A Rolling Horizon Approach for the Dynamic Scheduling of Flying Taxis

Sana Ikli

Hybrid Intelligence, Capgemini Engineering, 4 Avenue Didier Daurat, 31700 Blagnac, France

Keywords:

Flying Taxis, Dynamic Scheduling, Genetic Algorithm, Heuristic Solutions, Rolling Horizon Approaches.

Abstract:

Flying taxis are a promising alternative to ground transportation to alleviate the congestion problem in

metropolitan cities. The launching of the ﬁrst air taxis is expected in the next few years. The companies

operating air taxi services will deal with several real-time problems. Such problems include the scheduling

of ﬂying taxi operations, and the battery charging management as well as other maintenance issues. In this

work, we are interested in the dynamic scheduling of ﬂying taxis, so as to serve a set of clients. This problem

is on the one hand under-explored in the literature, as we will show in the next sections, and on the other hand,

it is more realistic than the static case. We present in this work a rolling-horizon approach, integrated with

three heuristics, to solve the dynamic scheduling of ﬂying taxis. We also construct new realistic and difﬁcult

instances to test and validate our algorithms. Our instances and implementations are publicly available for the

scientiﬁc community online. Finally, we perform a computational study on our generated instances to show

the beneﬁts and the limits of each heuristic.

1 INTRODUCTION

Air taxis are expected to serve as an alternative to

ground transportation to alleviate trafﬁc congestion

in metropolitan cities (Rajendran and Zack, 2019).

Several transportation pioneers and airline manufac-

turers are preparing to launch their Urban Air Mo-

bility (UAM)

services in the near future. Indeed,

Airbus Helicopters is currently working on new elec-

tric ﬂying taxis as a part of the CityAirbus Nextgen

project (Dumez, 2021). Their ﬂying taxis are ex-

pected to operate in 2025. Apart from Airbus, Uber

is also working on an air taxi service called Uber Ele-

vate, which is estimated to lunch in 2023 (Rajendran

and Zack, 2019).

Due to the dynamic nature of the problem, the

companies proposing air taxi service will deal with

several real-time decision problems. Such decisions

include (i) evaluating different candidate trips and

scheduling the ﬂying taxis so as to optimize a given

objective (e.g., reduce the operational costs, maxi-

mize the proﬁt from the trips, serve the maximum

number of demands, etc.), (ii) dynamic estimation

of the market demands, and (iii) battery charging

management as well as other maintenance related-is-

sues (Rajendran and Srinivas, 2020).

The scheduling of air taxi operations combines

two problems from the literature: parcel delivery

drones, and ground taxi demand scheduling. The for-

Acronyms meaning are also outlined in Table 3.

mer is used to derive the general characteristics of the

ﬂying taxis; the latter helps to design the schedul-

ing models, objectives, and constraints. The prob-

lem consists in dispatching a ﬂeet of air taxis so as

to serve the costumers, while respecting several op-

erational constraints. The constraints can be divided

in two categories: (i) ﬂying taxi-related constraints,

like the vertical take-off and landing restrictions, and

the battery recharging constraints, and (ii) customer’s

constraints, such as the time-windows that are a spec-

iﬁed period of time during which the customer can be

served. Other ﬂying taxi characteristics such as the

operating time, the battery recharging time, and bat-

tery consumption rate are also present in the parcel

delivery drones.

The ground taxi demand scheduling consists in

dispatching a ﬂeet of ground taxis to serve a set of

clients. Serving a client includes the transportation

from an origin to a destination point, taking into con-

sideration several operational constraints such as the

time-windows and the trafﬁc jam. A time-window is

a speciﬁed time slot during which a customer can be

served. The objective of this problem is usually to

maximize proﬁt. According to (Tangpattanakul and

Quenel, 2021), the proﬁt from a ground-taxi trip is

usually calculated using: (i) a base rate (initial charge

for the ﬁrst kilometers), (ii) a distance rate (count of

the next kilometers), and (iii) a minute rate (cost of

waiting time in case of congestion). The proﬁt from a

ﬂying taxi however should involve only the base and

Ikli, S.

