CN116258311A - Medical unmanned aerial vehicle scheduling model and solving algorithm for considering sample timeliness - Google Patents

Medical unmanned aerial vehicle scheduling model and solving algorithm for considering sample timeliness Download PDF

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CN116258311A
CN116258311A CN202211454497.5A CN202211454497A CN116258311A CN 116258311 A CN116258311 A CN 116258311A CN 202211454497 A CN202211454497 A CN 202211454497A CN 116258311 A CN116258311 A CN 116258311A
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裴植
翁克彪
陈勇
王成
易文超
张文珠
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Zhejiang University of Technology ZJUT
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Abstract

The invention provides a medical unmanned aerial vehicle scheduling model and a solving algorithm for considering sample timeliness, wherein the model establishment comprises the following processes: 1) Defining state parameters and variables of the unmanned aerial vehicle; 2) Determining an objective function of the model, wherein the objective function of the model is used for representing the time for minimizing the completion of all the inspection orders by the unmanned aerial vehicle; 3) Constraint conditions are determined. According to the invention, the medical unmanned aerial vehicle distribution taking sample timeliness into consideration under the field replacement scene is introduced, the optimal power replacement position of the unmanned aerial vehicle is decided according to the information such as sample inspection information, load, the residual capacity of the unmanned aerial vehicle and the like, the synchronous carrying out of sample collection and power replacement is realized, and the efficiency is improved. Under the constraint of sample timeliness, the overall detection efficiency and the service quality are improved. According to the invention, the problem is modeled as a mixed integer linear programming model, a branch pricing algorithm is designed for solving, and the mode of combining an accurate algorithm and a heuristic algorithm is adopted, so that the solving speed can be improved, and the problem can be solved to the optimal state.

Description

Medical unmanned aerial vehicle scheduling model and solving algorithm for considering sample timeliness
Technical Field
The invention relates to a medical unmanned aerial vehicle scheduling model for considering sample timeliness and a solving algorithm thereof.
Technical Field
In actual medical unmanned aerial vehicle scheduling, there are often scheduling demands of multiple community service points at the same time. Each community service point can generate scheduling requirements of samples to be detected, and each piece of scheduling requirement information comprises timeliness requirements of the samples to be detected and corresponding delivery unit hospitals. In the scheduling of nucleic acid detection sample unmanned aerial vehicles, energy consumption is a key factor affecting unmanned aerial vehicle mileage. In the conventional unmanned aerial vehicle delivery or truck-unmanned aerial vehicle combined delivery scheduling problem, it is often assumed that the battery power after each take-off of the unmanned aerial vehicle can always meet the delivery of all orders until the unmanned aerial vehicle returns to a warehouse or a truck. In addition, it is often assumed that the unmanned aerial vehicle performs power exchange or charging after completing the distribution of an order every time, and the actual residual capacity of the battery is not considered. This mode, while capable of performing scheduling tasks, is inefficient in battery usage. And each time of power change has power change time, which leads to the increase of the whole inspection time and influences the distribution efficiency and the timeliness of the samples.
By setting up nucleic acid service points in all communities in the city, the medical staff collects the nucleic acid samples to be detected on site and then sends the nucleic acid samples to all detection institutions for nucleic acid detection. After each community service point collects samples to be detected, unmanned aerial vehicles are used for sequentially conveying the samples of each community to a specified detection mechanism for detection. Further, since the validity of the sample gradually decreases over time, the timeliness of the sample is considered herein, thereby ensuring the quality of the sample for inspection. According to the invention, medical unmanned aerial vehicle distribution taking sample timeliness into consideration under the field change prospect is introduced. Each community service point is provided with a matched unmanned station, and the unmanned aerial vehicle can collect samples to be detected at each unmanned station. The unmanned aerial vehicle collects samples to be detected at a plurality of community service points by considering capacity constraint and energy consumption constraint of the unmanned aerial vehicle. According to the information such as sample sending and detecting information, load, unmanned aerial vehicle's residual capacity, etc. come the best position of trading of decision unmanned aerial vehicle to realize collecting the sample and trade the synchronous going on of electricity, raise the efficiency. Under the constraint of sample timeliness, the overall detection efficiency and the service quality are improved. The invention models the problem as a mixed integer linear programming model, and designs a branch pricing algorithm to solve the problem. Wherein the main problem is a set coverage model and the sub-problem is a constrained basic shortest path problem. In the solving of the sub-problem, a mode of combining an accurate algorithm and a heuristic algorithm is adopted. The designed label algorithm and heuristic algorithm can be effectively solved.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention aims to provide a medical unmanned aerial vehicle scheduling model and a solving algorithm for considering sample timeliness.
