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2011高教社杯全国大学生数学建模竞赛

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2011高教社杯全国大学生数学建模竞赛

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交巡警服务平台的设置与调度

摘要

本文主要分析研究的问题是在警务资源有限的前提下，如何根据城市的实际情况与需求合理的设置交巡警服务平台、分配各平台的管辖范围、调度警务资源。

针对问题一：1.满足在其所管辖范围内出现突发事件时，尽量能在3分钟内有交巡警到达事发地的条件下，合理为各交巡警服务台分配管辖范围，通过matlab编程用floyd算法求出两个节点之间的最短距离矩阵，根据这个距离矩阵建立一个以0-1为变量的整数矩阵。距离和速度一定，我们以到达时间最短为目标函数。得到0-1规划优化方程，然后用lingo软件编程得到每个警台的管辖范围（见表一）。

2.对于重大突发事件，为了达到快速封锁的目的必须在最短时间内封锁所有路口，所以最后一个节点完成封锁所用时间的长短决定了整个快速封锁所用的时间。我们从得到的最短距离矩阵D中提取出A区的巡警服务平台到各个路口的距离矩阵。每个警台最多封锁一个路口，用0-1整数规划模型以最后一个节点的时间最短为目标函数。通过输入lingo软件编程得到最优封锁方案（见表二）。

3.根据现有交巡警服务平台的工作量不均衡和有些地方出警时间过长的实际情况，我们只考虑各个警台所管辖的范围（即管辖的节点个数）及各个警台案发率和平均案发率的比值，这两个指标。将节点个数大于5，案发率排在前5名的节点挑出来，分别统计出各个警台到各自管辖节点的距离，距离最近的那个节点即为新增的警台分别为节点69，55，49，30，86。

针对问题二：1. 我们对全市进行分区分析，统计出与工作相关的一些因素，建立了以各个交巡警平台管辖的面积、人口、节点数以及各个区的总发案率为变量的评判函数，判断出各个区域的合理性，得出C,D,F三个区不合理，对不合理的区域建立以增加平台数尽可能少，工作量尽可能均匀的多目标线性优化模型进行合理分配。

2. 为了达到快速搜捕嫌犯的目的，围堵的范围越小越好。在巡警接警后嫌犯只可能在A、C、F三区，所以将A、C、F三区定位最终围捕范围出入A、C、F三区的路口节点号分别为12、14、21、23、24、28、29、177、202、203、248、2、317、483、1、572、578这十八个节点。每个警台最多封锁一个路口，用0-1整数规划模型以最后一个节点的时间最短为目标函数。通过输入lingo软件编程得到利用9.02分钟完成围堵。

关键词：floyd算法 0-1整数规划多目标线性优化层次分析法

1.问题重述

肩负着刑事执法、治安管理、交通管理、服务群众四大职能。为了更有效地贯彻实施这些职能，需要在市区的一些交通要道和重要部位设置职能和警力配备基本相同的交通巡警服务平台。由于警务资源是有限的，所以我们应该根据城市的实际情况与需求合理的设置交巡警服务平台、分配各平台的管辖范围、调度警务资源。

对于问题一：我们要处理三个小问题：

1.满足在其所管辖范围内出现突发事件时，尽量能在3分钟内有交巡警（警车的时速为60km/h）到达事发地的条件下，合理为各交巡警服务台分配管辖范围。

2.对于重大突发事件，需要对进出该区的13条交通要到实现快速全封锁，但实际中一个平台的警力最多封锁一个路口，这就需要合理的安排该区20个交巡警服务平台警力。

3.根据现有交巡警服务平台的工作量不均衡和有些地方出警时间过长的实际情况，拟在该区确定增加平台的具体个数（2至5）和位置。

对于问题二：我们要处理两个小问题：

1.针对全市（主城六区A，B，C，D，E，F）的具体情况，按照设置交巡警服务平台的原则和任务，分析研究该市现有交巡警服务平台设置方案的合理性，若有明显不合理，给出解决方案。

2.如果该市P点（第32个节点）处发生了重大刑事案件，在案发三分钟后接到报警，犯罪嫌疑人已驾车逃跑，为了快速搜捕，要求给出最佳的围堵方案。

2.问题分析

本文主要围绕“合理设置交巡警服务平台”、“分配各平台的管辖范围”、“调度警务资源”这三个问题进行分析研究。 2.1对于问题一：

1.通过对附件的深入分析，了解了A区的路线、节点以及警台的位置分布，首先通过matlab编程（程序见附录六）对图中的每一个节点进行编号如图1，然后由每个节点的坐标根据公式l(x2x1)2(y2y1)2找到每两个点之间的距离，再通过matlab编程用floyd算法求出两个节点之间的最短距离矩阵。我们从得到的最短距离矩阵D中提取出A区20个巡警服务平台到92个节点的距离矩阵根据这个距离矩阵建立一个以0-1为变量的整数矩阵。由于距离和速度一定，我们以到达时间最短为目标函数。得到0-1整数优化矩阵Bij（1i92，

1j20）建立以各警台到达各个节点时间最短的目标函数，然后用lingo软件编程得到每个警台的管辖范围。

图1

2.为了达到快速封锁的目的必须在最短时间内封锁所有路口，所以最后一个节点完成封锁所用时间的长短决定了整个快速封锁所用的时间。我们从得到的最短距离矩阵D中提取出A区20个巡警服务平台到13个路口的距离矩阵。每个警台最多封锁一个路口，采用0-1整数规划模型以最后一个节点的时间最短为目标函数。通过输入lingo软件编程得到最优封锁方案。

3. 要确定A区需增加交巡警服务平台的具体个数(2-5)和范围,我们需要依据交巡警服务平台的工作量不均衡和有些地方出警时间过长的实际情况来考虑该问题。在第一小问中，我们按照要求给各个交巡警服务平台分配了管辖范围，这就为我们这一小问提供了出警时间过长的实际情况的量化指标。可以初步确定新增警台节点就在这些节点范围内。因此，我们只需考虑工作量不均衡这一因素了。在衡量工作量均衡问题上，我们考虑了各个警台所管辖的范围（即管辖的节点个数）及各个警台案发率和平均案发率的比值，这两个指标。将节点个数大于5，案发率排在前5名的节点挑出来，然分别统计出各个警台到各自管辖节点的距离，距离最近的那个节点即为新增的警台。因为服务平台距各自管辖范围是最近的，所以选择离服务平台最近的那个节点，可以保证新增平台对该管辖范围内尽量多的节点在三分钟左右可以到达。 2.2对于问题二：

1. 我们采用层次分析法，对六个区平台设置合理性进行评估，得出C区和F区明显的不合理。我们考虑工作量不均衡这一因素。在衡量工作量均衡问题上，我们考虑了各个警台所管辖的范围（即管辖的节点个数）及各个警台案发率和平均案发率的比值，这两个指标。

2. 保守分析当警方接到报案后，不考虑反应时间，立即对逃犯进行封堵。基于floyd的数理统计，计算出p点距全市各个路口的最小距离，确定一个可靠相对较小的围堵范围，运用0-1规划建立优化模型用lingo软件编程得到最好的围堵方案。

3.基本假设

3.1基本假设

1.假设交巡警服务平台在同一时间接到报警

2.假设犯罪嫌疑人并没有很了解该市的交通路线，走每条路线都具有等可能性

3.假设犯罪嫌疑人驾车速度等于警车速度（60km/h） 4.假设犯罪嫌疑人想尽快逃出该市，而不是想隐藏在该市

5.假设增加平台个数时只考虑工作量不均衡和有些地方出警时间过长这两个因素

6.假设追捕犯罪嫌疑人前的准备时间忽略不计

7.假设追捕犯罪嫌疑人时道路畅通无阻，没有意外发生 8.假设在增加服务平台时，不考虑经费问题

4.符号说明

4.1符号说明

D 最短距离矩阵

dij 各节点之间的最短距离

Xij 0-1 整数规划矩阵

Pi 第i节点的案发率 Pj 每个警台的任务量 Si 第i个节点的任务量

m 每个区的节点个数为 q 每个区的警台数

5.模型建立与求解

5.1模型准备两个节点之间的直线距离矩阵

用matlab软件编程对附件中A区数据进行处理得到每（见附录一），再用floyd算法（算法程序见附录）用matlab编程得到各节点之间的最短距离矩阵D（见附录二），记各节点之间的最短距离为dij（i为节点，j为警台）。 5.2模型建立求解