A Rolling Horizon Approach for the Dynamic Scheduling of Flying Taxis.

DOI: 10.5220/0011376500003332

In Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022), pages 65-73

ISBN: 978-989-758-611-8; ISSN: 2184-3236

the distance rates, since there will be no trafﬁc jam in

low level airspace (Kellermann et al., 2020). In the

dynamic case, the scheduler must be ﬂexible to ac-

commodate unpredictable events that may occur, such

as: the trafﬁc jam, new requests, changes in the cus-

tomer location, etc.

The scheduling of ﬂying taxis can be classiﬁed in

two main categories, according to the availability of

the data:

• The static case, when all input data are known in

advance before the day of the operations.

• The dynamic or the real-time case, when all or

some input parameters are unknown for the con-

sidered scheduling horizon. This case is under-

explored in the literature, and to the best of our

knowledge, only the work of (Rajendran, 2021)

considers this problem.

In this work, we are interested in the dynamic

management of a ﬂeet of ﬂying taxis. The manage-

ment includes the dynamic scheduling of the ﬂying

taxis as well as the battery charging handling. This

work is one of the few (Rajendran, 2021) that consid-

ers the (more realistic) real-time problem, where de-

cisions have to be made dynamically to accommodate

the new changes in the air taxi system. The contribu-

tions of our paper are summarized as follows:

• Efﬁcient scheduling heuristics to solve small

problem instances. These heuristics are the ﬁrst-

come, ﬁrst-served, the nearest neighbor, and the

genetic algorithm.

• A Rolling Horizon (RH) framework coupled with

the above-mentioned heuristics to solve larger in-

stances and to tackle the dynamic case.

• New realistic and challenging problem instances

that are publicly available from https://github.c

om/sanaikli/Dynamic-Flying-Taxi-Scheduling.

• A comparative study of the proposed RH ap-

proaches.

2 LITERATURE REVIEW

The scheduling of ﬂying taxis is similar to two well-

known combinatorial optimization problems, namely

the Job-Shop Scheduling Problem (JSSP) and the Ve-

hicle Routing Problem (VRP). The analogy between

these problems is highlighted in Section 2.4. Since

the literature on the dynamic scheduling of ﬂying

taxis is very scarce, we propose in this section an

overview of the research articles addressing the gen-

eral problems of the dynamic machine scheduling and

vehicle routing. The goal of this literature review is

to give insights to the readers on how the dynamic

scheduling and routing are tackled for different well-

known problems, that are similar to the problem of

our interest.

2.1 Dynamic Machine Scheduling

The static scheduling assumes that all problem param-

eters are known in advance and they do not change.

In the actual production process, several disturbances

may occur, such as a delayed processing time, the

arrival of new jobs, etc., which make the previous

schedule obsolete. To accommodate the new changes,

one must constantly adjust the scheduled plan, in a

process known as dynamic scheduling.

A common strategy used in the literature to tackle

the dynamic scheduling is the Rolling Horizon (RH)

approach. The latter, also referred to as receding hori-

zon, usually subdivides the scheduling horizon into

smaller sub-horizons, and then solves the static prob-

lem on each sub-horizon sequentially. In the RH ap-

proaches, there are jobs that will start inside a sub-

horizon and ﬁnish outside that sub-horizon, regard-

less of its length. This kind of jobs is called cross-

window jobs. To deal with them, boundary conditions

have to be deﬁned for each sub-horizon. On the other

hand, the computation complexity is expected to be

reduced in the sub-horizons, since the problem size is

smaller. The RH scheduling approaches can be cate-

gorized into two types of strategies:

• The event-driven scheduling in which the rolling

horizon is a job window, i.e., a number of jobs

for scheduling and processing. This strategy ﬁrst

chooses a job window, which is deﬁned by the (al-

lowed) maximum number of jobs. Then, it divides

the set of jobs in three sub-sets: (i) the sub-set

of available jobs, (ii) the sub-set of current jobs,

and (iii) the sub-set of ﬁnished jobs. A selection

rule is then used to select jobs from the sub-set

of available jobs. Finally, an optimization algo-

rithm is required to solve the problem in the job

windows, and the three above-mentioned sets are

updated until all the jobs are processed. Notable

examples from the literature that use this approach

are (Chen et al., 2017; Fang and Xi, 1997). The

former work used this strategy to solve the online

workﬂow scheduling on cloud environment, and

the latter used it for the classical dynamic JSSP.