The medical unmanned aerial vehicle scheduling model for considering sample timeliness is established by the following steps:
3.1 symbol definition:
u: = {1,..k } unmanned numbering set;
h: = {1,..h } set of initial positions of drones;
c: = { h+1,.,. H+n } community service point set, i.e., a set of demand generation points for sample collection to be tested;
d: = { h+n+1,..h+2n } sample is sent to the set of unit sites;
e: = { h+2n+1} unmanned virtual endpoint;
n: set of all nodes of = { H } C } D };
a: the set of arcs between nodes = { (i, j) |i E n\ { E }, j E n\h, i +.j };
g: = (N, a) directed graph set;
d i : load demand for unmanned aerial vehicle inspection;
L i : unmanned aerial vehicle leaves node i and carries load;
f: unmanned aerial vehicle dead weight;
l: maximum load (kg) of the unmanned aerial vehicle;
[e i ，l i ]: the unmanned aerial vehicle sends out the time window of examining the demand, unmanned aerial vehicle must accomplish the taking and delivering of medical supplies in the time window; wherein,,
e i ，l i respectively representing the earliest and latest start service times;
[η min ，η max ]: sample timeliness; wherein eta min ，η max Representing the minimum and maximum time that the sample is effective, respectively;
t ij : time of flight from node i to node j;
ρ: full electric quantity of the unmanned aerial vehicle;
alpha: an energy consumption factor;
t bs : the power change time of the unmanned aerial vehicle;
Figure SMS_1
the time when the unmanned plane k reaches the node i;
Figure SMS_2
the unmanned aerial vehicle reaches the node i to consume power;
Figure SMS_3
the unmanned aerial vehicle leaves the node i and consumes power;
delta: sample timeliness factor;
gamma: energy-consuming time factor
M: a very large positive integer (e.g., M is greater than or equal to 100000);
3.2 variables:
Figure SMS_4
if unmanned plane k flies from node i to node j +.>
Figure SMS_5
Otherwise->
Figure SMS_6
y i : if the unmanned aerial vehicle performs power conversion operation at the node i, y is i =1, otherwise z i ＝0；
3.3 model objective function:
the problem is defined in a directed graph g= (N, a), where n= {1, 2..h+2n } is the set of all nodes, a= { (i, j) |i E n\e, j E n\h, i not equal j } is the set of arcs between nodes. We define h= { 1..h } as the drone initial position, u= { 1..k } as the drone number set. C= { h+1,..h+n } is defined as the community service point set, i.e. the demand generation point set for sample collection to be measured. D= { h+n+1,..h+2n } is a collection of sample unit sites, each requirement containing one sample collection site and unit site. E=k+2n+1 is defined as the drone virtual endpoint.
There is a sample load demand for each service point
Figure SMS_21
Wherein the load for the demand generation point is defined as +.>
Figure SMS_14
The requirement of the corresponding detection unit is +.>
Figure SMS_22
Setting the requirement of an initial node of the unmanned aerial vehicle>
Figure SMS_9
Each requirement has a requirement of time window, the time window of requirement i is defined as +.>
Figure SMS_19
The unmanned aerial vehicle must accomplish the fetching and delivering of medical supplies in the prescribed time. Furthermore, each sample has its own timeliness requirement, defined +.>
Figure SMS_10
For sample timeliness of unmanned aerial vehicle k reaching point i, each sampleThe product must meet the requirements of timeliness
Figure SMS_17
Defining L as the maximum effective load of the unmanned aerial vehicle, and F as the self-frame weight of the unmanned aerial vehicle. Definitions->
Figure SMS_12
And (5) loading for the unmanned aerial vehicle to leave the node i. />
Figure SMS_16
For the time of arrival of unmanned plane k at node i (i.e. +.>
Figure SMS_7
Representing the time at which drone k starts serving node i), the arrival time of each node must satisfy the constraints of the time window. ρ is the amount of electricity that the unmanned aerial vehicle is full. Defining eta as time unit factor, delta as time effect factor, t ij T is the time from node i to node j bs Is the power change time of the unmanned aerial vehicle. Definitions->
Figure SMS_15
For the power consumption of the unmanned aerial vehicle to reach node i, < >>
Figure SMS_13
And (5) consuming electricity for the unmanned aerial vehicle to leave the node i. y is i E {0,1} is a decision variable of whether the unmanned aerial vehicle is powered on at the service point i, when y i When=1, it means that the unmanned plane is powered up at service point i, at this time +.>
Figure SMS_20
Otherwise->
Figure SMS_11
Definitions->
Figure SMS_18
As decision variables, when->
Figure SMS_8
Representing that the unmanned aerial vehicle k flies through the arc (i, j); otherwise, indicating that the unmanned plane k does not fly through the arc(i, j). Based on the symbol definition, the section establishes an unmanned aerial vehicle scheduling model taking energy consumption constraint into consideration under the field change scene, and the specific model is expressed as follows:
Figure SMS_23
the objective function in this design modeling is to represent minimizing the time for the drone to complete all of the inspection orders.
3.4 determining constraint conditions:
Figure SMS_24
Figure SMS_25
Figure SMS_26
Figure SMS_27
Figure SMS_28
Figure SMS_29
Figure SMS_30
Figure SMS_31
Figure SMS_32
Figure SMS_33
Figure SMS_34
Figure SMS_35
Figure SMS_36
Figure SMS_37
Figure SMS_38
Figure SMS_39
Figure SMS_40
/>
Figure SMS_41
Figure SMS_42
constraint expression (2) indicates that the sample for any one demand must be serviced by the same drone. Constraint expression (3) indicates that the drone must start from the starting position. Constraint expression (4) ensures that each sample is collected and sent for inspection and that only one drone is serviced. Constraint expression (5) represents a flow-level constraint for a node. Constraint expression (6) indicates that each drone must eventually return to the virtual junction, i.e., to the drone virtual destination. Constraint expressions (7) - (8) represent the time-dependent constraint of the samples after sample decay. Constraint expression (9) represents the time order of access before and after the node. Constraint expression (10) represents unmanned payload constraint logic before and after a node. Constraint expression (11) indicates that the same inspection-required unmanned aerial vehicle must go to the community service point to collect the sample before being inspected. Constraint expression (12) represents a power constraint for the node access order. Constraint expressions (13) - (16) represent logical constraints of the post-power-change electric quantity. Constraint expression (17) represents a time window constraint of the unmanned access node. Constraint expression (18) represents a node load upper limit constraint. Constraint expressions (19) - (20) represent variable type constraints.