5.2.1交警服务平台合理分配

我们从得到的最短距离矩阵D中提取出A区20个巡警服务平台到92个节点的距离矩阵根据这个距离矩阵建立一个以0，1为变量的整数矩阵。由于距离和速度一定，我们以到达时间最短为目标函数。得到0-1整数优化矩阵Xij（1i92，1j20）

1,（第 i个节点受第 j个巡警服务台管辖） Xij=0,（第 i个节点不受第 j个巡警服务台管辖）目标函数TminXijdij*0.1

i1j1i92j20j20Xij1约束条件s.tj1B0或者1ij

把数据输入lingo软件进行求解（求解过程见附录三），分析结果可以得到A区每个巡警服务平台所管辖的节点。如下表：

表1 A区的分配方案服务平台 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 管辖节点 1 67 68 69 71 73 74 75 76 78 2 40 43 44 70 72 3 55 63 65 66 67 4 57 60 62 5 49 50 51 52 53 56 58 59 6 7 30 32 47 48 61 8 33 46 9 31 34 35 45 10 11 26 27 12 25 13 21 22 23 24 14 15 28 29 16 36 37 38 39 17 41 42 18 80 81 82 83 19 77 79 20 84 85 86 87 88 90 91 92 5.2.2选取最优快速封锁方案为了达到快速封锁的目的必须在最短时间内封锁所有路口，所以最后一个节点完成封锁所用时间的长短决定了整个快速封锁所用的时间。我们从得到的最短距离矩阵D中提取出A区20个巡警服务平台到13个路口的距离矩阵。每个警台最多封锁一个路口。以最后一个节点的时间最短为目标函数。得到0-1优化矩阵Xij(1i13,1j20)

1,（第 i个节点受第 j个巡警服务台管辖）Cij=

0,（第 i个节点不受第 j个巡警服务台管辖）目标函数tminT

i13Xijdij1i1j20约束条件 s.tXijdij1j1Xd*0.1T,X1或者0ijijij

把数据输入lingo软件进行求解（求解过程见附录四），分析结果可以得到最优封锁方案如表1：

表2 用Lingo求解0-1规划得到最优封锁方案警务平3 5 6 7 9 10 5

11 12 13 14 15 16 18

台出入境16 48 30 29 38 22 12 24 21 23 28 14 62 口数到达时6.02 2.47 3.21 8.57 4.72 7.7 3.79 3.59 2.7 6.47 4.75 6.74 6.73 间由表可知：完成快速封锁所用时间为8.57分钟。 5.2.3确定所加交巡警服务平台个数和位置

要确定A区需增加交巡警服务平台的具体个数(2-5)和范围,我们需要考虑交巡警服务平台的工作量不均衡和有些地方出警时间过长的实际情况。在第一小问中，我们按照要求给各个交巡警服务平台分配了管辖范围，这就为我们这一小问提供了出警时间过长的实际情况的量化指标。可以初步确定新增警台节点就在这些节点范围内。进而，我们考虑工作量不均衡这一因素。在衡量工作量均衡问题上，我们考虑了各个警台所管辖的范围（即管辖的节点个数）及各个警台案发率和平均案发率的比值，这两个指标（见表1）。将节点个数大于5，各平台案发率与平均案发率的比值排在前5的节点挑出来，然后分别统计出各个警台到各自管辖节点的距离，距离最近的那个节点即为新增的警台。（见表2）：

表2各平台节点个数和各平台案发率与平均案发率的比值

A区

服务平台管辖节点案发率平均案发率各平台与平均的作比节点个数

1 1 67 68 69 71 73 74 75 76 78 10.3 1.691297209 10 2 2 40 43 44 70 72 8.3 1.36284 6 3 3 55 63 65 66 67 8.7 1.428571429 8 4 4 57 60 62 4.4 0.7224955 4 5 5 49 50 51 52 53 56 58 59 7.2 1.18226601 9 6 6 2.5 0.410509031 1 7 7 30 32 47 48 61 9.6 1.576368 6 8 8 33 46 5 0.821018062 3 9 9 31 34 35 45 8.2 1.3469622 5 10 10 1.6 0.26272578 1

6.09 11 11 26 27 4.6 0.755336617 3

12 12 25 4 0.65681445 2 13 13 21 22 23 24 8.5 1.395730706 5 14 14 2.5 0.410509031 1 15 15 28 29 3.7 0.607553366 3 16 16 36 37 38 39 6.4 1.05090312 5 17 17 41 42 5.3 0.870279146 3 18 18 80 81 82 83 6.1 1.0012036 5 19 19 77 79 3.4 0.558292282 3

20 84 85 86 87 88 90 91 20 11.5 1.8883414 10

表3新增平台的具体位置

A区需增平台

服务平台距离服务平台最近的节点节点距离服务平台的距离

67 16.1941

68 12.071

需增的平台的节点 69（410,355）

69 71 73 74 75 76 78 55 63 65 66 67 49 50 51 52 53 56 58 59 30 32 47 48 61 84 85 86 87 88 90 91 92 5 12.3683 10.2961 6.265 9.3005 12.836 6.4031 22.70 12.659 30.11 21.061 15.23 18.3923 22.6349 5 8.4853 12.2932 16.5943 11.7082 20.8369 23.01 15.2087 5.831 11.4012 12.8062 12.902 41.902 11.7522 4.4721 3.6056 14.651 12.9507 9.4868 13.0223 15.9921 36.0171

55（371,353）

49（342,372）

30（314,367）

86（447,392）

新增的平台分别为节点69，55，49，30，86。 5.3.1分析交巡警服务平台设置的合理性

由题目中所提供的全市六区交通网与平台设置的数据可知，全市六区的警务平台都分布在各区的案发率较高的路口上，以达到缩短出警时间的目的，这一点是合理的。针对该问题，首先我们采用层次分析法，对六个区平台设置合理性进行评估，得出C区和F区明显的不合理。然后，基于第一问的第三小问的思想，我们对这两个区进行增设平台。

5.3.1.1合理性评估

层次图如下：

影响交巡警服务平台合理设置的因素

每个警台的案发率每个警台的出警时间每个警台管辖范围的大每个警台所管辖区域的平均人口密度

1331/312A1/31/211/31/21/232 21由matlab得到最大特征值λmax=4.1212

n4.012124CImax0.04041 n141 通过一致性检验

归一化处理得到权重每个警台的案发率0.4900，每个警台的出警时间0.2310 每个警台管辖范围的大小0.1634 每个警台所管辖区域的平均人口密度0.1155

对各区每个警台平均人口密度、案发率、出警时间和管辖范围大小，进行统计分析得到如下结果如下表4所示

表4四个指标分析每个警台区平均案发域率 A B C D E F 6.09 8.3 11.0117 7.5333 7.66 9.9272 每个警台平均出警时间 0.9671 2.5187 4.6211 2.4115 2.8751 4.1698 每个警台平均管辖范围大小 4.6 9 9 5.6667 6.8 9.7272 每个警台所管辖区平均人口密度 0.13 0.02 0.013 0.0212 0.0117 0.0176 再将表4数据进行归一化处理，得到表5，如下：表5归一化处理