• The periodic scheduling strategies in which the

rolling domain is a time window, i.e., a time slot

on the scheduling horizon. This strategy is used

in (Sun and Lin, 1994) to solve the dynamic JSSP.

In this work, the authors subdivide the planning

horizon, T , into two non-overlapping windows,

ECTA 2022 - 14th International Conference on Evolutionary Computation Theory and Applications

and T

. Some heuristic rules are used for this

subdivision. Then, they solve the (static) problem

on T

. Finally, they determine the set of cross-

window jobs and schedules them with the jobs in

the window T

The periodic scheduling is also used in (Tang

et al., 2010), but with a different rolling time-

window. In this context, the planning horizon, de-

noted [0,K], is subdivided in R time periods of

equal lengths. Then, the problem is solved in the

whole planning horizon at the beginning. As time

progresses, the window is shortened by one time

period, and the problem is again solved in the new

window, as illustrated in Fig. 1.

the 1st rolling window

the 2nd rolling window

the 3rd rolling window

T 2T K

Figure 1: A rolling horizon with three rolling windows.

2.2 Dynamic Vehicle Routing Problem

In the dynamic vehicle routing problem, the cus-

tomer orders are usually considered to be the dy-

namic events. The RH approach is also used to solve

this problem. For instance, in the work of (Hanshar

and Ombuki-Berman, 2007), the periodic scheduling

strategy is used, but with time-windows that differs

from (Sun and Lin, 1994) and (Tang et al., 2010). In-

deed, in (Hanshar and Ombuki-Berman, 2007) , the

authors subdivide the planing horizons into several

slices of equal lengths. Then, they sequentially solve

the (static) VRP on each slice. Furthermore, the au-

thors deﬁne a cutoff time, which postpones the late

orders to the next day. The genetic algorithm is then

used to solve the static problem on each time slice.

A number of heuristic solutions are proposed

in (Larsen et al., 2002) to solve the dynamic VRP.

Examples of such heuristics are:

• First-Come First-Served (FCFS) that serves the

clients in the order which they are.

• Nearest Neighbor (NN) that completes the de-

mands in one location, and then travels to the

nearest neighboring demand.

2.3 Real-time Scheduling and Routing

of Air Vehicles

The works in the literature addressing the real-time

scheduling and routing of air taxis are rare compared

to the machine scheduling or the VRP. Nonetheless,

the two recent works (Rajendran, 2021) and (Song

et al., 2016) consider this dynamic scheduling for two

types of air vehicles: the ﬂying taxis for the former

work, and the Unmanned Aerial Vehicle (UAV) for

the latter.

In (Song et al., 2016), the authors develop a real-

time tool to manage a ﬂeet of UAVs to serve cus-

tomers. The management includes visiting the service

station for battery recharging. The problem is formu-

lated as a mixed-integer program, and solved using

CPLEX solver (Holmstrom et al., 2009). The real-

time management is performed using the two RH ap-

proaches: the event-driven and the periodic schedul-

ing strategies presented in Section 2.1.

In the very recent work of (Rajendran, 2021), the

author considers the real-time dispatching of air taxis

in a centralized taxi network. Two objectives are

taken into account: minimizing the number of idle

taxis and minimizing the total travel time of air taxis

at inactive state. Since these two objectives are con-

ﬂicting, the author uses a goal programming algo-

rithm to solve the problem. The proposed strategy

to handle the real-time demands is similar to the one

used in (Sun and Lin, 1994). However, (Rajendran,

2021) does not consider explicit rolling windows, but

rather deﬁnes some control points on the schedul-

ing horizon, and re-solve the problem at each control

point. To the best of our knowledge, this is the only

work in the literature that considers the dynamic ﬂy-

ing taxi scheduling.