3.5 design of branch pricing algorithm:
the mixed integer linear programming models (1) - (20) designed above can be directly solved by using a commercial solver CPLEX, but CPLEX can only solve the sample-sending-inspection unmanned aerial vehicle scheduling problem of community service points under a small scale. When the number of community service points is medium-large, the solver CPLEX cannot obtain a viable solution in a given time. Based on this, a branch pricing algorithm is designed to solve the medical drone scheduling problem of medium and large scale. In the branch pricing algorithm, the questions are first modeled as a set coverage model and pricing sub-questions. In the pricing sub-problem, a pattern of combining a precise algorithm and a heuristic algorithm is designed. In the process of solving the sub-problem, the heuristic algorithm can effectively improve the solving speed, quicken finding out the path with the reduced cost as the negative number, and then add the path into the main problem until the path with the reduced cost as the negative number cannot be found out in the sub-problem. In this step, the accurate algorithm based on dynamic programming can ensure that the sub-problem is solved to the optimum, but the solving speed of the accurate algorithm is not fast. The heuristic algorithm has a faster solving speed, is convenient for quickly finding a path with a reduction cost of negative number, but cannot guarantee that the solving is optimal. The mode of combining the accurate algorithm and the heuristic algorithm can not only improve the solving speed, but also ensure that the sub-problems are solved to the optimal.
The aggregate coverage model modeling process is as follows:
3.5.1 symbol definition:
TABLE 1 set overlay model symbols and meanings
Figure SMS_43
3.5.2 set coverage model:
the aggregate coverage model is constructed as follows: since the solution set R corresponding to the path R is very large, the solution cannot be directly performed at this time. With the column-based generation (Column Generation) framework, the aggregate coverage model is first considered in one partial solution space, and then the solution space aggregate is gradually expanded by solving the pricing sub-problem. And limiting the solution set in the set coverage model based on the limitation to obtain a limited main problem model. Define R' as a subset of the set Ω, at this point
Figure SMS_44
Variable e in the subject problem to be restricted r Relaxation, linear relaxation models (21) - (24) of the following constrained main problem are obtained. />
(RMLP)min C r e r #(21)
Figure SMS_45
Figure SMS_46
Figure SMS_47
Definition of the definition
Figure SMS_48
For the dual variable of constraint (22), +.>
Figure SMS_49
As a dual variable of constraint (23), it can be analyzed that the set-based overlay model is better than the set partition model.
3.5.3 pricing sub-problem:
in the pricing sub-problem, it is necessary to find all paths for which the reduce cost is negative, where
Figure SMS_50
The path is then added to the constrained main problem, and the sub-problem is updated by the dual variables obtained after solving the constrained main problem. The solution is repeated until all paths with the reduction cost negative are found. Solving the pricing sub-problem is effectively solving a basic shortest path problem with resource constraints (Elementary Shortest Path Problem with Resource Constraints ESPPRC).
According to the definition above, the reduce cost of path r in the sub-problem can be constructed by the dual variables in RMLP. In the solving of the sub-problem, the cost of the arcs in the sub-problem is updated by the dual variables. The reduce cost defining path r is:
Figure SMS_51
wherein:
Figure SMS_52
Figure SMS_53
update formula (25) is rewritten as the following formula (28):
Figure SMS_54
wherein the method comprises the steps of
Figure SMS_55
A' represents a set of arcs between nodes of a child problem;
n' represents the set of all nodes of the child problem.
After the pricing sub-problem is built, a design algorithm is needed to solve. The combination of a label algorithm based on dynamic programming and two heuristic algorithms is designed for the ESPPRC problem.
3.6 sub-problem labeling algorithm:
in the current broad sense, ESPPRC is an NP-hard problem. In this context, a combination of dynamic programming and heuristic algorithms is used for solving. First, a label algorithm based on dynamic programming concept is designed. The solution framework algorithm can be expressed as: from one source node, each node along the way generates several labels. In the expansion process, the same node has a plurality of different labels, and the dominant rule is needed to be used for pruning, so that the search space is reduced.
Firstly, defining a label L, wherein the information of the label L mainly comprises the node position of the current label: p (L); t (L) is the time of arrival of the tag L at the current location; w (L) is the accumulated load of the label L; b (L) is the current residual capacity of the label L; c (L) is the accumulated consumption cost of the label L; s (L) is the sample timeliness of label L. In addition, O (L) is defined as a node set of the label L, wherein only the picking of goods is finished and the delivery of goods is not finished yet; v (L) is a set of nodes that have completed service; UR (L) is a node where the label L cannot be extended. Pseudo code for the tag algorithm as shown in algorithm 1 below, the extension and dominance rules of the tag algorithm will be set forth in the following section.
