求解应急医疗设施分层递进式选址问题的改进免疫算法

doi:10.15960/j.cnki.issn.1007-6093.2021.02.002

摘要/Abstract

摘要：

针对应急医疗设施的特点，提出分层递进式选址方法，对应急医疗设施进行合理选址。首先，通过熵权法对选址所需要考虑的因素进行权重计算，并进行初步选址；其次，考虑设施点的服务容量、重大公共卫生事件下轻重症患者的治疗与转移的实际情况，建立双层级整数规划模型；再次，根据模型的具体特点，设计改进的免疫优化算法对其进行求解；最后，以湖北省孝感市针对突发公共卫生事件的应急医疗设施选址问题为案例进行分析，给出相应的合理选址方案，验证了模型与算法的可行性。

关键词: 应急医疗设施选址, 改进的免疫优化算法, 熵权法, 双层级模型, 分层递进式选址

Abstract:

According to the characteristics of emergency medical facilities, a hierarchical and progressive location method is proposed to reasonably locating them. Firstly, the entropy weight method is used to calculate the weight of factors related to the location problem, and the preliminary location is also carried out. Secondly, a two-level integer programming model is formulated, which considers the service capacity of the facility, and the actual situation of treating and transferring the mild and severe patients under major public health events. Thirdly, according to the characteristics of the proposed model, an improved immune optimization algorithm is designed to effectively solve it. Finally, the location of emergency medical facilities for public health events in Xiaogan City, Hubei Province is studied as a case, and the reasonable location scheme is obtained for it, which verifies the feasibility of the proposed model and algorithm.

Key words: location of emergency medical facilities, improved immune optimization algorithm, entropy wight method, two-level model, hierarchical and progressive location

中图分类号:

O221.7

周宇阳, 张惠珍, 马良. 求解应急医疗设施分层递进式选址问题的改进免疫算法[J]. 运筹学学报, 2021, 25(2): 15-34.

Yuyang ZHOU, Huizhen ZHANG, Liang MA. An improved immune algorithm for solving hierarchical and progressive location problem of emergency medical facilities[J]. Operations Research Transactions, 2021, 25(2): 15-34.

图/表 17

图1

图2

图3

表1

需求点的坐标和需求量"