2.4 Analogy and Complexity

The problem of scheduling ﬂying taxi operations

is similar to two well-known combinatorial opti-

mization problems, namely the Job-Shop Schedul-

ing Problem (JSSP) and the Vehicle Routing Problem

(VRP).

The analogy between a JSSP and the scheduling

and routing of air taxis can be described as follows.

The machines represent the ﬂying taxis, and the jobs

represent the demands. The trip duration of a given

demand can be interpreted as the processing time of

a job in the JSSP framework. A fundamental aspect

of the ﬂying taxis framework is the battery charging;

the latter can be translated to the JSSP model as the

machine breakdown.

In addition, the scheduling and routing of air taxis

is clearly similar to the VRP. In the two frameworks,

we have vehicles to dispatch and clients to serve. The

classical time-windows constraints (Belhaiza et al.,

2019) in the VRP framework can directly be trans-

lated to the scheduling of ﬂying taxis. Finally, the

battery charging of an air taxi can be viewed as the

A Rolling Horizon Approach for the Dynamic Scheduling of Flying Taxis

vehicle refueling.

As a consequence of these analogies, we can de-

rive two conclusions. On the one hand, the prob-

lem of scheduling ﬂying taxis, the JSSP, and the

VRP have the same complexity: they are NP-hard

problems (JSSP and the VRP are already proven to

be NP-hard (Mohan et al., 2019; Derigs and Vogel,

2014)). On the other hand, exact methods may require

long computation times as the problem size increases.

Hence, heuristic methods are more suitable to solve

this scheduling problem, especially the dynamic case,

where decisions have to be made in real-time.

3 DYNAMIC FLYING TAXI

SCHEDULING: ROLLING

HORIZON APPROACH

In the static ﬂying taxi scheduling, it is assumed that

complete information about customers requests are

known in advance. In the dynamic case however,

new requests may arrive on the planning horizon and

the solution must be revised. Hence, it is appropriate

to adopt a rolling-horizon approach, to accommodate

the new changes and reschedule the demands accord-

ingly.

3.1 Rolling Horizon Framework

The RH approach we adopt in this work is the pe-

riodic scheduling strategy, introduced in Section 2.1.

The rolling domain in this context is a time-window,

i.e., a time slot on the scheduling horizon. Figure 2

illustrates how this approach works.

Move unserved requests to next window

.. .... ........ . ... .. . .

window

t (min)

T (1440)

...

Figure 2: Rolling-horizon strategy illustration.

In the context of our RH strategy, the static prob-

lem is solved in the ﬁrst rolling window, using heuris-

tic methods for creating a ﬂying taxi schedule. In this

work, we propose three heuristic methods: one is the

GA of (Tangpattanakul and Quenel, 2021) adapted to

our problem; the remaining two heuristics are bor-

rowed from the VRP literature and adapted to the ﬂy-

ing taxis framework. At the end of the ﬁrst rolling

window, the RH strategy moves the unserved requests

to the beginning of the next window, and schedules

them together with the new available requests. The

battery level for all the available ﬂying taxis is set to

100% at the beginning of the RH approach. Then, its

is updated at the end of each rolling window accord-

ing to the battery consumption rate.

3.2 Heuristic Solutions for Creating

Flying Taxi Schedules

In this subsection we describe two heuristic meth-

ods and a genetic algorithm that we use to solve the

static problem inside each rolling window. The ﬁrst

two heuristics, named “the First-Come, First-Served”

(FCFS) and the “Nearest-Neighbor” (NN), are bor-

rowed from the VRP literature.

3.2.1 First-Come, First-Served

The FCFS is a classical heuristic method used in prac-

tice to solve several optimization problems, including

the VRP. This heuristic serves the requests according

to the order given by their pick-up times. Indeed, the

demands are sorted according to the non-decreasing

order of their pick-up times. The advanced requests

are served (without considering their location), on

their pick-up times or in an interval – deﬁned by the

user – centered around the pick-up time. The pro-

cess continues until no request is available. The bat-

tery level is checked before each customer pick-up,

and updated after each customer drop-off, according

to the battery consumption rate. If the battery level

of the available taxi is not enough to serve the next

client, then the ﬂying taxi is sent to the center for bat-

tery recharging.