区域 A B C D E F

每个警台平均案发率

0 0.449 1 0.293 0.319 0.78

每个警台平均出警时间

0 0.425 1 0.395 0.522 0.877

每个警台平均管辖范围大小

0 0.858 0.858 0.208 0.429 1

每个警台所管辖区平

均人口密度

1 0.11 0.01 0.076 0 0.047

总利弊指数 0.116 0.471 0.862 0.278 0.347 0.753

由上表可以得出，C区和F区明显不合理。

5.3.1.2增设平台方案

基于第一问第三小问的思想，依据距离平台位置最近的条件，先通过matlab编程用floyd算法求出两个节点之间的最短距离矩阵，根据这个距离矩阵建立一个以0-1为变量的整数矩阵。距离和速度一定，我们以到达时间最短为目标函数。得到0-1规划优化方程，然后用lingo软件编程得到每个警台的管辖范围。然后，我们考虑工作量不均衡这一因素。在衡量工作量均衡问题上，我们考虑了各个警台所管辖的范围（即管辖的节点个数）及各个警台案发率和平均案发率的比值，这两个指标。

对于C区和F区，将节点个数大于10，且各平台案发率与平均案发率的比值大于10的节点挑出来（分别见表6、表8），然后分别统计出各个警台到各自管辖节点的距离，距离最近的那个节点即为新增的警台（分别见表7、表9）。

表6各平台节点个数和各平台案发率与平均案发率的比值服务平台 166 167 168 169 170 172 173 174 175 176 177 案发率平均各平台案与平均发的作比率节点个数管辖节点 166 262 263 2 265 167 248 249 250 251 252 255 258 259 260 261 168 1 190 191 192 169 2 170 222 223 224 225 226 276 277 282 172 217 218 227 228 229 173 232 233 234 235 236 237 238 239 245 247 174 211 212 213 214 219 220 221 175 183 193 194 195 196 197 198 199 176 184 185 186 187 188 177 200 201 202 6.3 13.5 4.7 3.4 10.5 15 8.3 10.1 11 8.1 4.3 11 5.315 5 11.3 11 3.965 5 2.868 2 8.858 9 13.076 12 12.6 6 7.002 11 8.521 8 1.19.280 9 85 6.833 6 3.628 4 9.280 12 14.0 16 171 171 215 216 230 231 240 241 242 243 244 246 253 15.5 178 178 203 204 205 206 207 208 209 210 283 285 286 179 179 274 275 277 278 279 280 281 282 284 287 288 2 16.7 290 293 294 180 268 269 270 271 295 296 297 298 299 300 301 302 180 303 304 305 306 307 308 309 310 311 312 313 314 315 29.3 316 317 181 182 181 266 267 268 317 318 319 182 256 257 272 273 291 292 7.9 10.5 24.718 27 6.665 7 8.858 7 表7新增平台的具体位置区需增平台服务平台 167 距离服务平台最近的节点 167 248 节点距离服务平台的距离 0.000 12.369 需增的平台的节点 C249(155,396) 9

249 250 251 252 255 258 259 260 261 171 215 216 230 231 171 240 241 242 243 244 246 253 179 274 275 277 278 279 280 179 281 282 284 287 288 2 290 293 294 180 268 180 269 270 271 295 10

9.849 37.706 38.133 26.077 18.772 34.584 28.672 35.743 207.343 0.000 36.274 9.605 8.944 7.211 49.040 27.827 59.580 11.944 14.711 29.491 58.259 0.000 48.313 14.866 21.574 24.224 18.839 26.203 46.150 28.179 36.425 44.671 56.704 38.676 29.1 46.742 13.4 0.000 12.500 19.000 21.346 30.021 24.500 C308(184,463.5) C294(219,451) C231(288,403)

296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 36.2 .290 40.497 22.574 28.8 38.239 46.500 53.583 47.500 40.500 30.500 17.500 6.021 6.021 16.329 24.535 15.035 24.049 33.049 45.059 36.559 47.070 表8各平台节点个数和各平台案发率与平均案发率的比值服务平台 475 476

平

案均各平台发案与平均管辖节点

率发的作比

率 15.

475 550 551 555 556 557 558 559 561 563 5 565 15.725

9 13.

476 532 533 534 535 3 4 5 6 7 552 553 5 13.451

477 492 493 494 495 496 497 498 499 500 501 502 503

18.

504 505 506 507 508 509 516 517 518 519 520 521 522 18.099

523 529 530

478 512 513 514 515 524 525 526 527 528 536 537 538 15.

0115.429

539 2 6

479 575 576 577 578 579 580 581 582 9.1 9.000 480 562 566 567 568 569 570 574 8.6 8.505 481 486 490 491 531 8 9 8.6 8.505

482 487 488 4 560 6.7 6.626

483 510 511 4.4 4.352 484 0 1 3.9 3.857 485 571 572 573 4.5 4.451

节

点个数 12 13

477 29

478 479 480 481 482 483 484 485

15 9 8 7 5 3 3 4

表9新增平台的具体位置 F区需增平台服务平台距离服务平台最近的节点 475 550 551 555 556 475 557 558 559 561 563 5 565 476 532 533 534 535 3 476 4 5 6 7 552 553 5 477 492 493 494 495 496 477 497 498 499 500 501 502 503 504 12

节点距离服务平台的距离 0.000 27.655 15.655 7.159 4.610 4.301 20.526 35.333 43.8 19.5 10.343 13.829 0.000 21.310 32.356 24.122 17.568 14.000 10.000 4.031 5.612 11.112 14.127 8.246 10.482 0.000 24.561 17.490 18.704 11.900 19.059 12.748 5.099 12.379 7.071 7.280 12.291 24.385 25.492 需增的平台的节点 F557(380,270.5) F5(369,249.5) F498(325,220)

505 506 507 508 509 516 517 518 519 520 521 522 523 529 530 478 512 513 514 515 524 525 478 526 527 528 536 537 538 539 2 39.634 45.238 32.200 38.908 48.408 49.666 43.583 35.444 30.709 24.744 28.867 46.5 52.395 13.605 32.768 0.000 47.350 55.735 42.697 55.697 50.3 37.106 35.678 30.587 22.029 18.029 10.512 15.040 21.731 9.220 F2(394,2) 5.3.2犯罪嫌疑人逃跑范围确定犯罪嫌疑人的逃跑速度以每分钟一公里记，由于案发地32号节点距离出入A区的30号、48号、16号路口的距离分别为1.7、2.4、3.3分钟的车程，所以该嫌犯在案发3分钟后有逃出A区的可能，为了达到快速搜捕嫌犯的目的，围堵的范围越小越好。在巡警接警后嫌犯只可能在A、C、F三区，所以将A、C、F三区定位最终围捕范围

围堵方案的距离

出入A、C、F三区的路口节点号分别为12、14、21、23、24、28、29、177、202、203、248、2、317、483、1、572、578这十八个节点。由问题（1.2）所给出的模型，应用lingo软件编程得最佳围捕方案如下

表10 序号 12 14 围堵节点 12 14 13

到达时间 0 0

372 11 13 15 173 175 177 178 167 166 181 483 481 484 485 479 21 23 24 28 29 177 202 203 248 2 317 483 486 1 572 578 2.51867 4.6751 2.38537 4.75184 7.92872 9.02130 6.4609 4.44777 3.67875 6.62234 5.47516 0 3.94653 7.04178 1.65529 5.75752 由上表可知到达封锁地点的时间是9.02分钟，而案发后嫌犯21号节点最快逃出A、E、F三区最短时间为13.3分钟，所以该围堵方案是合理的。

6.模型评价与改进

6.1模型的评价

本文所用模型运用了floyd算法、lingo多目标优化模型、0-1规划模型,对数据进行了深入分析与处理，妥善的安排了各个警点的执勤任务，保证全市警力任务的高效执行。具有很强的可操作性。由于现实中很难做到实时出警，道路毫无拥堵等情况，所以本文所建模型具有一定的局限性 6.2模型的改进