序号	经纬度坐标	人口数量	序号	经纬度坐标	人口数量
1	113.907 66, 30.929 63	79 932	59	113.572 33, 30.941 56	134 010
2	113.925 79, 30.915 38	329 000	60	113.585 79, 30.967 80	53 096
3	114.024 62, 31.009 43	27 395	61	113.616 05, 30.946 33	24 438
4	113.860 91, 31.042 15	39 443	62	113.712 77, 30.920 19	40 684
5	113.982 37, 30.869 55	38 586	63	113.741 20, 30.861 15	23 504
6	114.142 45, 30.900 70	33 700	64	113.462 98, 31.034 75	17 390
7	113.928 85, 30.966 84	44 708	65	113.593 19, 31.098 20	40 871
8	113.950 51, 30.789 30	23 963	66	113.690 21, 30.989 25	26 475
9	113.937 27, 30.953 38	40 221	67	113.689 46, 30.909 55	48 732
10	113.933 73, 30.924 49	157 648	68	113.591 00, 30.905 65	38 314
11	114.110 41, 31.031 76	63 794	69	113.591 00, 30.777 92	40 700
12	113.947 42, 31.077 98	82 949	70	113.512 82, 30.764 59	26 773
13	114.067 54, 30.948 93	44 079	71	113.480 99, 30.860 99	42 523
14	113.992 51, 30.984 70	32 780	72	113.411 82, 30.906 40	26 525
15	113.911 62, 30.902 92	53 290	73	113.363 29, 30.911 80	13 522
16	114.031 38, 30.800 80	10 200	74	113.704 78, 31.288 00	132 486
17	113.966 78, 31.258 75	128 455	75	113.706 61, 31.212 50	21 735
18	113.988 51, 31.322 15	32 868	76	113.860 09, 31.419 48	29 411
19	113.986 94, 31.397 30	32 868	77	113.763 55, 31.221 22	22 166
20	114.069 13, 31.348 01	42 038	78	113.645 37, 31.165 85	40 338
21	113.898 69, 31.142 27	51 237	79	113.597 90, 31.244 39	25 578
22	114.125 04, 31.298 96	17 154	80	113.525 58, 31.297 63	30 400
23	114.125 10, 31.166 58	60 969	81	113.396 69, 31.332 22	25 927
24	114.171 40, 31.117 82	27 819	82	113.584 93, 31.334 01	36 269
25	114.042 38, 31.087 44	59 263	83	113.533 32, 31.394 37	24 765
26	113.867 19, 31.197 77	43 071	84	113.707 04, 31.338 02	29 112
27	113.917 18, 31.301 76	34 162	85	113.829 49, 31.272 97	28 808
28	114.019 13, 31.208 02	48 224	86	113.642 26, 31.121 68	28 791
29	114.002 88, 31.263 82	10 249	87	113.561 56, 31.234 26	19 661
30	114.127 70, 31.566 40	88 732	88	113.764 19, 31.421 57	22 057
31	114.122 06, 31.499 46	21 341	89	113.726 89, 31.265 17	51 086
32	114.117 48, 31.399 18	25 507	90	113.838 99, 30.641 82	165 230
33	114.282 99, 31.494 58	43 307	91	113.834 90, 30.559 47	83 313
34	114.311 71, 31.420 15	31 340	92	113.609 05, 30.506 33	27 745
35	114.386 55, 31.372 68	31 648	93	113.776 79, 30.625 37	55 994
36	114.446 26, 31.321 08	55 000	94	113.665 07, 30.582 85	57 285
37	114.416 17, 31.423 09	26 775	95	113.542 36, 30.500 34	63 494
38	114.490 84, 31.508 06	27 779	96	113.459 92, 30.534 86	34 310
39	114.509 58, 31.579 50	15 899	97	113.515 04, 30.518 96	31 343
40	114.502 18, 31.690 85	70 362	98	113.527 53, 30.712 38	29 810
41	114.394 44, 31.629 33	30 092	99	113.444 41, 30.782 54	11 918
42	114.162 05, 31.723 93	33 074	100	113.702 90, 30.783 25	25 204
43	114.218 41, 31.801 34	25 694	101	113.825 36, 30.754 66	45 181
44	114.241 49, 31.593 31	40 826	102	113.924 44, 30.673 03	131 298
45	114.373 52, 31.535 00	33 208	103	113.799 62, 30.597 01	33 263
46	114.217 75, 31.704 56	28 817	104	113.659 61, 30.530 59	27 140
47	113.756 82, 31.039 44	132 892	105	113.683 97, 30.486 33	44 678
48	113.784 77, 31.131 69	34 077	106	113.707 86, 30.595 15	22 807
49	113.820 31, 30.985 72	33 772	107	113.782 60, 30.503 78	41 557
50	113.766 77, 30.827 62	24 030	108	113.880 06, 30.612 39	27 614
51	113.666 70, 31.075 06	28 726	109	113.575 95, 30.585 55	24 590
52	113.838 76, 30.936 23	32 886	110	113.608 43, 30.677 56	30 619
53	113.717 34, 31.099 15	44 549	111	113.510 55, 30.637 25	21 483
54	113.809 98, 31.041 64	32 475	112	113.714 37, 30.621 57	11 368
55	113.846 11, 30.836 90	51 422	113	113.626 69, 30.621 93	4 777
56	113.739 83, 30.945 08	61 227	114	113.736 43, 30.668 19	9 809
57	113.739 08, 31.190 70	24 647	115	113.925 78, 30.685 75	100 137
58	113.705 15, 31.037 25	26 876