3.2.2 Nearest Neighbor

The NN is also borrowed from the ﬁeld of vehicle

routing problems. This heuristic serves the closest

requests to the current location of the taxi. Indeed,

for each taxi, the NN scheduler serves ﬁrst the clos-

est demand to the center. After completing service

at the location of the ﬁrst demand, the taxi travels

to the nearest neighboring demand and so forth. The

key difference between a FCFS and a NN scheduler is

that the former sorts the customers at the beginning of

the scheduling and then serves them, while the latter

needs to recompute the distances from current request

location to all other unserved requests, to serve the

closest one. This process is repeated after each cus-

tomer drop-off to ﬁnd the next one to serve. Hence,

this heuristic may lead to longer computation times

than the FCFS. As for the FCFS, the battery level of

each taxi is checked before the customer pick-up, and

updated after its drop-off.

ECTA 2022 - 14th International Conference on Evolutionary Computation Theory and Applications

3.2.3 Genetic Algorithm

Genetic algorithms are evolutionary algorithms in-

spired by the process of natural selection. They have

shown their efﬁciency in solving complex combinato-

rial optimization problems, such as the aircraft land-

ing problem (Hu and Di Paolo, 2011), and the vehi-

cle routing problems (Hanshar and Ombuki-Berman,

2007).

The genetic algorithm we consider in this section

is based on (Tangpattanakul and Quenel, 2021). In

this work, a chromosome is composed of genes whose

values are randomly generated in the interval [0,1].

Each gene represents a demand which is served by a

ﬂying taxi. For example, if we consider an instance

with 3 requests and 2 ﬂying taxis, the total number

of genes is equal to 6 (Figure 3). A solution of the

scheduling problem is constructed from the chromo-

somes, and it contains the following information:

• The sequences of the selected demands which will

be serviced by the ﬂying taxis, and the battery

recharging tasks.

• The set of starting time of each task/demands.

• The set of ﬁnishing time of each task/demands.

• The operational time of the selected demands.

Chromosome:

Request 1

served by

Taxi 1

0.5

Request 1

served by

Taxi 2

0.5

Request 2

served by

Taxi 1

0.6

Request 2

served by

Taxi 2

0.1

Request 3

served by

Taxi 1

0.2

Request 3

served by

Taxi 2

0.9

Figure 3: Example of a chromosome with six genes (3 re-

quests/2 taxis).

In our adaptation of this algorithm, the demands

can be served during an acceptable time-window,

which is more realistic than serving them on strict

pick-up times, as it is assumed in (Tangpattanakul

and Quenel, 2021). The ﬁrst population of chromo-

somes is randomly generated. At each iteration, a

new population is generated from three sets of chro-

mosomes: the elite set for the selection process, the

crossover set for the crossover operations and the mu-

tation set for the mutation operations. The elite set

copies the best chromosomes from the previous iter-

ation. The crossover set contains the offspring chro-

mosomes whose gene values are generated from two

different parent chromosomes. The ﬁrst and the sec-

ond parent are respectively selected from the elite and

the non-elite sets. As for the initial population, the

mutation set is also randomly generated, to help es-

caping from local optimum. The process of mutation

and crossover continues until the stopping criteria is

satisﬁed. The latter corresponds to a number of iter-

ations since the last improvement. The ﬁtness func-

tion corresponds to the total service time, that the GA

seeks to maximize. The parameters of the GA are

shown in Table 1.

Table 1: Values of the GA parameters.

Parameter Value

Population size 2× (chromosome size)

Elite set size 10% of the population size

Mutation set size 20% of population size

Crossover set size 70% of population size

Crossover probability 0.7

Stopping criterion 30

4 COMPUTATIONAL RESULTS

This section reports the computational results of

implementing the above-mentioned heuristics, inte-

grated in the rolling horizon approach. All experi-

ments are run on a computer under Windows operat-

ing system, processor Intel(R) Core(TM) i5-10310U

with 8 GB of RAM.