在第二题的第一问中可以考虑的因素有很多，另外对这些因素的数据进行量化处理得到最后的总权值可以使模型更加精密。得到的结果也最接近现实情况。

7.参考文献

[1]:薛定宇，陈阳泉.初等运用数学效果的 matlab 求解[M].北京:清华大学出版社,2004.,8

[2]：石辛民，郝正清.基于 matlab 的适用数值计算[M].北京：清华大学出版，北京交通大学出版社，2006,2

[3]:在筠，郑汉鼎等.LINGO 教程[M].北京:清华大学出版社 2006,2

8.附录

附录一：两个节点之间的直线距离矩阵

0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5 Inf Inf Inf Inf 6.2982 9.300538 Inf Inf 6.403124 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf

Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 19.14419 Inf Inf 8 9.486833 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf

Inf Inf 8.602325 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 11.6297 42.469 Inf Inf Inf Inf Inf Inf Inf Inf Inf 12.659 Inf Inf Inf Inf Inf Inf Inf Inf Inf 15.23975 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf 45.60976 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf 18.681 Inf Inf Inf Inf 3.5 10.30776 Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 14.56022 Inf 5 8.485281Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 14.86607 Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf 16.03122 Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf Inf 38.18377Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 5.830952 Inf11.40175 Inf Inf Inf Inf 30.41381 Inf Inf Inf Inf Inf Inf Inf InfInf 12.80625 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 11.59741 Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf8.2773 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 9.30053820.79663 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 11.59741 0 Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf5.024938 4.2421 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf

Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf 35.38361 Inf Inf Inf Inf Inf Inf Inf49.21636 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf Inf InfInf Inf Inf Inf 32.69557 Inf Inf 20.02498 9 Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf 17.888 Inf 33.04921 Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf Inf Inf InfInf Inf Inf Inf 9.055385 5 23.85372 Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0 Inf 67.41662Inf Inf Inf Inf 32.966 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 38.18377 Inf Inf Inf Inf Inf Inf Inf 0Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 47.51842 Inf Inf29.681 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 67.41662 Inf 0Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf 6.082763 Inf 34.05877 Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf

Inf Inf Inf Inf 26.87936 8.5 9.848858 Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 40.22437 Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 0Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf19.72308 Inf Inf Inf Inf Inf Inf 8.062258 6.708204 Inf 5.385165Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf 9.848858 Inf 4.472136 Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf 0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf InfInf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 4.472136 3.605551Inf Inf 9.486833 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 32.966 InfInf Inf Inf Inf

附录二A最短路径矩阵D

0 18.98749 38.83884 45.35217 93.742 95.37518 115.003590.22625 92.238 146.4957 190.8793 222.3615 220.0175160.2847 142.4932 92.86812 35.91205 25.572 17.5834652.63199 192.9344 210.9621 225.0175 228.932 210.9043181.8793 1.3123 190.0116 195.1581 120.8344 112.8115103.6017 98.50272 97.27932 88.01174 90.82363 95.9226558.80935 55.80935 38.13168 44.41205 26.0632 18.0009428.47432 81.30353 80.92571 108.3031 118.5011 88.74286.06732 82.25943 80.65577 82.03468 59.23118 51.4978376.41313 .03371 71.53371 79.34396 62.74461 97.4577248.85217 35.0444 25.902 23.59909 20.43681 16.1941712.07107 5 10.38516 11.40312 16.40312 10.29611 6.29829.300538 12.83607 16.40312 6.403124 13.11133 17.5834632.35393 36.43921 31.030 40.87974 48.15985 56.23751.942 47.91087 43.87974 45.17134 49.91475 69.93974

18.98749 0 21.116 56.85068 78.33711 98.42077 97.2811972.50394 74.53207 128.7734 173.157 204.6392 201.03141.2972 124.7709 73.88063 25.91112 43.8476 36.5709570.83387 173.9469 191.9747 206.03 211.2097 193.182

1.157 171.59 172.23 177.4358 103.1121 95.02385.87943 80.78041 79.55701 70.243 71.83614 76.9351639.82186 36.82186 19.14419 34.41112 16.06226 8 9.48683363.58123 63.2034 92.733 103.09 73.33711 83.2819679.47408 75.17291 66.621 43.82 33.77553 79.4155575.53222 83.03222 82.355 74.24312 108.9562 60.3506846.291 37.48753 31.65657 28.4943 24.25166 21.0585613.98749 8.602325 20.39061 16.06226 24.12452 25.2524725.58625 29.12178 33.59392 25.39061 32.09882 36.5709550.5558 .109 49.23276 59.08162 66.36173 74.4394270.14388 66.11275 62.08162 63.37321 68.11663 80.72796 38.83884 21.116 0 40.43385 57.22058 77.30423 76.165 51.3874 53.415 107.6568 152.0404 183.5227 187.4051 127.6723 103.63 60.25566 47.02765 58.9491 41.94257 85.93536 160.3219 178.3497 192.4051 190.0932 172.06 143.0404 150.4735 151.1728 156.3192 81.9956 73.9727 .7629 59.66388 58.44047 49.1729 .1729 59.27191 60.9384 57.9384 40.26073 55.52765 37.17879 29.116 11.6297 42.469 42.08687 71.7808 81.97884 52.22058 62.163 58.357 .05638 45.51237 22.70886 12.659 58.29902 59.11539 66.61539 61.27302 57.8263 92.53941 43.93385 30.12609 21.0707 15.23975 18.40203 22.467 26.76777 33.83884 29.71886 40.24197 37.17879 45.24105 45.10382 31.15711 27.62157 32.09371 42.09371 46.4147 50.88684 65.6573 69.74259 .33426 74.18312 81.46323 .092 85.24538 81.21425 77.18312 78.47471 83.21813 101.8445

45.35217 56.85068 40.43385 0 49.20044 50.02301 76.5669 83.27283 .86668 144.108 188.4916 219.9738 209.8179 150.0851 114.7507 82.66853 74.70525 63.84362 46.83709 67.9888 182.7348 200.7626 214.8179 226.43 208.5166 179.4916 186.9246 162.2691 155.3534 81.02976 99.67336 87.96866 91.93 94.162 85.62404 80.62404 85.72306 48.60976 45.60976 63.28743 83.20525 .85639 56.79413 47.36384 79.97229 73.97229 63.76066 73.95869 50.55581 40.71515 36.90727 35.3036 43.8476 34.494 44.441 31.06096 18.681 26.181 33.99179 17.39244 52.10555 3.5 10.30776 19.36315 25.1941 28.35638 32.59902 36.72213 43.79319 49.17836 50.19632 55.19632 55.828 51.61715 36.05163 32.5161 36.98823 46.98823 51.30923 55.78136 70.55182 74.63711 69.22878 70.79677 63.51666 71.59435 81.85903 77.8279 73.79677 77.33231 80.86928 100.43

93.742 78.33711 57.22058 49.20044 0 29.42629 27.367 35.35685 46.927 100.4161 144.7997 176.2819 186.5506

129.6963 117.0395 135.7997 38.76822 94.21119 68.85028 12.29317 30.518 58.69849 65.55023 162.3459 143.2327 43.63333 91.21119 50.65739 16.59433 23.018 67.75387 62.27967 177.4952 113.0687 51.1997 97.4813 44.65739 11.7082 15.208 72.46033 104.2482 191.5506 106.1529 51.19691 112.7482 14.56022 34.51171 38.6583 75.62261 112.2343 95.22781182.8524 1.824731.82933 50.4729256.19691 57.78024.39937 86.3371124.75826 5 8.48528144.56159 20.8369753.75826 52.5507579.86525 83.9883591.05942 84.44235 118.9425 130.9098 95.37518 35.6627 130.0021 117.8621 136.1055 39.07407 94.51704 88.93394 22.758 27.4905 53.37332 86.74514 101.02 105.8044 121.4677 150.7676 115.0035 24.77725 109.0122 144.406 108.6671 11.40175 73.52711 87.79435 35.85175 48.20344 79.91722 102.9324 121.2685 127.0515 148.0116

86.93944 80.90682 123.0278 126.8787 98.42077 47.26012 65.85608 162.6518 143.5386 43.93918 91.51704 50.96324 18.9467 31.34147 60.33077 93.8162 86.074 120.5748 131.7324 97.28119 29.09208 38.18377 141.6619 116.1002 16.50077 70.52711 40.04293 39.659 57.88536 86.095 110.0035 107.3218 141.822 158.2762

