无人机与卡车联合配送-论文代码复现
原博客链接 https://blog.csdn.net/HsinglukLiu/article/details/107871295
Introduction
本代码主要是复现了2015年发表在
Transportation Research Part C: Emerging Technologies上的关于无人机与卡车联合配送的文章中的模型部分的求解器求解代码。论文题目为The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery.
代码求解结果可视化效果如图
例如：
Model
min t c + 1 s.t. ∑ i ∈ N 0 i ≠ j x i j + ∑ i ∈ N 0 ∑ k ∈ N + i ≠ j y i j k = 1 , ∀ j ∈ C ∑ j ∈ N + x 0 j = 1 , ∑ i ∈ N 0 x i , c + 1 = 1 , u i − u j + 1 ≤ ( c + 2 ) ( 1 − x i j ) , ∀ i ∈ C , j ∈ { N + : j ≠ i } ∑ i ∈ N 0 x i j = ∑ k ∈ N + i ≠ j x j k , ∀ j ∈ C ∑ j ∈ C ∑ k ∈ N t j ≠ i ( j , j ) ∈ P y i j k ≤ 1 , ∀ i ∈ N 0 ∑ i ∈ N 0 i ≠ k ∑ j ∈ C i ≠ i , j , k ⟩ ∈ P y i j k ≤ 1 , ∀ k ∈ N + 2 y i j k ≤ ∑ h ∈ N 0 h ≠ i x h i + ∑ l ∈ C l ≠ k x l k , ∀ i ∈ C , j ∈ { C : j ≠ i } , k ∈ { N + : ⟨ i , j , k ⟩ ∈ P } y 0 j k ≤ ∑ h ∈ N 0 h ≠ k x h k , ∀ j ∈ C , k ∈ { N + : ⟨ 0 , j , k ⟩ ∈ P } u k − u i ≥ 1 − ( c + 2 ) ( 1 − ∑ j ∈ C y i j k ) , ∀ i ∈ C , k ∈ { N + : k ≠ i } t i ′ ≥ t i − M ( 1 − ∑ j ∈ C ∑ k ∈ N + j ≠ i y i j k ) , ∀ i ∈ C t i ′ ≤ t i + M ( 1 − ∑ j ∈ C j ≠ i ∑ k ∈ N + ⟨ i , j ⟩ ∈ P y i j k ) , ∀ i ∈ C t k ′ ≥ t k − M ( 1 − ∑ i ∈ N 0 ∑ j ∈ C i ≠ k y i j k ) , ∀ k ∈ N + t k ′ ≤ t k + M ( 1 − ∑ i ∈ N 0 i ≠ k ( i j , k ) ∈ P y i j k ) , ∀ k ∈ N + t k ≥ t h + τ h k + s L ( ∑ l ∈ C ∑ m ∈ N + l ≠ k y k l m ) + s R ( ∑ i ∈ N 0 ∑ j ∈ C y i j k ) − M ( 1 − x h k ) , ∀ h ∈ N 0 , k ∈ { N + : k ≠ h } t j ′ ≥ t i ′ + τ i j ′ − M ( 1 − ∑ k ∈ N + ⟨ i , j , k ) ∈ P y i j k ) ∀ j ∈ C ′ , i ∈ { N 0 : i ≠ j } t k ′ ≥ t j ′ + τ j k ′ + s R − M ( 1 − ∑ i ∈ N 0 ⟨ i , j , k ∈ P y i j k ) ∀ j ∈ C ′ , k ∈ { N + : k ≠ j } t k ′ − ( t j ′ − τ i j ′ ) ≤ e + M ( 1 − y i j k ) ∀ k ∈ N + , j ∈ { C : j ≠ k } , i ∈ { N 0 : ⟨ i , j , k ⟩ ∈ P } u i − u j ≥ 1 − ( c + 2 ) p i j ∀ i ∈ C , j ∈ { C : j ≠ i } u i − u j ≤ − 1 + ( c + 2 ) ( 1 − p i j ) ∀ i ∈ C , j ∈ { C : j ≠ i } p i j + p j i = 1 ∀ i ∈ C , j ∈ { C : j ≠ i } t l ′ ≥ t k ′ − M ( 3 − ∑ j ∈ C y i j k − ∑ m ∈ C ∑ n ∈ N + { i j , k ∈ P y l m n − p i l ∀ i ∈ N 0 , k ∈ { N + : k ≠ i } , l ∈ { C : l ≠ i , l ≠ k } t 0 = 0 , t 0 ′ = 0 , p 0 j = 1 , ∀ j ∈ C x i j ∈ { 0 , 1 } , ∀ i ∈ N 0 , j ∈ { N + : j ≠ i } y i j k ∈ { 0 , 1 } , ∀ i ∈ N 0 , j ∈ { C : j ≠ i } , k ∈ { N + : ⟨ i , j , k ⟩ ∈ P } 1 ≤ u i ≤ c + 2 , ∀ i ∈ N + t i ≥ 0 , ∀ i ∈ N t i ′ ≥ 0 ∀ i ∈ N p i j ∈ { 0 , 1 } , ∀ i ∈ N 0 , j ∈ { C : j ≠ i } \begin{aligned} \min & \quad t_{c+1} \\ \text { s.t. } & \sum_{i \in N_{0} \atop i \neq j} x_{i j}+\sum_{i \in N_{0}} \sum_{k \in N_{+} \atop