In section 4.1, we introduce new data-sets of in-

stances that we generate for the numerical study.

Then, in Section 4.2 we present computational results

of implementing our three heuristics FCFS, NN, and

the GA, all integrated in the RH approach. The test

instances and implementations are publicly available

from the following Link: https://github.com/sanaikli/

Dynamic-Flying-Taxi-Scheduling.

4.1 New Generated Instances

We randomly generate 10 test instances, based on

the instance generator of (Tangpattanakul and Quenel,

2021). In addition to being more congested, our in-

stances deﬁne a time window for each demand during

which it can be served, which is more realistic than

imposing a strict pick-up time.

Table 2 summarizes some important characteris-

tics of our instances. Throughout this table, the ﬁrst,

second and third columns present the name, the to-

tal number of requests, and the total number of air

taxis in each instance (respectively). The fourth col-

umn “req/h” reports the average request per hour in

each instance, which measures how dense the latter

is. The remaining columns show the minimum, av-

erage, and the maximum duration of request trips in

each instance.

A Rolling Horizon Approach for the Dynamic Scheduling of Flying Taxis

Table 2: Characteristics of the new constructed instances.

Instance name #req #taxis req/h min

duration

average

duration

max

duration

instance10 2 10 2 0.42 17.52 28.16 44.12

instance30 2 30 2 1.25 12.22 26.31 40.61

instance50 3 50 3 2.08 12.16 24.41 43.81

instance80 4 80 4 3.33 11.81 28.58 45.98

instance100 3 100 3 4.17 11.00 26.80 48.57

instance100 4 100 4 4.17 11.48 26.33 48.35

instance200 5 200 5 8.33 11.25 26.97 50.04

instance500 5 500 5 20.83 10.31 27.12 48.33

instance500 10 500 10 20.83 10.74 27.14 51.51

instance1000 15 1000 15 41.67 10.49 27.20 49.35

4.2 Results and Discussion

To compare the quality of the solutions provided by

our heuristics, we deﬁne the following performance

indicators:

• The objective-value that indicates the total ser-

vice time (in minutes) that we seek to maximize.

• The non-proﬁtable trips duration that corre-

sponds to the total travel time without passengers.

This may occur when a taxi ﬂies to the center to

recharge its battery, or between two requests.

• The CPU time that indicates the computation

times in seconds.

Figure 4 shows the results of the FCFS, the NN,

and the GA heuristics on the basis of our three perfor-

mance measures. The tests are performed on our gen-

erated instances, involving 10 to 1000 requests and

2 to 15 ﬂying taxis. The name of each instance is

showed in the x-axis of each ﬁgure. For these tests,

the parameter of the rolling-window length, R, is cho-

sen to be 60 minutes.

It can be seen in Figure 4 that the three heuristics

obtain similar performances in terms of the objective-

value, for the ﬁrst six instances. However, in terms

of the non-proﬁtable trips, the NN obtains (as ex-

pected) better results. This may be explained by the

fact that in the NN heuristic, Taxis ﬂy to the near-

est neighboring demand location, which minimizes

the non-proﬁtable trip between two demands loca-

tion. In Figure 4c, we can observe that the FCFS

heuristic requires very short computation times, even

for the very large instances involving more than 100

requests. On the other hand, the computation times

for the GA explodes for instances involving more

than 100 requests, and we couldn’t get any solu-

tion with this heuristic for instances involving 200 or

more requests. With the NN heuristic, we obtain so-

lutions for all the instances in our data set, but the

computation times remain long for the following in-

stances: “instance500 5”, “instance500 10”, and

“instance1000 15‘”.

To improve the performance of the NN heuristic,

in terms of computation times, we relied on the work

(a) Objective value.

(b) Non-proﬁtable trips.

Figure 4: Comparison of the FCFS with the NN heuristic

on the basis of three performance indicators.

of (Mocnik, 2020). The latter proposes to decom-

pose the space where demands are located into sev-

eral zones, as illustrated in Figure 5. Then, searching

in the current taxi zone for the next neighboring. If no

neighbor is found in the zone, our algorithm extends

the search to the global zone. The author proves that,

by choosing a suitable zone size, the complexity of

the algorithm can be reduced.