97.462 94.39937 85.375 95.375 117.6195 119.8475 122.8475 126.3831 77.30423 50.02301 100.7219 145.1055 62.58552 124.3319 177.8011 191.8565 113.3745 106.4588 51.50555 51.50276 109.1947 132.8319 44.96324 14.86607 23.24786 31.79186 23.84147 16.03122 69.38616 75.21711 99.20137 100.2193 82.53911 87.01124 124.6601 119.2518 127.7012 123.6701 76.165 76.5669 73.28351 117.6671 41.59559 115.0841 150.3627 1.4181 85.70218 80.157 24.06715 33.33473 88.20478 113.6052 34.07778 12.80625 43.9608 39.07467 50.38536 42.57511 95.12034 91.4044 105.8835 116.4066 103.7862 108.2584 145.9072 140.49 1.2451

150.214

102.4616 100.007999.69995 104.1721112.5674 120.51129.92 149.945

29.42629 0 27.67232176.5878 186.8565113.8666 96.8601183.1583 165.130532.13518 50.7787756.50276 58.08613114.483 106.420825.011 33.194.59537 .52539.48088 .01178.37939 82.62203105.2193 105.671397.01124 101.3322120.6701 113.39127.2056 130.742627.367 27.67232 0149.1494 159.4181135.1137 118.1072155.7199 137.69215.830952 23.10535.51283 30.41381113.3434 105.281212.90202 32.36761.87818 63.5056666.02477 41.9020294.56668 98.80932113.3434 121.4057118.2584 122.5794147.214 139.9339153.7495

157.2865

159.922 90.22625 24.77725 94.33943 137.3228 100.4428 13.379 58.834 63.01711 72.50394 51.3874 83.27283 35.35685 35.6627

0 11.59741 65.0592 109.4428 140.9251 151.1938.76184 26.92282 98.41506 110.3365 93.32997126.91 142.1384 156.1938 147.4956 129.4678107.8759 102.2803 104.9318 30.6082 25.080198.2773 15.84285 15.84005 20.84005 25.9390755.834 73.53201 98.93239 88.5662 80.5039415.300 9.300538 20.79663 30.99467 40.35683.84214 56.19383 86.77283 78.15518 96.49123 102.2742 140.9283 145.2492 92.238 29.09208 82.74202 139.3509 .62491 17.69033 47.25692 65.04524 55.43955 67.79124 93.36668 80.18331 98.51936 104.3024 142.9565 133.6518 146.4957 73.28351 127.7566 193.5922 35.38361 61.88175 101.4982 119.2865 108.9013 121.253 147.608

47.65002 65.87575 72.96506 85.22625 82.451 117.0447 136.6328 74.53207 11.59741 50.23881 115.3917 97.05794 12.59131 44.25692 10.95084 59.24744 77.47316 80.61537 87.238 84.572 119.0728 138.6609 128.7734 65.0592 94.43023 95.10693 42.81665 56.78273 98.49822 65.19214 112.7092 130.935 134.8567

51.95118 47.06506 48.77829 38.7284258.37575 50.5655 74.01516 59.9946772.45811 66.62716 69.743 74.0320781.10627 91.62937 88.5662 96.6284679.008 83.48111 93.48111 97.80211121.13 115.7217 125.5705 132.8506132.6017 128.5705 129.8621 134.605553.415 .86668 46.927 47.260120 .2413 98.62491 130.1071 140.375915.32 88.81395 112.36 95.3581131.3205 145.3759 136.6776 118.9997.75722 107.2441 34.92304 20.557165.024938 4.2421 9.2421 14.3416661.93459 87.33497 90.59433 82.5320716.95084 32.39405 41.9941 51.92763.86 58.66247 56.4286 46.3787269.97316 62.16291 85.61257 70.994174.48624 68.65529 71.81756 76.060283.1344 93.6575 90.59433 98.6565981.03711 85.50924 95.50924 99.83024123.1581 117.7498 127.5987 134.8788134.6298 130.5987 131.02 136.6337107.6568 144.108 100.4161 100.7219.2413 0 44.38361 75.86585 86.1345669.5667 143.0553 166.6059 149.599477.07918 91.13456 82.43635 .4086141.9486 151.4355 79.11446 .7485849.21636 58.48394 63.48394 68.58296116.1759 141.5763 144.8356 136.773471.19214 85.85584 86.18553 105.4161117.0104 112.1243 110.6699 100.62123.435 115.6247 139.0744 115.1855128.7275

122.66 126.05 130.3015

134.4246 141.4957 137.3757 147.88 144.8356 152.79152.7607 138.8139 135.2784 139.7505 149.7505 1.0715158.37 173.3141 177.3994 171.9911 181.84 1.1201197.1977 192.9022 188.8711 184.84 186.1315 190.875187.31

190.8793 173.157 152.0404 188.4916 144.7997 145.1055117.6671 109.4428 98.62491 44.38361 0 37.91353 41.7509583.37298 138.8138 113.9503 187.43 210.95 193.983

237.9758 50.72332 32.69557 46.75095 38.05274 20.02498 916.43303 186.3323 195.8191 123.4981 109.1322 106.26101.1663 93.59997 102.8675 107.8675 112.9666 145.8818142.8818 160.5595 185.9599 1.2192 181.157 163.6701109.5758 115.5758 130.2395 130.5691 149.7997 153.285157.0928 161.394 156.5079 155.0535 145.0036 165.6366175.3186 167.8186 160.0083 183.458 159.5691 191.9916179.2403 173.1111 167.2802 170.4425 174.6851 178.8082185.8793 181.7593 192.2824 1.2192 197.2815 197.1443183.1976 179.662 184.1342 194.1342 198.4551 202.9273217.6977 221.783 216.3747 226.2236 233.5037 241.5814237.2858 233.27 229.2236 230.5152 235.2586 232.2767 222.3615 204.6392 183.5227 219.9738 176.2819 176.5878149.1494 140.9251 130.1071 75.86585 37.91353 0 59.77002119.5028 170.2961 145.4326 218.9211 242.4718 225.4653269.458 86.85316 68.821 .77002 35.9163 17.88840.48224 33.04921 217.8145 227.3013 1.9803 140.6144137.7476 132.86 125.0822 134.3498 139.3498 144.4488177.31 174.31 192.0417 217.4421 220.7015 212.6392195.1524 141.058 147.058 161.7217 162.0514 181.2819184.7672 188.5751 192.8762 187.9901 186.5357 176.4859197.11 206.8008 199.3008 191.4906 214.9402 191.0514223.4738 210.7225 204.5934 198.7624 201.9247 206.1674210.2905 217.3615 213.2415 223.77 220.7015 228.7637228.6265 214.6798 211.1443 215.61 225.61 229.9374234.4095 249.18 253.2653 247.8569 257.7058 2.9859273.0636 268.7681 2.7369 260.7058 261.9974 ......