表1

表2

表3

图4

表4

表5

表6

图5

表7

表8

图6

图7

图8

表9

参考文献 23

1	Ye F , Zhao Q H , Xi M H , et al. Chinese National Emergency Warehouse Location Research based on VNS algorithm[J]. Electronic Notes in Discrete Mathematics, 2015, 47, 61- 68. doi: 10.1016/j.endm.2014.11.009
2	彭春, 李金林, 冉伦, 等. 需求不确定下应急医疗服务站鲁棒配置模型与算法[J]. 运筹与管理, 2017, 26 (9): 21- 28.
3	Su Q , Luo Q Y , Huang S H . Cost-effective analyses for emergency medical services deployment: A case study in Shanghai[J]. International Journal of Production Economics, 2015, 163 (5): 112- 123.
4	Shishebori D , Babadi A Y . Robust and reliable medical services network design under uncertain environment and system disruptions[J]. Transportation Research Part E, 2015, 77e (5): 268- 288.
5	Sudtachat K , Mayorga M E , Mclay L A . A nested-compliance table policy for emergency medical service systems under relocation[J]. Omega, 2016, 58, 154- 168. doi: 10.1016/j.omega.2015.06.001
6	Liu K L , Li Q F , Zhang Z H . Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints[J]. Transportation Research Part B, 2019, 119, 79- 101. doi: 10.1016/j.trb.2018.11.012
7	Bashiri M , Rezanezhad M , Tavakkoli-Moghaddam R , et al. Mathematical modeling for a p-mobile hub location problem in a dynamic environment by a genetic algorithm[J]. Applied Mathematical Modelling, 2018, 54, 151- 169. doi: 10.1016/j.apm.2017.09.032
8	万志远, 刘勤明, 叶春明, 等. 突发事件下的医院应急资源动态分配模型研究[J]. 计算机应用研究, 2019, 37 (2): 456- 459+469.
9	刘成堃, 贾涛, 高琦丽, 等. 基于改进遗传算法的省级医疗中心选址研究[J]. 计算机工程与应用, 2016, 52 (06): 17- 22+29.
10	杨建芳, 高岩. 营救设备数量受限的应急疏散模型和算法[J]. 运筹学学报, 2014, 18 (2): 77- 86.
11	Khayal D , Pradhananga R , Pokharel S , et al. A model for planning locations of temporary distribution facilities for emergency response[J]. Socio-Economic Planning Sciences, 2015, 52, 22- 30. doi: 10.1016/j.seps.2015.09.002
12	陈刚, 付江月, 何美玲. 考虑居民选择行为的应急避难场所选址问题研究[J]. 运筹与管理, 2019, 28 (9): 6- 14.
13	朱建明. 损毁情景下应急设施选址的多目标决策方法[J]. 系统工程理论与实践, 2015, 35 (3): 720- 727.
14	Xi J F , Mu K , Ding T Q , et al. A macroscopic and hierarchical location model of regional road traffic disaster relief material repository[J]. Advances in Mechanical Engineering, 2019, 11 (1)
15	王竹荣, 薛伟, 黑新宏, 等. 多阶段粒子群优化算法求解容量约束P-中位问题[J]. 计算机学报, 2020, 43 (6): 1139- 1160.
16	张磊, 李占雷, 杨金廷. 基于熵权修正Shapley值法的共同物流商业模式合作风险分担研究[J]. 数学的实践与认识, 2019, 49 (23): 49- 59.
17	Qiao J F , Li F , Yang S X , et al. An adaptive hybrid evolutionary immune multi-objective algorithm based on uniform distribution selection[J]. Information Sciences, 2020, 512, 446- 470.
18	Zhang Q , Xiong S W . Routing optimization of emergency grain distribution vehicles using the immune ant colony optimization algorithm[J]. Applied Soft Computing, 2018, 71, 917- 925.
19	Qiao J F , Li F , Yang S X , et al. An adaptive hybrid evolutionary immune multi-objective algorithm based on uniform distribution selection[J]. Information Sciences, 2020, 512, 446- 470.
20	Diabat A , Kannan D , Kaliyan M , et al. An optimization model for product returns using genetic algorithms and artificial immune system[J]. Resources Conservation and Recycling, 2013, 74, 156- 169.
21	Wang Y H , Wen Z G , Li H F . Symbiotic technology assessment in iron and steel industry based on entropy TOPSIS method[J]. Journal of Cleaner Production, 2020, 260
22	Zhang B , Pan Q K , Gao L , et al. An effective modified migrating birds optimization for hybrid flowshop scheduling problem with lot streaming[J]. Applied Soft Computing, 2017, 52, 14- 27.
23	Zhang X W , Dong S H , Liu Y H . P-hub median location optimization of hub-and-spoke air transport networks in express enterprise[J]. Concurrency and Computation: Practice and Experience, 2019, 31 (9): e4981.1- e4981.12.