3.6.1 expansion of tags:
when the tag L is extended back to the node j, the tag L may be extended toward the node j if the following condition is satisfied in the extension. If and only if the following conditions hold:
t(L)+t p(L)，j ≤l j #(29)
w(L)+d j ≤L#(30)
b(L)-ep p(L)，j ≥0#(31)
s(L)-sc p(L)，j ≥η min #(32)
wherein ep a(L)，j Representing power consumption from the current tag position p (L) to node j, sc p(L)，j Indicating the timeliness, t, of the post-sample from the current tag position p (L) to node j p(L)，j Meaning the time from the tag p (L) to the node j; equation (29) represents extending the time window constraint that needs to be satisfied by the node; equation (30) indicates that the upper load limit of the unmanned aerial vehicle is not allowed to be exceeded in the expansion; equation (31) represents that the power constraint needs to be satisfied in the expansion; equation (32) represents the sample timeliness constraint required in the extension.
If an extension from the current label L to node j is a viable extension, then a new label L 'will be generated at node j, the information of label L' being as follows:
p(L′)＝j#(42)
t(L′)＝max{p j ，t(L)+t p(L)，j }#(43)
l(L′)＝l(L)+d j #(44)
c(L′)＝c(L)+t p(L)，j #(45)
b(L′)＝b(L)-ec p(L)，j #(46)
Figure SMS_56
Figure SMS_57
formulas (42) - (46) set the node location, time, load, cost, and power of the new tag; formulas (47) and (48) are used to update the sets O and V of labels L'.
3.6.2 tag dominance rules:
in the process of solving the pricing sub-problem by the label setting algorithm, a large number of labels are generated on each node. If the labels on the nodes are not pruned reasonably, the difficulty of solving the sub-problems is increased. According to the label information designed in the prior art, each label carries information such as own resources and the like. On the same node, the label deletion is stopped by designing the label dominant rule. The reasonable label dominant rule can effectively reduce the solving difficulty of the sub-problem, thereby improving the solving efficiency.
p(L)＝p(L′)#(49)
c(L)≤c(L′)#(50)
t(L)≤t(L′)#(51)
b(L)≥b(L′)#(52)
Equation (49) indicates that the current positions of the tag L and the tag L' agree; equation (50) shows that label L costs less than label L' ； Equation (51) shows that the accumulated time of tag L is shorter than tag L'; equation (52) indicates that the remaining power of the tag L is greater than the tag L'.
Tag algorithm pseudocode:
Figure SMS_58
3.7 sub-problem heuristic:
when the pricing sub-problem is solved, the problem can be solved to the optimal degree by using the label algorithm, but the solving speed of the label algorithm is slow. In order to improve the speed of solving the sub-problem, a heuristic algorithm is designed to solve. It is well known that heuristic algorithms, while capable of increasing the solution speed, cannot guarantee that all paths with negative reduction costs in the sub-problem are found. According to the respective advantages of the label algorithm and the heuristic algorithm, a mode of combining the label algorithm and the heuristic algorithm is adopted. In the initial stage of solving, a heuristic algorithm is used for solving. As long as the heuristic can find paths for which the reduce cost is negative, the found paths are added to the restricted master question. With the sub-problem being solved, the heuristic starts to converge at this time, and a column with a negative reduction cost cannot be found out quickly. But in this case, there may still be a path where the reduced cost is negative, but this cannot be found using heuristic algorithms. At this point, the labeling algorithm begins solving the sub-problem, and the labeling algorithm is used to ensure that all paths with all reduce costs negative are found.
In solving the sub-problem, firstApplied to the solution is a heuristic algorithm. The nodes are randomly selected from the path for removal and then reinserted in a random manner. The removal factor and the insertion factor are generated in a random manner, and the reception criterion is adopted by the Metropolis standard. Given an initial solution sol and a search scale scal, an initial optimal solution is first set as the initial solution sol best =sol, define the current solution sol cur =sol. Algorithm iterations are then started. Definition cur sol For the temporary solution, then randomly de-cur sol Selecting the scal nodes for removing operation. Inserting the removed node into the path in a random manner, and comparing target obj (sol) of sub-problem heuristic after the insertion is completed best ) And obj (cur) sol ). If obj (sol) best )＞obj(cur sol ) Then the current optimal solution sol best ＝cur sol . Otherwise, adopting Metropolis standard to receive the current solution, repeating the above steps until the algorithm meets the termination condition, and then outputting the optimal solution sol best . Heuristic pseudocode is shown below.
Heuristic algorithm pseudocode:
Figure SMS_59
the branch pricing algorithm is composed of a column generating algorithm and a branch delimitation algorithm, and after the column generating algorithm is solved, a linear relaxation solution is obtained. The solution at this point is a solution at the root node in branch-and-bound, often not an integer solution. For an integer programming problem, branches are typically used to process when non-integer solutions are obtained. In the branching process, by branching a non-integer solution into two sub-problems, then solving again based on the sub-problems until an integer solution is obtained. In branch-and-bound solutions, each of the integer and non-integer solutions is an upper bound and a lower bound. And solving through continuous iteration of the algorithm until the gap of the upper and lower boundaries is 0, wherein the obtained integer solution is the optimal solution. The solution flow of the branch pricing algorithm is shown in fig. 1 below, and is mainly composed of column generation and branch delimitation.
Description of the drawings:
FIG. 1 is a flow chart of a branch pricing algorithm;
fig. 2 is a schematic illustration of medical drone scheduling.
Description of the preferred embodiments
The invention will be further described with reference to examples and drawings, to which reference is made by way of illustration, but not limitation, for the understanding of those skilled in the art.