78 119.27 137.4077 147.6058 124.2029 114.3622 110.108.9507 117.4947 95.95665 .84211 104.708 92.3286399.82863 107.63 84.122 118.9023 70.29677 71.7698862.71449 61.94337 58.78109 60.07392 55.95081 48.87974.291 48.09151 46.01936 37.95711 41.98823 53.0970849.56155 45.041 37.47662 30.76842 26.29628 17.2926

12.26766 12.84886 3 10.28011 13.09238 8.062258 4.0311290 3.535534 7.07251 27.09749

45.17134 63.37321 78.47471 77.33231 126.3831 127.2056153.7495 129.8621 131.02 186.1315 230.5152 261.9974262.7466 203.0139 182.1291 135.5972 53.98143 19.5256236.53215 13.02237 235.6635 253.6913 267.7466 268.5679250.01 221.5152 228.9482 229.75 232.536 158.2124152.4474 143.2376 138.1386 136.9152 127.76 132.76137.7466 101.5385 98.53846 80.86079 62.48143 63.43755.37321 72.86005 120.9394 120.5616 140.9433 151.1413126.76 117.78 114.09 112.4862 120.0518 97.2482491.1337 108.2436 95.816 103.32 111.1744 87.72475122.4379 73.83231 73.06147 .00609 63.23496 60.0726861.36551 57.24241 50.17134 55.5565 49.38311 47.3109639.2487 43.27983 .38867 50.85314 46.381 38.7682132.06001 27.58787 13.75706 8.732125 14.14045 6.53553413.815 16.62792 11.59779 7.566663 3.535534 0 4.74341624.7684

49.91475 68.11663 83.21813 80.86928 129.92 130.7426157.2865 134.6055 136.6337 190.875 235.2586 266.7408267.4901 207.7573 186.8725 140.3407 58.72485 24.2690341.27556 15.9877 240.4069 258.4347 272.4901 273.3113255.2836 226.2586 233.6916 234.3909 236.073 161.7494157.1908 147.981 142.882 141.6586 132.391 137.391142.49 106.2819 103.2819 85.60421 66.34183 68.17860.11663 77.60346 125.6828 125.305 144.4803 1.6783131.27 121.4348 117.6269 116.0232 124.5672 101.991795.87712 111.7806 99.40114 106.9011 114.7114 91.26173125.9748 77.36928 77.804 68.7495 67.97838 .816166.103 61.98582 .91475 60.29992 .12652 52.03743.99212 48.02324 59.13209 55.59656 51.12442 43.5116336.80343 32.33129 18.50048 13.475 18.88387 10.0725117.35262 12.38215 7.07251 3.041381 7.07251 4.743416 020.02498

69.93974 80.72796 101.8445 100.43 149.945 150.7676159.922 145.2492 133.6518 187.31 232.2767 263.759247.6031 187.8703 183.06 120.4537 .81684 44.2940261.30055 36.01269 220.5199 238.77 252.6031 270.3295252.3017 223.2767 230.7098 231.409 240.0766 165.7531.209 151.3421 146.2431 138.6768 129.4092 124.4092129.5082 86.394 .394 81.6962 46.31684 .665772.72796 90.21479 136.1174 142.1174 1.5052 172.824151.3004 141.4597 137.6518 136.0482 144.5922 122.0166114.5035 131.8055 119.4261 126.9261 134.73 111.2867145.9998 97.39427 97.82987 88.77449 88.00336 84.8410986.13391 82.01081 74.93974 80.3249 74.15151 72.07936

.0171 68.04823 79.15707 75.621 71.1494 63.5366156.82841 52.35627 38.526 33.50053 38.90885 30.0974937.3776 32.40714 21.37756 23.06637 27.09749 24.7684

20.02498 0 附录三： model: sets:

department/1..92/; type/1..20/;

benefit(department,type):d,x; endsets

min=@sum(benefit(i,j):d(i,j)*x(i,j)); @for(benefit:@bin(x)); @for(department(i):

@sum(type(j):x(i,j))=1); @for(type(i):x(i,i)=1); data:

d=@ole('C:\\Documents and Settings\\Administrator\\\\123.xls',data);

enddata end

Global optimal solution found.

Objective value: 1058.939 Objective bound: 1058.939 Infeasibilities: 0.000000 Extended solver steps: 0 Total solver iterations: 0

Model Class: PILP

Total variables: 1820 Nonlinear variables: 0 Integer variables: 1820

Total constraints: 93 Nonlinear constraints: 0

Total nonzeros: 30 Nonlinear nonzeros: 0

Value

D( 0.000000

D( 23

桌面

1) 2)

1, 1,

18.98750

D( 38.82900

D( 111.6766

D( 93.74290

D( 1, 1, 1, 1, 3) 4) 5) 6) 113.8265

D( 121.1093

D( 96.59420

D( 92.24450

D( 146.4858

D( 190.8694

D( 222.3516

D( 226.2345

D( 166.5013

D( 142.4832

D( 99.08470

D( 35.91220

D( 25.570

D( 17.58340

D( 52.63200

D( 18.98750

D( 0.000000

D( 21.11650

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2,

7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 1) 2) 3) 4)

110.47

D( 78.33710

D( 98.42070

D( 103.6235

D( 2, 2, 2, 2, 5) 6) 7) 8) 78.88170

D( 74.53200

D( 128.7733

D( 173.1569

D( 204.6391

D( 208.5220

D( 148.7888

D( 124.7707

D( 81.37220

D( 25.91120

D( 43.84760

D( 36.57090

D( 70.83390

D( 38.82900

D( 21.11650

D( 0.000000

D( .35990

D( 57.22060

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3,

9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 1) 2) 3) 4) 5) 6)

77.30420

D( 82.50700

D( 57.76520

D( 53.41550

D( 3, 3, 3, 3, 7) 8) 9) 10) 107.6568

D( 152.0404

D( 183.5226

D( 187.4055

D( 127.6723

D( 103.62

D( 60.25570

D( 47.02770

D( 58.93930

D( 41.93280

D( 85.92560

D( 111.6766

D( 110.47

D( .35990

D( 0.000000

D( 49.20040

D( 50.02290

D( 76.56680

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,

11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 1) 2) 3) 4) 5) 6) 7) 8)

84.55720

D( .86670

D( 144.1080

D( 188.4916

D( 4, 4, 4, 4, 9) 10) 11) 12) 219.9738

D( 213.8567

D( 1.1235

D( 114.7506

D( 86.70690

D( 131.3033

D( 86.03090

D( 103.0374

D( 67.98880

D( 93.74290

D( 78.33710

D( 57.22060

D( 49.20040

D( 0.000000

D( 29.42630

D( 27.360

D( 35.35680

D( 46.920

4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,

13) 14) 15) 16) 17) 18) 19) 20) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

100.4161

D( 5, 144.7997

D( 5, 176.2819

D( 5, 186.5507

D( 5, 129.6962

D( 5, 65.55020

D( 5, 16) 附录四：

model: sets:

department/1..20/; type/1..13/; a/1..20/:c;

benefit(department,type):d,x; endsets

min=@max(benefit(i,j):d(i,j)*x(i,j)); @for(benefit:@bin(x)); @for(department(i):

@sum(type(j):x(i,j))<1); @for(type(j):

@sum(department(i):x(i,j))>1); data:

d=@ole('C:\\Documents and Settings\\Administrator\\桌\\7.xls',Data);

enddata end

Local optimal solution found.

Objective value: 131.3205 Objective bound: 131.3205 Infeasibilities: 0.000000 Extended solver steps: 193 Total solver iterations: 23736

Model Class: MINLP

Total variables: 280 Nonlinear variables: 257 Integer variables: 260

11) 12) 13) 14) 15) 面

Total constraints: 34 Nonlinear constraints: 1

Total nonzeros: 777 Nonlinear nonzeros: 257

Variable Value

C( 0.000000

C( 29

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

0.000000

C( 0.000000

D( 1, 222.3516

D( 1, 19) 20) 1) 2) 204.6391

D( 183.5226

D( 219.9738

D( 176.2819

D( 176.5878

D( 149.1488

D( 140.9251

D( 130.1071

D( 75.86580

D( 37.91400

D( 0.000000

D( 59.77050

D( 119.5037

D( 170.2960

D( 145.4325

D( 230.5503

D( 242.4619

D( 225.45

D( 30

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2,

3) 4) 5) 6) 7) 8) 9) 1) 2) 3) 4) 5) 6) 7)

10) 11) 12) 13)

269.4482

附录五： model: sets:

jindian/wh1..wh20/; lukou/x1..x13/;

links(jindian ,lukou):juli,x; endsets data:

juli=@ole('C:\\Documents and Settings\\Administrator\\\\7.xls',Data3);

@text(C:\\114.txt)=x; enddate min=0.1*T

@for(links:jiuli*x(links:@bin(x)); @sum(links:x)=13;

