A Multi-visit Traveling Salesman Problem with Multi-Drones

A Multi-visit Traveling Salesman
Problem with Multi-Drones
Dr. Heba Askr
Faculty of Computers and Artificial Intelligence (FCAI), University of Sadat City, Egypt
hebamaskr@gmail.com
Member of Scientific Research Group in Egypt (SRGE)
Advanced Intelligent Systems for Sustainable Development (AISSD 2021) 20-22 August 2021

Agenda
2
1 • Introduction
2 • Problem Definition
3 • Proposed Approach
4
• Experimental Results
5
• Conclusion
6
• Future Points for research
7
• References

Introduction
 Parcel delivery is a type of the last-mile delivery.
 The use of drones for parcel delivery recently
improve the efficiency of the last-mile delivery.
 Parcel delivery is considered as a routing problem
that can be solved using Traveling Salesman
Problem (TSP) technique.
3
What is Parcel Delivery Problem?

What is Traveling Salesman Problem (TSP)?
• Several cities are linked together by arcs.
• The problem is to find the shortest route for
the salesman from a given city, visiting n
cities once and then finally returning to the
origin city [depot or hub].
4
Introduction
4
depot
In TSP,

Why adding the drones to the TSP trip?
5
Introduction
Time savings by truck-drone delivery

6
Problem Definition
 Parcel Delivery by TSP is NP-hard optimization problem, means for
large scale TSP, there is no exact algorithm is known to find a solution
in polynomial time.
 This opens the door for using the heuristic techniques to find the near
optimal solutions in large scale problem to overcome the problems of
time and space complexity.

7
Problem Definition
Finding the optimal schedule for the parcel delivery problem using multi-visit
TSP with multi-drones that can deliver multiple packages per a trip (applied
for small, medium and large-scale problems).

Contribution
8
Proposed Approach
The proposed model :
• Employs a drone flight endurance model based on the payload of the multiple
parcels and its flight time.
• Deploys multiple drones from the truck.
• Allows multiple deliveries per drone trip.
• Allows multiple operations at any customer node and the depot.

Methodology
9
Proposed Approach
The problem is
formulated as a
Mixed Integer
Linear Program
(MILP) model
A Multi-Start Tabu
Search (MSTS)
algorithm is
proposed with
tailored
neighborhood
structure
Two-level solution
evaluation
method based on
the Critical Path
Method (CPM).

10
Experimental Results
 Customized data sets is used.
 Test instances with 8, 10, 25, 50 and 100 customers
are used.
 Drones of sizes 1,2,3,and 4 are used with different
profiles (L – M - H).
 CPLEX solver is used to solve small scale problems
with a run time limit of 2hrs.

11

12
 The table shows that the MSTS obtains the same BSF for each of the ten
runs for 26 of test instances with 8 customers and for 12 of the test
instances with 10 customers.
 the GAP avg is less than 1% for most of the test instances.
Analysis on small scale instances comparison on CPLEX
 This shows that the MSTS performs consistently well in solving the
small-scale test instances.

13
Experimental Results (large-scale)
 Table reports the cost of the best-found solution and the average cost
of the solutions found for each test instance.
Analysis on medium and large-scale instances

14
14
 The results show
that for each
instance with the
same number of
customers, the
solution cost
decreases gradually
when the drones of
the same profile are
increases or when
the profile of drone
increases.

15
 the column ”ratio” under n = 50 and n = 100 represent the increase in CBSF
versus the increase in customer sizes.
 under n = 50 is defined as (CBSF for n = 50/ CBSF for n = 25) for the same instance.

16
The average ratio across all test instances is consistent with the ratio between customer
sizes

17
Conclusion
• The proposed model determines the shortest critical path for a single truck
equipped with a homogeneous fleet of drones capable of serving multiple
customers in a single flight.
• It is formulated and solved by commercial solvers for small-size instances. multi-
start tabu search (MSTS) algorithm is proposed to tackle medium and large-size
instances which are more practical for real-world scenarios.
• The computational results show great potential in cost reduction with multi-visit,
multi-drones, and drones with higher capacity.

18
Future Points for Research
 Developing Ant Colony Optimization Algorithm instead of the MSTS
Algorithm.
 Each Ant will build a feasible truck-drone schedule with its fitness value.
 Choosing the best schedule by all ants to be the optimal schedule (the best
fitness value).
 Comparing the results between the two algorithms using the same data set.

19
References
Zhihao Luoa,c, Mark Poonc,*, Zhenzhen Zhangb, Zhong Liua, Andrew Limd,e,
“The Multi-visit Traveling Salesman Problem with Multi-Drones”, Elsevier, 128
(2021) 103172.

A Multi-visit Traveling Salesman Problem with Multi-Drones

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