i \neq j} y_{i j k}=1, \quad \forall j \in C \\ &\sum_{j \in N_{+}} x_{0 j}=1, \\ &\sum_{i \in N_{0}} x_{i, c+1}=1 , \\ &u_{i}-u_{j}+1 \leq (c+2)\left(1-x_{i j}\right), \quad \forall i \in C, j \in\left\{N_{+}: j \neq i\right\} \\ &\sum_{i \in N_{0}} x_{i j}=\sum_{k \in N_{+} \atop i \neq j} x_{j k}, \quad \forall j \in C \\ &\sum_{j \in C} \sum_{k \in N_{t} \atop j \neq i(j, j) \in P} y_{i j k} \leq 1, \quad \forall i \in N_{0} \\ &\sum_{i \in N_{0} \atop i \neq k} \sum_{j \in C \atop i \neq i, j, k\rangle \in P} y_{i j k} \leq 1, \quad \forall k \in N_{+} \\ &2 y_{i j k} \leq \sum_{h \in N_{0} \atop h \neq i} x_{h i}+\sum_{l \in C \atop l \neq k} x_{l k}, \quad \\ & \hspace{2cm} \forall i \in C, j \in\{C: j \neq i\}, k \in\left\{N_{+}:\langle i, j, k\rangle \in P\right\} \\ &y_{0 j k} \leq \sum_{h \in N_{0} \atop h \neq k} x_{h k}, \quad \forall j \in C, k \in\left\{N_{+}:\langle 0, j, k\rangle \in P\right\} \\ &u_{k}-u_{i} \geq 1-(c+2)\left(1-\sum_{j \in C} y_{i j k}\right), \quad \\ &\hspace{2cm}\forall i \in C, k \in\left\{N_{+}: k \neq i\right\} \\ &t_{i}^{\prime} \geq t_{i}-M\left(1-\sum_{j \in C} \sum_{k \in N_{+} \atop j \neq i} y_{i j k}\right), \quad \forall i \in C \\ &t_{i}^{\prime} \leq t_{i}+M\left(1-\sum_{j \in C \atop j \neq i} \sum_{k \in N_{+} \atop\langle i, j\rangle \in P} y_{i j k}\right), \quad \forall i \in C \\ &t_{k}^{\prime} \geq t_{k}-M\left(1-\sum_{i \in N_{0}} \sum_{j \in C \atop i \neq k} y_{i j k}\right), \quad \forall k \in N_{+} \\ &t_{k}^{\prime} \leq t_{k}+M\left(1-\sum_{i \in N_{0} \atop i \neq k(i j, k) \in P} y_{i j k}\right), \quad \forall k \in N_{+} \\ &t_{k} \geq t_{h}+\tau_{h k}+s_{L}\left(\sum_{l \in C} \sum_{m \in N_{+} \atop l \neq k} y_{k l m}\right)+s_{R}\left(\sum_{i \in N_{0}} \sum_{j \in C} y_{i j k}\right)-M\left(1-x_{h k}\right), \\ &\hspace{2cm}\forall h \in N_{0}, k \in\left\{N_{+}: k \neq h\right\} \\ &t_{j}^{\prime} \geq t_{i}^{\prime}+\tau_{i j}^{\prime}-M\left(1-\sum_{k \in N_{+} \atop\langle i, j, k) \in P} y_{i j k}\right) \quad \forall j \in C^{\prime}, i \in\left\{N_{0}: i \neq j\right\} \\ &t_{k}^{\prime} \geq t_{j}^{\prime}+\tau_{j k}^{\prime}+s_{R}-M\left(1-\sum_{i \in N_{0} \atop\langle i, j, k \in P} y_{i j k}\right) \quad \\ &\hspace{2cm}\forall j \in C^{\prime}, k \in\left\{N_{+}: k \neq j\right\} \\ &t_{k}^{\prime}-\left(t_{j}^{\prime}-\tau_{i j}^{\prime}\right) \leq e+M\left(1-y_{i j k}\right) \quad \\ &\hspace{2cm}\forall k \in N_{+}, j \in\{C: j \neq k\}, i \in\left\{N_{0}:\langle i, j, k\rangle \in P\right\} \\ &u_{i}-u_{j} \geq 1-(c+2) p_{i j} \forall i \in C, j \in\{C: j \neq i\} \\ &u_{i}-u_{j} \leq-1+(c+2)\left(1-p_{i j}\right) \forall i \in C, j \in\{C: j \neq i\} \\ &p_{i j}+p_{j i}=1 \quad \forall i \in C, j \in\{C: j \neq i\} \\ &t_{l}^{\prime} \geq t_{k}^{\prime}-M(3-\sum_{j \in C} y_{i j k}-\sum_{m \in C} \sum_{n \in N_{+} \atop\{i j, k \in P} y_{l m n}-p_{i l} \\ &\hspace{2cm} \forall i \in N_{0}, k \in\left\{N_{+}: k \neq i\right\}, l \in\{C: l \neq i, l \neq k\} \\ &t_{0}=0 , \\ &t_{0}^{\prime}=0 , \\ &p_{0 j}=1, \quad \forall j \in C \\ &x_{i j} \in\{0,1\}, \quad \forall i \in N_{0}, j \in\left\{N_{+}: j \neq i\right\} \\ &y_{i j k} \in\{0,1\} , \quad \forall i \in N_{0}, j \in\{C: j \neq i\}, k \in\left\{N_{+}:\langle i, j, k\rangle \in P\right\} \\ &1 \leq u_{i} \leq c+2, \quad \forall i \in N_{+} \\ &t_{i} \geq 0, \quad \forall i \in N \\ &t_{i}^{\prime} \geq 0 \quad \forall i \in N \\ &p_{i j} \in\{0,1\}, \quad \forall i \in N_{0}, j \in\{C: j \neq i\} \end{aligned} min s.t. tc+1i=ji∈N0∑xij+i∈N0∑i=jk∈N+∑yijk=1,∀j∈Cj∈N+∑x0j=1,i∈N0∑xi,c+1=1,ui−uj+1≤(c+2)(1−xij),∀i∈C,j∈{ N+:j=i}i∈N0∑xij=i=jk∈N+∑xjk,∀j∈Cj∈C∑j=i(j,j)∈Pk∈Nt∑yijk≤1,∀i∈N0i=ki∈N0∑i=i,j,k⟩∈Pj∈C∑yijk≤1,∀k∈N+2yijk≤h=ih∈N0∑xhi+l=kl∈C∑xlk,∀i∈C,j∈{ C:j=i},k∈{ N+:⟨i,j,k⟩∈P}y0jk≤h=kh∈N0∑xhk,∀j∈C,k∈{ N+:⟨0,j,k⟩∈P}uk−ui≥1−(c+2)⎝⎛1−j∈C∑yijk⎠⎞,∀i∈C,k∈{ N+:k=i}ti′≥ti−M⎝⎜⎛1−j∈C∑j=ik∈N+∑yijk⎠⎟⎞,∀i∈Cti′≤ti+M⎝⎜⎛1−j=ij∈C∑⟨i,j⟩∈Pk∈N+∑yijk⎠⎟⎞,∀i∈Ctk′≥tk−M⎝⎜⎛1−i∈N0∑i=kj∈C∑yijk⎠⎟⎞,∀k∈N+tk′≤tk+M⎝⎜⎛1−i=k(ij,k)∈Pi∈N0∑yijk⎠⎟⎞,∀k∈N+tk≥th+τhk+sL⎝⎜⎛l∈C∑l=km∈N+∑yklm⎠⎟⎞+sR⎝⎛i∈N0∑j∈C∑yijk⎠⎞−M(1−xhk),∀h∈N0,k∈{ N+:k=h}tj′≥ti′+τij′−M⎝⎜⎛1−⟨i,j,k)∈Pk∈N+∑yijk⎠⎟⎞∀j∈C′,i∈{ N0:i=j}tk′≥tj′+τjk′+sR−M⎝⎜⎛1−⟨i,j,k∈Pi∈N0∑yijk⎠⎟⎞∀j∈C′,k∈{ N+:k=j}tk′−(tj′−τij′)≤e+M(1−yijk)∀k∈N+,j∈{ C:j=k},i∈{ N0:⟨i,j,k⟩∈P}ui−uj≥1−(c+2)pij∀i∈C,j∈{ C:j=i}ui−uj≤−1+(c+2)(1−pij)∀i∈C,j∈{ C:j=i}pij+pji=1∀i∈C,j∈{ C:j=i}tl′≥tk′−M(3−j∈C∑yijk−m∈C∑{ ij,k∈Pn∈N+∑ylmn−pil∀i∈N0,k∈{ N+:k=i},l∈{ C:l=i,l=k}t0=0,t0′=0,p0j=1,∀j∈Cxij∈{ 0,1},∀i∈N0,j∈{ N+:j=i}yijk∈{ 0,1},∀i∈N0,j∈{ C:j=i},k∈{ N+:⟨i,j,k⟩∈P}1≤ui≤c+2,∀i∈N+ti≥0,∀i∈Nti′≥0∀i∈Npij∈{ 0,1},∀i∈N0,j∈{ C:j=i}
Quick start
Data类：存储算例数据
Solution类：提取问题最优解的类
其中函数
getSolution(self, data, model)用于提取最优解的信息
readData(data, path, customerNum): 读取文件路径path中的数据，客户点的个数设置为customerNum个，返回一个data类型的实例。
Dependencies
gurobi
numpy
math
re
matplotlib
pandas
Dataset Format
Solomon VRP benchmark instance
下载地址https://www.sintef.no/projectweb/top/vrptw/solomon-benchmark/100-customers/