@for(lukou(j):@sum(jindian(i):x(i,j)=1); @for(jindian(i):@sum(lukou(j):x(i,j)<=1); End

附录六： x=[413 403 383.5 381 339 335 317 334.5 333 282 247 219 225 280 290 337 415 432 418 444 251 234

桌面

225 212 227 256 250.5 243 246 314 315 326 327 328 336 336 331 371 371 388.5 411 419 411 394 342 342 325 315 342 345 348.5 351 348 370 371 3 363 357 351 369 335 381 391 392 395 398

401 405 410 408 415 418 422 418.5 405.5 405 409 417 420 424 438 438.5 434 438 440 447 448 444.5 441 440.5 445 444 ];

y=[359 343 351 377.5 376 383 362 353.5 342 325 301 316 270 292 335 328 335

371 374 394 277 271 265 290 300 301 306 328 337 367 351 355 350 342.5 339 334 335 330 333 330.5 327.5 344 343 346 342 348 372 374 372 382 380.5 377 369 363 353 374 382.5 387 382 388 395

381 375 366 361 362 359 360 355 350 351 347 3 356 3.5 368 370 3 370 372 368 373 376 385 392 392 381 383 385 381.5 380 360

];hold on

plot(x,y,'r*')

text(x(1),y(1),'1'); text(x(2),y(2),'2'); text(x(3),y(3),'3'); text(x(4),y(4),'4'); text(x(5),y(5),'5'); text(x(6),y(6),'6'); text(x(7),y(7),'7'); text(x(8),y(8),'8'); text(x(9),y(9),'9'); text(x(10),y(10),'10'); text(x(11),y(11),'11');

text(x(12),y(12),'12'); text(x(13),y(13),'13'); text(x(14),y(14),'14'); text(x(15),y(15),'15'); text(x(16),y(16),'16'); text(x(17),y(17),'17'); text(x(18),y(18),'18'); text(x(19),y(19),'19'); text(x(20),y(20),'20'); text(x(21),y(21),'21'); text(x(22),y(22),'22'); text(x(23),y(23),'23'); text(x(24),y(24),'24'); text(x(25),y(25),'25'); text(x(26),y(26),'26'); text(x(27),y(27),'27'); text(x(28),y(28),'28'); text(x(29),y(29),'29'); text(x(30),y(30),'30'); text(x(31),y(31),'31'); text(x(32),y(32),'32'); text(x(33),y(33),'33'); text(x(34),y(34),'34'); text(x(35),y(35),'35'); text(x(36),y(36),'36'); text(x(37),y(37),'37'); text(x(38),y(38),'38'); text(x(39),y(39),'39'); text(x(40),y(40),'40'); text(x(41),y(41),'41'); text(x(42),y(42),'42'); text(x(43),y(43),'43'); text(x(44),y(44),'44'); text(x(45),y(45),'45'); text(x(46),y(46),'46'); text(x(47),y(47),'47'); text(x(48),y(48),'48'); text(x(49),y(49),'49'); text(x(50),y(50),'50'); text(x(51),y(51),'51'); text(x(52),y(52),'52'); text(x(53),y(53),'53'); text(x(),y(),''); text(x(55),y(55),'55');

text(x(56),y(56),'56'); text(x(57),y(57),'57'); text(x(58),y(58),'58'); text(x(59),y(59),'59'); text(x(60),y(60),'60'); text(x(61),y(61),'61'); text(x(62),y(62),'62'); text(x(63),y(63),'63'); text(x(),y(),''); text(x(65),y(65),'65'); text(x(66),y(66),'66'); text(x(67),y(67),'67'); text(x(68),y(68),'68'); text(x(69),y(69),'69'); text(x(70),y(70),'70'); text(x(71),y(71),'71'); text(x(72),y(72),'72'); text(x(73),y(73),'73'); text(x(74),y(74),'74'); text(x(75),y(75),'75'); text(x(76),y(76),'76'); text(x(77),y(77),'77'); text(x(78),y(78),'78'); text(x(79),y(79),'79'); text(x(80),y(80),'80'); text(x(81),y(81),'81'); text(x(82),y(82),'82'); text(x(83),y(83),'83'); text(x(84),y(84),'84'); text(x(85),y(85),'85'); text(x(86),y(86),'86'); text(x(87),y(87),'87'); text(x(88),y(88),'88'); text(x(),y(),''); text(x(90),y(90),'90'); text(x(91),y(91),'91'); text(x(92),y(92),'92'); hold on

plot(x,y,'r*')

text(x(1),y(1),'1'); text(x(2),y(2),'2'); text(x(3),y(3),'3'); text(x(4),y(4),'4'); text(x(5),y(5),'5');

text(x(6),y(6),'6'); text(x(7),y(7),'7'); text(x(8),y(8),'8'); text(x(9),y(9),'9'); text(x(10),y(10),'10'); text(x(11),y(11),'11'); text(x(12),y(12),'12'); text(x(13),y(13),'13'); text(x(14),y(14),'14'); text(x(15),y(15),'15'); text(x(16),y(16),'16'); text(x(17),y(17),'17'); text(x(18),y(18),'18'); text(x(19),y(19),'19'); text(x(20),y(20),'20'); text(x(21),y(21),'21'); text(x(22),y(22),'22'); text(x(23),y(23),'23'); text(x(24),y(24),'24'); text(x(25),y(25),'25'); text(x(26),y(26),'26'); text(x(27),y(27),'27'); text(x(28),y(28),'28'); text(x(29),y(29),'29'); text(x(30),y(30),'30'); text(x(31),y(31),'31'); text(x(32),y(32),'32'); text(x(33),y(33),'33'); text(x(34),y(34),'34'); text(x(35),y(35),'35'); text(x(36),y(36),'36'); text(x(37),y(37),'37'); text(x(38),y(38),'38'); text(x(39),y(39),'39'); text(x(40),y(40),'40'); text(x(41),y(41),'41'); text(x(42),y(42),'42'); text(x(43),y(43),'43'); text(x(44),y(44),'44'); text(x(45),y(45),'45'); text(x(46),y(46),'46'); text(x(47),y(47),'47'); text(x(48),y(48),'48'); text(x(49),y(49),'49');

text(x(50),y(50),'50'); text(x(51),y(51),'51'); text(x(52),y(52),'52'); text(x(53),y(53),'53'); text(x(),y(),''); text(x(55),y(55),'55'); text(x(56),y(56),'56'); text(x(57),y(57),'57'); text(x(58),y(58),'58'); text(x(59),y(59),'59'); text(x(60),y(60),'60'); text(x(61),y(61),'61'); text(x(62),y(62),'62'); text(x(63),y(63),'63'); text(x(),y(),''); text(x(65),y(65),'65'); text(x(66),y(66),'66'); text(x(67),y(67),'67'); text(x(68),y(68),'68'); text(x(69),y(69),'69'); text(x(70),y(70),'70'); text(x(71),y(71),'71'); text(x(72),y(72),'72'); text(x(73),y(73),'73'); text(x(74),y(74),'74'); text(x(75),y(75),'75'); text(x(76),y(76),'76'); text(x(77),y(77),'77'); text(x(78),y(78),'78'); text(x(79),y(79),'79'); text(x(80),y(80),'80'); text(x(81),y(81),'81'); text(x(82),y(82),'82'); text(x(83),y(83),'83'); text(x(84),y(84),'84'); text(x(85),y(85),'85'); text(x(86),y(86),'86'); text(x(87),y(87),'87'); text(x(88),y(88),'88'); text(x(),y(),''); text(x(90),y(90),'90'); text(x(91),y(91),'91'); text(x(92),y(92),'92');

plot([x(1);x(75)],[y(1);y(75)]);