An unmanned plane distribution network optimization solving algorithm for urban instant distribution has the following modeling process:
4.1 symbol definition:
u: = {1,..k } unmanned numbering set;
h: = {1,..h } set of initial positions of drones;
c: = { h+1,.,. H+n } community service point set, i.e., a set of demand generation points for sample collection to be tested;
d: = { h+n+1,..h+2n } sample is sent to the set of unit sites;
e: = { h+2n+1} unmanned virtual endpoint;
n: set of all nodes of = { H } P } D };
a: the set of arcs between nodes = { (i, j) |i E n\ { E }, j E n\h, i +.j };
g: = (N, a) directed graph set;
d i : load demand for unmanned aerial vehicle inspection;
L i : unmanned aerial vehicle leaves node i and carries load;
f: unmanned aerial vehicle dead weight;
l: maximum load (kg) of the unmanned aerial vehicle;
[e i ，l i ]: the unmanned aerial vehicle sends out the time window of examining the demand, unmanned aerial vehicle must accomplish the taking and delivering of medical supplies in the time window; wherein,,
e i ，l i respectively representing the earliest and latest start service times;
[η min ，η max ]: sample timeliness; wherein eta min ，η max Representing the minimum and maximum time that the sample is effective, respectively;
t ij : time of flight from node i to node j;
ρ: full electric quantity of the unmanned aerial vehicle;
alpha: an energy consumption factor;
t bs : the power change time of the unmanned aerial vehicle;
Figure SMS_60
the time when the unmanned plane k reaches the node i;
Figure SMS_61
the unmanned aerial vehicle reaches the node i to consume power;
Figure SMS_62
the unmanned aerial vehicle leaves the node i and consumes power;
delta: sample timeliness factor;
gamma: energy-consuming time factor
M: a very large positive integer (e.g., M is greater than or equal to 100000);
4.2 variables:
Figure SMS_63
if unmanned plane k flies from node i to node j +.>
Figure SMS_64
Otherwise->
Figure SMS_65
y i : if the unmanned aerial vehicle performs power conversion operation at the node i, y is i =1, otherwise z i ＝0；
4.3 model objective function:
Figure SMS_66
the objective function in this design modeling is to represent minimizing the time for the drone to complete all of the inspection orders.
4.4 constraint:
Figure SMS_67
Figure SMS_68
Figure SMS_69
/>
Figure SMS_70
Figure SMS_71
Figure SMS_72
Figure SMS_73
Figure SMS_74
Figure SMS_75
Figure SMS_76
Figure SMS_77
Figure SMS_78
Figure SMS_79
Figure SMS_80
Figure SMS_81
Figure SMS_82
Figure SMS_83
Figure SMS_84
Figure SMS_85
constraint (2) indicates that for any one desired sample must be serviced by the same drone ；
Constraint (3) indicates that the drone must start from the starting position ；
Constraint (4) ensures that each sample is collected and submitted and that only one unmanned aerial vehicle is serviced ；
Constraint (5) represents a flow-leveling constraint for a node ；
Constraint (6) indicates that each drone must eventually return to the virtual meeting point ；
Constraints (7) - (8) represent the time-dependent constraints of the sample after sample decay ；
Constraint (9) represents the chronological order of access before and after a node ；
Constraint (10) represents unmanned aerial vehicle payload constraint logic around a node ；
Constraint (11) indicates that the same unmanned aerial vehicle with inspection requirements must go to a community service point to collect samples before inspection ；
Constraint (12) represents a power constraint for node access order ；
Constraints (13) - (16) represent logical constraints of post-power-change power ；
Constraint (17) represents a time window constraint of the unmanned aerial vehicle access node ；
Constraint (18) represents a node load upper limit constraint ；
Constraints (19) - (20) represent variable type constraints.
4.5 aggregate coverage model:
according to the symbol definition, the following set coverage model is constructed:
(RMLP)min C r e r #(21)
Figure SMS_86
Figure SMS_87
Figure SMS_88
4.5 pricing sub-problem:
Figure SMS_89
4.6 expansion of tags:
t(L)+t p(L)，j ≤l j #(29)
w(L)+d j ≤L#(30)
b(L)-ep p(L)，j ≥0#(31)
s(L)-sc p(L)，j ≥η min #(32)
example 1
As an example, this embodiment 1 was performed to verify the scientificity and effectiveness of the above-described solution algorithm for unmanned aerial vehicle distribution network optimization for urban instant distribution:
as shown in fig. 2 below, the community service point C1 needs to send the sample to the detection unit H1 for detection, and at this time, the service point C5 needs to send the sample to be detected to the detection unit H1 for detection, but at this time, the location of the service point C5 is temporarily free from the unmanned aerial vehicle for detection service. The drone D1 starts from the service point C1, then goes to the C5 service point, and finally sends the samples of the C1 and C5 service points to the H1 detection unit for detection. Because the residual electric quantity of the unmanned aerial vehicle D1 can meet the service of the present time, the unmanned aerial vehicle D1 does not need to perform power conversion service at a C5 service point. Similarly, the service points C2 and C3 have the requirement that a sample to be detected is sent to an H2 detection unit for inspection, at the moment, the unmanned aerial vehicle D2 starts from the service point C2, the electric quantity after reaching the service point C3 cannot support the unmanned aerial vehicle D2 to fly to the H2 detection unit, so that the unmanned aerial vehicle D2 changes electricity at the service point C3, and the timeliness requirement of the sample is not influenced after the time accumulation of the electricity change. The C4 service point needs the H2 detection unit to send a batch of medical detection articles to the service point, so that the unmanned aerial vehicle D3 starts from the detection unit H2, carries medical materials to fly to the C4 service point, and meets the time window requirement of the C4 service point. In the medical unmanned aerial vehicle scheduling process, time windows of requirements and timeliness constraints of samples need to be considered. The flight route and the power change of the unmanned aerial vehicle can influence the completion time of the requirements, and the power change must be considered while the path planning is carried out.