C101
VEHICLE
NUMBER CAPACITY
25 200
CUSTOMER
CUST NO. XCOORD. YCOORD. DEMAND READY TIME DUE DATE SERVICE TIME
0 40 50 0 0 1236 0
1 45 68 10 912 967 90
2 45 70 30 825 870 90
3 42 66 10 65 146 90
4 42 68 10 727 782 90
5 42 65 10 15 67 90
6 40 69 20 621 702 90
7 40 66 20 170 225 90
8 38 68 20 255 324 90
9 38 70 10 534 605 90
10 35 66 10 357 410 90
11 35 69 10 448 505 90
12 25 85 20 652 721 90
13 22 75 30 30 92 90
14 22 85 10 567 620 90
15 20 80 40 384 429 90
16 20 85 40 475 528 90
17 18 75 20 99 148 90
18 15 75 20 179 254 90
19 15 80 10 278 345 90
20 30 50 10 10 73 90
21 30 52 20 914 965 90
22 28 52 20 812 883 90
23 28 55 10 732 777 90
24 25 50 10 65 144 90
25 25 52 40 169 224 90
26 25 55 10 622 701 90
27 23 52 10 261 316 90
28 23 55 20 546 593 90
29 20 50 10 358 405 90
30 20 55 10 449 504 90
31 10 35 20 200 237 90
32 10 40 30 31 100 90
33 8 40 40 87 158 90
34 8 45 20 751 816 90
35 5 35 10 283 344 90
36 5 45 10 665 716 90
37 2 40 20 383 434 90
38 0 40 30 479 522 90
39 0 45 20 567 624 90
40 35 30 10 264 321 90
41 35 32 10 166 235 90
42 33 32 20 68 149 90
43 33 35 10 16 80 90
44 32 30 10 359 412 90
45 30 30 10 541 600 90
46 30 32 30 448 509 90
47 30 35 10 1054 1127 90
48 28 30 10 632 693 90
49 28 35 10 1001 1066 90
50 26 32 10 815 880 90
51 25 30 10 725 786 90
52 25 35 10 912 969 90
53 44 5 20 286 347 90
54 42 10 40 186 257 90
55 42 15 10 95 158 90
56 40 5 30 385 436 90
57 40 15 40 35 87 90
58 38 5 30 471 534 90
59 38 15 10 651 740 90
60 35 5 20 562 629 90
61 50 30 10 531 610 90
62 50 35 20 262 317 90
63 50 40 50 171 218 90
64 48 30 10 632 693 90
65 48 40 10 76 129 90
66 47 35 10 826 875 90
67 47 40 10 12 77 90
68 45 30 10 734 777 90
69 45 35 10 916 969 90
70 95 30 30 387 456 90
71 95 35 20 293 360 90
72 53 30 10 450 505 90
73 92 30 10 478 551 90
74 53 35 50 353 412 90
75 45 65 20 997 1068 90
76 90 35 10 203 260 90
77 88 30 10 574 643 90
78 88 35 20 109 170 90
79 87 30 10 668 731 90
80 85 25 10 769 820 90
81 85 35 30 47 124 90
82 75 55 20 369 420 90
83 72 55 10 265 338 90
84 70 58 20 458 523 90
85 68 60 30 555 612 90
86 66 55 10 173 238 90
87 65 55 20 85 144 90
88 65 60 30 645 708 90
89 63 58 10 737 802 90
90 60 55 10 20 84 90
91 60 60 10 836 889 90
92 67 85 20 368 441 90
93 65 85 40 475 518 90
94 65 82 10 285 336 90
95 62 80 30 196 239 90
96 60 80 10 95 156 90
97 60 85 30 561 622 90
98 58 75 20 30 84 90
99 55 80 10 743 820 90
100 55 85 20 647 726 90
solomon相关数据集、最优解等详细信息见官网：solomon benchmark
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