
---|---|---|---|
Maximum | Minimum | Standard Deviation | |
0.8 | 2.3879 | 0.3917 | 0.6854 |
1 | 4.1041 | 0.4799 | 0.5018 |
1.2 | 7.2491 | 0.3702 | 0.8662 |
1.4 | 12.4549 | 0.2694 | 1.4351 |
1.6 | 20.2442 | 0.1849 | 2.2596 |
1.8 | 30.8292 | 0.1206 | 3.3662 |
2 | 44.0078 | 0.0756 | 4.7404 |
2.2 | 59.2022 | 0.0460 | 6.3264 |
2.4 | 75.5945 | 0.0275 | 8.0405 |
The Number of RCFs | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|---|---|---|---|---|---|---|---|---|---|---|
Objective Function Value | 0.6722 | 0.6323 | 0.6012 | 0.6283 | 0.6501 | 0.6766 | 0.7149 | 0.7364 | 0.7626 | 0.7943 | 0.8243 |
RCF No. | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
The number of beds | 285 | 181 | 257 | 247 | 143 | 80 |
Objectives | Results | ||
---|---|---|---|
Current Situation | Optimized Scheme | Optimization Rate | |
Equity | 56.2886 | 17.2883 | 64.23% |
Efficiency (%) | — | 84.24 | 84.24% |
Travel cost (m/person) | 544.9192 | 389.4611 | 18.53% |
Profits of investor (RMB/month/RCF) | 111,785 | 145,120 | 29.82% |
Gini coefficient | 0.5563 | 0.1225 | 77.98% |
Max travel distance to nearest RCF (m) | 2150 | 1374 | 36.09% |
Average travel distance to nearest RCF (m) | 526 | 373 | 29.09% |
The average number of beds available within one-hour service radius (beds/person) | 1.5624 | 3.3986 | 117.52% |
Objectives | Results | |||
---|---|---|---|---|
GA | PSO | IA | MIA | |
Equity (number of beds/person)2 | 19.6840 | 20.5275 | 18.2745 | 17.2883 |
Efficiency (%) | 82.41 | 83.14 | 83.67 | 84.24 |
Travel cost (m/person) | 408.4216 | 424.4999 | 411.8927 | 389.4611 |
Profits of investor (RMB/ month) | 141,970 | 138,940 | 145,120 | 145,120 |
Comprehensive objective value | 0.7323 | 0.8064 | 0.6401 | 0.6012 |
Number of iterations | 650 | 680 | 700 | 480 |
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Cheng, M.; Cui, X. Spatial Optimization of Residential Care Facility Configuration Based on the Integration of Modified Immune Algorithm and GIS: A Case Study of Jing’an District in Shanghai, China. Int. J. Environ. Res. Public Health 2020, 17, 8090. https://doi.org/10.3390/ijerph17218090
Cheng M, Cui X. Spatial Optimization of Residential Care Facility Configuration Based on the Integration of Modified Immune Algorithm and GIS: A Case Study of Jing’an District in Shanghai, China. International Journal of Environmental Research and Public Health. 2020; 17(21):8090. https://doi.org/10.3390/ijerph17218090
Chicago/Turabian StyleCheng, Min, and Xiao Cui. 2020. "Spatial Optimization of Residential Care Facility Configuration Based on the Integration of Modified Immune Algorithm and GIS: A Case Study of Jing’an District in Shanghai, China" International Journal of Environmental Research and Public Health 17, no. 21: 8090. https://doi.org/10.3390/ijerph17218090
APA StyleCheng, M., & Cui, X. (2020). Spatial Optimization of Residential Care Facility Configuration Based on the Integration of Modified Immune Algorithm and GIS: A Case Study of Jing’an District in Shanghai, China. International Journal of Environmental Research and Public Health, 17(21), 8090. https://doi.org/10.3390/ijerph17218090