Claims (7)

1. A medical unmanned aerial vehicle scheduling model for taking sample timeliness into account, characterized in that the model is built up by the following procedures:
1) The unmanned aerial vehicle state parameters and variables are defined, and parameter symbols are defined as follows:
u: = {1,..k } unmanned numbering set;
h: = {1,..h } set of initial positions of drones;
c: a= { h+1, …, h+n } community service point set, namely a demand generation point set for collecting a sample to be tested;
d: = { h+n+1, …, h+2n } sample is sent to the unit site collection;
e: = { h+2n+1} unmanned virtual endpoint;
n: set of all nodes of = { H } C } D };
a: an arc set between nodes = { (i, j) |i E n\ { E }, j E n\h, i +.j };
g: = (N, a) directed graph set;
d i load demand of unmanned aerial vehicle sending inspection;
L i the unmanned aerial vehicle leaves the node i and carries the load;
f, unmanned aerial vehicle dead weight;
l is the maximum load (kg) of the unmanned aerial vehicle;
[e i ,l i ]the unmanned aerial vehicle send out the time window of examining the demand, unmanned aerial vehicle must finish the taking and delivering of the medical supplies in the time window; wherein e i ,l i Respectively representing the earliest and latest start service times;
[η min ,η max ]sample timeliness; wherein eta min ,η max Representing the minimum and maximum time that the sample is effective, respectively;
t ij time of flight from node i to node j;
rho is full electric quantity of the unmanned aerial vehicle;
alpha is an energy consumption factor;
t bs the power change time of the unmanned aerial vehicle;
Figure FDA0003952835040000021
the time when the unmanned plane k reaches the node i;
Figure FDA0003952835040000022
the unmanned aerial vehicle reaches the node i to consume power;
Figure FDA0003952835040000023
the unmanned aerial vehicle leaves the node i and consumes power;
delta is the sample timeliness factor;
gamma energy-consuming time factor
M: a very large positive integer;
Figure FDA0003952835040000024
if unmanned plane k flies from node i to node j +.>
Figure FDA0003952835040000025
Otherwise->
Figure FDA0003952835040000026
y i If the unmanned aerial vehicle performs power conversion operation at the node i, y i =1, otherwise z i ＝0；
2) Determining an objective function of the model:
the objective function of the model is to represent that the time for the unmanned aerial vehicle to complete all the inspection orders is minimized, and the operation mode is shown in a formula (1):
Figure FDA0003952835040000027
3) Determining constraint conditions including the following constraint process
1. The sample which is restricted to any one delivery requirement must be served by the same unmanned aerial vehicle, namely, each delivery requirement has a pick-up point and a delivery point, and the two positions must be served by one unmanned aerial vehicle;
2. the restraining unmanned aerial vehicle must start from a starting position;
3. restricting the collection and the inspection of each sample to be detected to be all and only one unmanned aerial vehicle to serve;
4. constraining the flow of the node balance;
5. constraining each unmanned aerial vehicle to finally return to the virtual unmanned aerial vehicle terminal;
6. the effectiveness of the sample to be tested gradually decreases along with the time, so that the timeliness of the sample after the sample is attenuated is restrained;
7. the time sequence of the front and back access of the nodes is restrained, namely the earliest service time of the next node is larger than or equal to the service time of the previous node and the flight time of the unmanned aerial vehicle;
8. establishing effective load constraint logic of unmanned aerial vehicles before and after nodes;
9. unmanned aerial vehicles which restrict the same inspection requirement can be inspected after the unmanned aerial vehicles go to a community service point to collect samples;
10. constraining the electric quantity of the node access sequence;
11. establishing logic constraint of electric quantity after power change of the unmanned aerial vehicle;
12. establishing time window constraint of access nodes of the unmanned aerial vehicle;
13. and establishing node load upper limit constraint.
2. A medical unmanned aerial vehicle scheduling model for taking sample timeliness into account as claimed in claim 1, wherein in step 3), the basic constraints of the course of action of the unmanned aerial vehicle are as shown in equations (2) - (6):
Figure FDA0003952835040000031
Figure FDA0003952835040000032
Figure FDA0003952835040000033
Figure FDA0003952835040000034
Figure FDA0003952835040000035
expression (2) indicates that for any one desired sample must be serviced by the same drone; expression (3) indicates that the drone must start from the starting position; expression (4) ensures that each sample is collected and sent for inspection and that only one drone is serviced; expression (5) represents the flow balance constraint for the node. Expression (6) indicates that each drone must eventually return to the virtual junction, i.e., to the drone virtual destination.
3. A medical unmanned aerial vehicle scheduling model for taking sample timeliness into account as claimed in claim 1, wherein in step 3), the basic constraints on sample timeliness are as shown in formulas (7) - (8):
Figure FDA0003952835040000041
Figure FDA0003952835040000042
expressions (7) - (8) represent the timeliness constraint of the samples after sample decay.