We implemented this zone decomposition in our

ECTA 2022 - 14th International Conference on Evolutionary Computation Theory and Applications

Demand space

Figure 5: Illustration of the decomposition of the space of

requests into 25 zones: the blue dots represent the demands,

and the red numbers represent the zones.

NN algorithm using different number of zones: 4, 6,

9, 15, and 20. Figure 6 shows the new computation

times of our algorithm with this decomposition. In

Figure 6, the curve in red color represents the compu-

tation times when considering only one zone (space

of demand). The remaining curves (shades of blue)

show the results for different number of zones, rang-

ing from 4 to 20. It can be seen in this ﬁgure that the

computation times are signiﬁcantly reduced for the

improved NN heuristic (blue curves), compared to the

naive NN (red curve), for the three above-mentioned

large instances. In particular, for the instance named

“instance1000 15”, the computation times were di-

vided by three in the improved NN with 20 zones.

Figure 6: Computation times of the improved NN heuristic.

Effect of the Window Length

In the previous tests, the rolling-window length was

chosen to be 60 minutes. In this study, we test dif-

ferent values for this parameter in order to choose an

appropriate value for it. These tests are performed on

the FCFS and the improved NN heuristics. For the

rolling window length, ten values are chosen in our

study: 10, 30, 90, 180, 240, 360, 480, 720, 840, and

1440. The latter value correspond to the scheduling

horizon of one day. We perform the tests on our 10

generated instances from Table 2, and the results are

averaged over these tests. In Figure 7, the relation-

ship between the length of the rolling window and

our three performance indicators is plotted, for each

scheduling heuristic.

(a) Objective-value.

(b) Non-proﬁtable trips.

Figure 7: Effect of the window length on the performance

indicators.

First, we observe that the value of our per-

formance indicators (objective value, non-proﬁtable

trips, and CPU time) decreases with increasing val-

ues of the windows length. In particular, the CPU

of the improved NN heuristic drastically decreases in

the interval [10, 180] (Figure 7c). Results in Figure 7

suggest that a window length in the interval [90, 180]

can be a good compromise between the quality of the

solutions – in terms of the objective-value and the du-

ration of the non-proﬁtable trips – and the CPU time.

A Rolling Horizon Approach for the Dynamic Scheduling of Flying Taxis

5 CONCLUSION AND

PERSPECTIVES

In this paper, we consider the problem of the dynamic

scheduling of ﬂying taxis. In this context, all or some

problem parameters are unknown in the considered

scheduling horizon. We propose a rolling-horizon ap-

proach, coupled with some heuristics from the litera-

ture to solve the dynamic case. The heuristics are: the

First-Come, First-Served (FCFS), the Nearest Neigh-

bor (NN), and the Genetic Algorithm (GA).

We conduct several computational experiments to

compare the FCFS and the NN heuristics with the ge-

netic algorithm. Results suggest that the FCFS is a

good alternative to the GA, because it obtains com-

petitive results and has very short computation times.

Moreover, the computation times of the NN heuristic

are improved by integrating the decomposition pro-

posed in (Mocnik, 2020). The GA is efﬁcient to solve

small and medium instances, involving less than 80

demands. However, for the large instances, this algo-

rithm requires very long computation times, making

it unsuitable for a real-time application.

For future studies, we will allow taxis to serve

multiple requests in one trip, because serving one

client at a time may not be very proﬁtable for the taxi

company. We will also construct additional perfor-

mance measures that could express better the proﬁt

obtained from the ﬂying taxi trips.

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ECTA 2022 - 14th International Conference on Evolutionary Computation Theory and Applications

APPENDIX: ACRONYMS

Table 3: Table of acronyms.

Acronym Meaning

JSSP Job-Shop Scheduling Problem

RH Rolling Horizon

UAM Urban Air Mobility

UAV Unmanned Aerial Vehicle

VRP Vehicle Routing Problem

A Rolling Horizon Approach for the Dynamic Scheduling of Flying Taxis