序号	经纬度坐标	容量/万人	吸引力因子
1	113.938 27, 30.946 93	1.931 6	1
2	113.843 45, 30.664 18	0.064 3	1.3
3	113.592 49, 30.948 18	1.860 0	1.2
4	114.017 00, 31.285 44	0.064 3	1
5	113.915 78, 30.941 41	0.512 0	1.2
6	113.707 13, 31.252 71	3.426 9	1.1
7	114.140 94, 31.571 07	10.789 2	1.1
8	113.932 17, 30.913 36	11.437 8	1.1
9	113.954 47, 30.908 31	4.043 2	1
10	114.070 08, 31.357 24	1.297 3	1
11	113.778 25, 31.020 14	2.745 9	1
12	113.847 58, 30.570 91	0.302 7	1.1
13	113.841 91, 30.839 23	1.186 2	1
14	113.819 30, 30.651 50	1.016 2	1.3
15	113.535 99, 30.496 71	0.749 2	1
16	113.747 94, 31.040 91	3.017 0	1.1
17	114.046 63, 31.089 46	0.345 9	1
18	113.719 47, 31.097 06	0.605 4	1
19	113.958 31, 31.027 13	2.162 2	1
20	114.001 57, 31.252 27	4.043 2	1.2
21	113.697 42, 31.274 61	0.447 3	1.2
22	113.569 59, 30.942 64	1.729 7	1.3
23	113.786 06, 31.128 03	1.382 3	1

序号	经纬度坐标	序号	经纬度坐标
1	113.918 62, 30.934 46	5	113.995 18, 31.250 09
2	113.581 87, 30.953 84	6	114.129 53, 31.581 13
3	113.681 33, 31.266 19	7	113.760 58, 31.026 18
4	113.833 99, 30.651 95

	交通便利度	患者可达性	设施点的容量	区域人口密度	医院数量
信息熵值	7.866 0	9.575 3	8.089 2	9.662 3	9.816 3
熵权重	0.171 6	0.214 3	0.177 2	0.216 5	0.220 4

参数	水平
参数	1	2	3	4
overbest	282 444	282 505	282 443	282 709
ps	282 436	282 422	282 458	282 427
pcross	282 427	282 404	282 402	282 315
length	282 457	282 433	282 460	282 313
极差	30	101	58	396
等级	4	2	3	1

需求点	设施点	后方医院
57, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89	6	3
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46	7	6
1, 2, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 50, 52, 55	8	1
90, 91, 93, 100, 101, 102, 103, 106, 107, 108, 112, 114, 115	12	4
69, 70, 92, 94, 95, 96, 97, 98, 99, 104, 105, 109, 110, 111, 113	15	2
4, 47, 48, 49, 51, 53, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 86	16	7
3, 11, 12, 23, 24, 25	17	5
17, 18, 19, 20, 21, 22, 26, 27, 28, 29, 76	20	5