4. A medical unmanned aerial vehicle scheduling model for taking sample timeliness into account as claimed in claim 1, wherein in step 3) the basic constraints on the time sequence, load and power of the unmanned aerial vehicle access nodes are shown in equations (9) - (18), and the constraints on the type of variables involved are shown in equations (19) - (20):
Figure FDA0003952835040000043
Figure FDA0003952835040000044
Figure FDA0003952835040000045
Figure FDA0003952835040000046
Figure FDA0003952835040000047
Figure FDA0003952835040000048
Figure FDA0003952835040000049
Figure FDA00039528350400000410
Figure FDA00039528350400000411
Figure FDA00039528350400000412
Figure FDA00039528350400000413
Figure FDA00039528350400000414
expression (9) represents the chronological order of the access before and after the node,
Figure FDA00039528350400000415
representing the time when the unmanned plane k starts to serve the node i;
expression (10) represents unmanned aerial vehicle payload constraint logic before and after the node;
expression (11) shows that the same inspection-for-purpose unmanned aerial vehicle must first go to a community service point to collect a sample and then can be inspected;
expression (12) represents a power constraint of the node access order;
expressions (13) - (16) represent logical constraints of the amount of power after power conversion;
expression (17) represents a time window constraint of the unmanned access node;
expression (18) represents a node load upper limit constraint;
expressions (19) - (20) represent variable type constraints.
5. A solution algorithm for a medical drone dispatch model taking sample timeliness into account as claimed in claim 1, characterised by comprising the following process:
a branch pricing algorithm is designed to solve the scheduling problem of the medical unmanned aerial vehicle in a medium-large scale; in a branch pricing algorithm, firstly, the medical unmanned aerial vehicle scheduling model is optimized and modeled again to form a set coverage model and a pricing sub-problem; in the pricing sub-problem, a mode of combining an accurate algorithm and a heuristic algorithm is designed for solving;
1) The aggregate coverage model modeling process is as follows:
first, set of overlay model symbols and meanings
R: all feasible path sets;
C r : the cost of path r;
n ir : the number of times node i is accessed by path r;
Figure FDA0003952835040000051
a variable representing 0 or 1, 1 if path r has accessed an arc (i, j), or 0 otherwise;
e r : a variable representing 0 or 1, 1 if path r is selected, and 0 otherwise;
second, build a set coverage model:
because the solution set R corresponding to the path R is huge, the solution cannot be directly carried out at the moment; adopting a frame based on column generation, firstly considering a set coverage model in a partial solution space, and then gradually expanding a solution space set by solving a pricing sub-problem; limiting the solution set in the set coverage model based on the limitation to obtain a limited main problem model; define R' as a subset of set R, at which time
Figure FDA0003952835040000052
Variable e in the subject problem to be restricted r Relaxation, linear relaxation model equations (21) - (24) get the following constrained main problem:
(RMLP)minC r e r #(21)
Figure FDA0003952835040000061
Figure FDA0003952835040000062
Figure FDA0003952835040000063
definition of the definition
Figure FDA0003952835040000064
For the dual variable of constraint (22), +.>
Figure FDA0003952835040000065
As the dual variables of constraint (23), the set-based coverage model is better than the set partition model;
third, pricing sub-problem:
in the pricing sub-problem, it is necessary to find paths where all reduce costs are negative, where reduce
Figure FDA0003952835040000066
Then adding the path into the limited main problem, and updating the sub-problem through the dual variables obtained after solving the limited main problem; repeatedly solving until all paths with the reduction cost as negative numbers are found; solving the pricing sub-problem is actually solving a basic shortest path problem with resource constraints;
according to the definition, the reduce cost of the path r in the sub-problem can be constructed through the dual variables in the RMLP; in the solving of the sub-problem, updating the cost of the arcs in the sub-problem by means of the dual variables; the reduce cost defining path r is:
Figure FDA0003952835040000067
wherein:
Figure FDA0003952835040000068
Figure FDA0003952835040000069
update formula (25) is rewritten as the following formula (28):
Figure FDA0003952835040000071
wherein the method comprises the steps of
Figure FDA0003952835040000072
A' represents a set of arcs between nodes of a child problem;
n' represents a set of all nodes of the child problem;
2) And solving the pricing sub-problem based on a method of combining a label algorithm and a heuristic algorithm of dynamic programming.