plot([x(1);x(78)],[y(1);y(78)]); plot([x(2);x(44)],[y(2);y(44)]); plot([x(3);x(45)],[y(3);y(45)]); plot([x(3);x(65)],[y(3);y(65)]); plot([x(4);x(39)],[y(4);y(39)]); plot([x(4);x(63)],[y(4);y(63)]); plot([x(5);x(49)],[y(5);y(49)]); plot([x(5);x(50)],[y(5);y(50)]); plot([x(6);x(59)],[y(6);y(59)]); plot([x(7);x(32)],[y(7);y(32)]); plot([x(7);x(47)],[y(7);y(47)]); plot([x(2);x(44)],[y(2);y(44)]); plot([x(8);x(47)],[y(8);y(47)]); plot([x(8);x(9)],[y(8);y(9)]); plot([x(9);x(35)],[y(9);y(35)]); plot([x(10);x(34)],[y(10);y(34)]); plot([x(11);x(22)],[y(11);y(22)]); plot([x(11);x(26)],[y(11);y(26)]); plot([x(12);x(25)],[y(12);y(25)]); plot([x(14);x(21)],[y(14);y(21)]); plot([x(15);x(7)],[y(15);y(7)]); plot([x(15);x(31)],[y(15);y(31)]); plot([x(16);x(14)],[y(16);y(14)]); plot([x(16);x(38)],[y(16);y(38)]); plot([x(17);x(40)],[y(17);y(40)]); plot([x(17);x(42)],[y(17);y(42)]); plot([x(17);x(81)],[y(17);y(81)]); plot([x(18);x(81)],[y(18);y(81)]); plot([x(18);x(83)],[y(18);y(83)]); plot([x(19);x(79)],[y(19);y(79)]); plot([x(20);x(86)],[y(20);y(86)]); plot([x(21);x(22)],[y(21);y(22)]); plot([x(22);x(13)],[y(22);y(13)]); plot([x(23);x(13)],[y(23);y(13)]); plot([x(24);x(13)],[y(24);y(13)]); plot([x(24);x(25)],[y(24);y(25)]); plot([x(25);x(11)],[y(25);y(11)]); plot([x(26);x(27)],[y(26);y(27)]); plot([x(26);x(10)],[y(26);y(10)]); plot([x(27);x(12)],[y(27);y(12)]); plot([x(28);x(29)],[y(28);y(29)]); plot([x(28);x(15)],[y(28);y(15)]); plot([x(29);x(30)],[y(29);y(30)]); plot([x(30);x(7)],[y(30);y(7)]);

plot([x(30);x(48)],[y(30);y(48)]); plot([x(31);x(32)],[y(31);y(32)]); plot([x(31);x(34)],[y(31);y(34)]); plot([x(32);x(33)],[y(32);y(33)]); plot([x(33);x(34)],[y(33);y(34)]); plot([x(33);x(8)],[y(33);y(8)]); plot([x(34);x(9)],[y(34);y(9)]); plot([x(35);x(45)],[y(35);y(45)]); plot([x(36);x(35)],[y(36);y(35)]); plot([x(36);x(37)],[y(36);y(37)]); plot([x(36);x(16)],[y(36);y(16)]); plot([x(36);x(39)],[y(36);y(39)]); plot([x(37);x(7)],[y(37);y(7)]); plot([x(38);x(39)],[y(38);y(39)]); plot([x(38);x(41)],[y(38);y(41)]); plot([x(39);x(40)],[y(39);y(40)]); plot([x(40);x(2)],[y(40);y(2)]); plot([x(41);x(17)],[y(41);y(17)]); plot([x(41);x(92)],[y(41);y(92)]); plot([x(42);x(43)],[y(42);y(43)]); plot([x(43);x(2)],[y(43);y(2)]); plot([x(43);x(72)],[y(43);y(72)]); plot([x(3);x(65)],[y(3);y(65)]); plot([x(44);x(3)],[y(44);y(3)]); plot([x(45);x(46)],[y(45);y(46)]); plot([x(28);x(29)],[y(28);y(29)]); plot([x(46);x(8)],[y(46);y(8)]); plot([x(46);x(55)],[y(46);y(55)]); plot([x(47);x(48)],[y(47);y(48)]); plot([x(47);x(5)],[y(47);y(5)]); plot([x(47);x(6)],[y(47);y(6)]); plot([x(31);x(34)],[y(31);y(34)]); plot([x(48);x(61)],[y(48);y(61)]); plot([x(49);x(50)],[y(49);y(50)]); plot([x(49);x(53)],[y(49);y(53)]); plot([x(50);x(51)],[y(50);y(51)]); plot([x(51);x(52)],[y(51);y(52)]); plot([x(51);x(59)],[y(51);y(59)]); plot([x(52);x(56)],[y(52);y(56)]); plot([x(53);x(52)],[y(53);y(52)]); plot([x(53);x()],[y(53);y()]); plot([x();x(55)],[y();y(55)]); plot([x();x(63)],[y();y(63)]); plot([x(55);x(3)],[y(55);y(3)]);

plot([x(56);x(57)],[y(56);y(57)]); plot([x(57);x(58)],[y(57);y(58)]); plot([x(57);x(60)],[y(57);y(60)]); plot([x(57);x(4)],[y(57);y(4)]); plot([x(58);x(59)],[y(58);y(59)]); plot([x(60);x(62)],[y(60);y(62)]); plot([x(61);x(60)],[y(61);y(60)]); plot([x(62);x(4)],[y(62);y(4)]); plot([x(62);x(85)],[y(62);y(85)]); plot([x(63);x()],[y(63);y()]); plot([x();x(65)],[y();y(65)]); plot([x();x(76)],[y();y(76)]); plot([x(65);x(66)],[y(65);y(66)]); plot([x(66);x(67)],[y(66);y(67)]); plot([x(66);x(76)],[y(66);y(76)]); plot([x(67);x(44)],[y(67);y(44)]); plot([x(67);x(68)],[y(67);y(68)]); plot([x(68);x(69)],[y(68);y(69)]); plot([x(68);x(75)],[y(68);y(75)]); plot([x(69);x(70)],[y(69);y(70)]); plot([x(69);x(71)],[y(69);y(71)]); plot([x(69);x(1)],[y(69);y(1)]); plot([x(70);x(2)],[y(70);y(2)]); plot([x(70);x(43)],[y(70);y(43)]); plot([x(70);x(72)],[y(70);y(72)]); plot([x(71);x(72)],[y(71);y(72)]); plot([x(71);x(74)],[y(71);y(74)]); plot([x(72);x(73)],[y(72);y(73)]); plot([x(73);x(74)],[y(73);y(74)]); plot([x(73);x(18)],[y(73);y(18)]); plot([x(74);x(1)],[y(74);y(1)]); plot([x(74);x(80)],[y(74);y(80)]); plot([x(75);x(76)],[y(75);y(76)]); plot([x(76);x(77)],[y(76);y(77)]); plot([x(77);x(78)],[y(77);y(78)]); plot([x(77);x(19)],[y(77);y(19)]); plot([x(78);x(79)],[y(78);y(79)]); plot([x(79);x(80)],[y(79);y(80)]); plot([x(80);x(18)],[y(80);y(18)]); plot([x(81);x(82)],[y(81);y(82)]); plot([x(82);x(83)],[y(82);y(83)]); plot([x(82);x(90)],[y(82);y(90)]); plot([x(83);x(84)],[y(83);y(84)]); plot([x(84);x(85)],[y(84);y(85)]);

plot([x(85);x(20)],[y(85);y(20)]); plot([x(86);x(87)],[y(86);y(87)]); plot([x(86);x(88)],[y(86);y(88)]); plot([x(87);x(88)],[y(87);y(88)]); plot([x(87);x(92)],[y(87);y(92)]); plot([x(88);x()],[y(88);y()]); plot([x(88);x(91)],[y(88);y(91)]); plot([x();x(20)],[y();y(20)]); plot([x();x(84)],[y();y(84)]); plot([x();x(90)],[y();y(90)]); plot([x(90);x(91)],[y(90);y(91)]); plot([x(91);x(92)],[y(91);y(92)]); hold off

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