6. A solution algorithm for a medical drone dispatch model taking sample timeliness into account as claimed in claim 5, wherein the process of the labeling algorithm of the sub-problem is as follows:
designing a label algorithm based on a dynamic programming idea, wherein the solution framework algorithm can be expressed as follows: starting from a source node, each node along the way generates a plurality of labels; in the expansion process, a plurality of different labels are arranged on the same node, and a dominant rule is needed to be used for pruning, so that the search space is reduced;
firstly, defining a label L, wherein the information of the label L mainly comprises the node position of the current label: p (L); t (L) is the time of arrival of the tag L at the current location; w (L) is the accumulated load of the label L; b (L) is the current residual capacity of the label L; c (L) is the accumulated consumption cost of the label L; s (L) is the sample timeliness of the label L; in addition, O (L) is defined as a node set of the label L, wherein only the picking of goods is finished and the delivery of goods is not finished yet; v (L) is a set of nodes that have completed service; UR (L) is a node whose label L cannot be extended;
1) Expansion of the tag:
when the tag L extends back to the node j, the tag L may extend to the node j if and only if the following condition is met in the extension:
t(L)+t p(L),j ≤l j #(29)
w(L)+d j ≤L#(30)
b(L)-ep p(L),j ≥0#(31)
s(L)-sc p(L),j ≥η min #(32)
wherein ep a(L),j Representing power consumption from the current tag position p (L) to node j, sc p(L),j Indicating the timeliness, t, of the post-sample from the current tag position p (L) to node j p(L),j Meaning the time from the tag p (L) to the node j; equation (29) represents extending the time window constraint that needs to be satisfied by the node; equation (30) indicates that the upper load limit of the unmanned aerial vehicle is not allowed to be exceeded in the expansion; equation (31) represents that the power constraint needs to be satisfied in the expansion; equation (32) represents the sample timeliness constraint required in the extension;
if an extension from the current label L to node j is a viable extension, then a new label L 'will be generated at node j, the information of label L' being as follows:
p(L′)＝j#(42)
t(L′)＝max{p j ,t(L)+t p(L),j }#(43)
l(L′)＝l(L)+d j #(44)
c(L')＝c(L)+t p(L),j #(45)
b(L′)＝b(L)-ec p(L),h #(46)
Figure FDA0003952835040000081
Figure FDA0003952835040000082
formulas (42) - (46) set the node location, time, load, cost, and power of the new tag; formulas (47) and (48) are used to update the sets O and V of the label L';
2) Tag dominance rules:
in the process of solving the pricing sub-problem by the label setting algorithm, a large number of labels are generated on each node, and if the labels on the nodes are not reasonably pruned, the difficulty of solving the sub-problem is increased; according to the label information designed in the prior art, each label is provided with information of own resources; on the same node, label deletion is carried out by designing a label dominant rule; the reasonable label dominant rule can effectively reduce the solving difficulty of the sub-problem, thereby improving the solving efficiency;
p(L)＝p(L′)#(49)
c(L)≤c(L')#(50)
t(L)≤t(L')#(51)
b(L)≥b(L')#(52)
equation (49) indicates that the current positions of the tag L and the tag L' agree; equation (50) indicates that label L is less costly than label L'; equation (51) shows that the accumulated time of tag L is shorter than tag L'; equation (52) indicates that the remaining power of the tag L is greater than the tag L'.
7. A solution algorithm for a medical drone scheduling model taking sample timeliness into account as claimed in claim 6, characterized in that the procedure of the heuristic algorithm of the sub-problem is as follows:
when the pricing sub-problem is solved, the problem can be solved to the optimal state by using a label algorithm, but the solving speed of the label algorithm is slow; in order to improve the speed of solving the sub-problem, a heuristic algorithm is designed to solve, and although the heuristic algorithm can improve the solving speed, paths with negative numbers of all reduce costs in the sub-problem cannot be found; according to the advantages of the label algorithm and the heuristic algorithm, a mode of combining the label algorithm and the heuristic algorithm is adopted; in the initial stage of solving, firstly, a heuristic algorithm is used for solving, and the found path is added into the limited main problem as long as the heuristic algorithm can find the path with the reduced cost as a negative number; with the continuous solving of the sub-problem, the heuristic starts to converge at this time, and a column with a negative number of the reduce cost cannot be quickly found out; in this case, there may still be a path with a negative reduction cost, but this cannot be found using heuristic algorithms; at this time, the label algorithm starts to solve the sub-problem, and the label algorithm is utilized to ensure that all paths with the reduction cost as negative numbers are all found;
when solving the sub-problem, the method is firstly applied to solving a heuristic algorithm; randomly selecting nodes from the paths to remove, and then reinserting the removed nodes in a random mode; the removal factor and the insertion factor are generated in a random manner, and the receiving criterion adopts the Metropolis standard; given an initial solution sol and a search scale scal, an initial optimal solution is first set as the initial solution sol best =sol, define the current solution sol cur =sol; then starting algorithm iteration; definition cur sol For the temporary solution, then randomly de-cur sol Selecting scal nodes to perform removing operation; inserting the removed node into the path in a random manner, and comparing target obj (sol) of sub-problem heuristic after the insertion is completed best ) And obj (cur) sol ) The method comprises the steps of carrying out a first treatment on the surface of the If obj (sol) best )>obj(cur sol ) Then the current optimal solution sol best ＝cur sol Otherwise, receiving the current solution by adopting a Metropolis standard; repeating the above steps until the algorithm meets the termination condition, and then outputting the optimal solution sol best ；
The heuristic algorithm has the following operation processes:
input: initial feasible solution: a sol; search scale: scal;
1) Initializing an optimal solution and a current solution: sol best ＝sol，cur sol ＝sol；
2) While loop, algorithm termination condition is not satisfied:
3) Current decor sol Copying: cur's' sol ＝cur sol ；
4) For solving cur' sol Performing a removal operation;
5) For solving cur' sol Performing an insertion operation;
6) Target obj (sol) if sub-problem heuristics best) >obj(cur' sol ) Then the current optimal solution is updated: sol best ＝'cur sol ；
7) If step 6) is not satisfied, then the current solution cur 'is received using the Metropolis criterion' sol ；
And (3) outputting: optimal solution sol best
The branch pricing algorithm is composed of a column generating algorithm and a branch delimitation algorithm, and after the column generating algorithm is solved, a linear relaxation solution is obtained. The solution at this point is a solution at the root node in branch-and-bound, often not an integer solution. For an integer programming problem, branches are typically used to process when non-integer solutions are obtained. In the branching process, by branching a non-integer solution into two sub-problems, then solving again based on the sub-problems until an integer solution is obtained. In branch-and-bound solutions, each of the integer and non-integer solutions is an upper bound and a lower bound. And solving through continuous iteration of the algorithm until the gap of the upper and lower boundaries is 0, wherein the obtained integer solution is the optimal solution.
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