Variety-aware Routing Encoding for Efﬁcient Design Space Exploration

of Automotive Communication Networks

Fedor Smirnov

, Behnaz Pourmohseni

, Michael Glaß

and J¨urgen Teich

Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg (FAU), Erlangen, Germany

Ulm University, Ulm, Germany

Keywords:

DSE, Network Optimization, Automotive Networks.

Abstract:

The introduction of sophisticated ADAS has given rise to larger and more complex automotive communica-

tion networks whose efﬁcient (in effort) and optimal (in quality) design necessarily depends on automated

network design techniques. Typically, these techniques either (a) optimize communication routes based on

topology-independent constraint systems that encode the inclusion of each network component in the route of

a message or (b) depend on a time- and memory-expensive enumeration of all possible transmission routes

to identify the optimal route. In this paper, we propose a novel approach which combines the advantages of

these two strategies to enable an efﬁcient exploration of the routing search space: First, the given network is

preprocessed to identify so-called proxy areas in which each pair of nodes can be connected by exactly one

route. Contrary to network areas with a variety of different routing possibilities, proxy areas do not offer any

room for optimization. We propose two approaches—both integrable into existing constraint systems—which

exploit the knowledge gathered on proxy areas to improve the exploration efﬁciency during the routing opti-

mization process. Experimental results for two mainstream topologies of automotive networks give evidence

that, compared to state-of-the-art routing optimization approaches, the proposed approaches (a) offer an ex-

ploration speedup of up to ×185, (b) deliver network designs of equal or higher quality, and (c) enable an

automated design of signiﬁcantly larger automotive systems.

1 INTRODUCTION

In recent years, a tremendous number of innovations

have been developed in automotive electronics. New

infotainment and driver assistance features introduce

a high demand of both computation and communica-

tion power and cause a rapid growth in the number of

electronic control units (ECUs) installed in a vehicle,

and, subsequently, an immense rise in the size and

complexity of automotive communication networks.

Indeed, modern automotive wiring harnesses feature

roughly 23kg in weight and 1.2 km in length (Interna-

tional Cablemakers Federation, 2015) which signiﬁ-

cantly contributes to the overall weight and the mon-

etary cost of the vehicle. At the same time, the distri-

bution of safety-critical applications, e.g., airbag con-

trol or driver assistance, across multiple logically and

physically separated ECUs necessitates the underly-

ing communication network (interconnecting those

ECUs) to be regarded as safety-critical as well. As a

consequence, each design decision related to the com-

munication network must be evaluated with respect to

many, oftentimes conﬂicting, design objectives such

as monetary cost, weight, transmission timing, and

transmission reliability, which renders the manual de-

sign of these networks impractical, if at all feasible.

Compared to a manual design, approaches for de-

sign automationoffer an interesting opportunityto ad-

dress this challenge, as they reduce design errors and

offer design solutions of higher quality (Sangiovanni-

Vincentelli and Di Natale, 2007). Consequently, de-

sign automation has become an area receiving great

attention from the scientiﬁc community. As ﬁnding

the optimal network design is an NP-hard problem,

an enumeration of all possible combinations of de-

sign decisions is computationally infeasible, except

for very small problem sizes. Furthermore, especially

in case of complex communication networks, many

possible combinations of design decisions result in

infeasible solutions, e.g., a network design lacking

transmission routes between senders and receivers.

To cope with this problem, most design automation

approaches rely on constraint sets that describe con-

ditions that must be satisﬁed for a network design to

242

Smirnov, F., Pourmohseni, B., Glaß, M. and Teich, J.

Variety-aware Routing Encoding for Efﬁcient Design Space Exploration of Automotive Communication Networks.

DOI: 10.5220/0007797802420253

In Proceedings of the 5th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2019), pages 242-253

ISBN: 978-989-758-374-2

be valid, e.g., constraints to enforce that a valid net-

work contains a transmission path between the sender

and the receiver(s) of each communication. The re-

solution of the constraint set, i.e., ﬁnding an assign-

ment of the design decision variables that satisﬁes

all constraints, is then either used as the main opti-

mization mechanism (Neubauer et al., 2018) or as a

repair mechanism (to repair infeasible designs into

valid ones) as part of a dedicated optimizer, e.g., an

evolutionary algorithm (Lukasiewycz et al., 2007).

In the embedded domain, the system design prob-

lem, i.e., the implementation of an application on a

given network architecture, is typically represented

by a set of constraints that encode a valid binding of

the application’s tasks onto the network’s resources, a

valid allocation of the required resources, and a valid

routing of messages that are transmitted between re-

sources executing data-dependenttasks (Blickle et al.,

1998). The computational effort for the generation

and the resolution of these constraints typically scales

exponentially with the number of encoded decision

variables and has an immense impact on the efﬁ-

ciency and even the feasibility of the overall opti-

mization (Richthammer and Glaß, 2018). Except for

the most trivial network topologies, the routing con-

straints constitute the most complex part of the con-

straint set and introduce the largest share of encoded

decision variables.

The majority of state-of-the-art routing encoding

approaches fall into one of the following two classes:

(a) so-called route preprocessing (RP) approaches

which rely on a preprocessing phase to ﬁnd all pos-

sible routes connecting each pair of nodes (Laursen

et al., 2016; Gavrilut et al., 2017). During the op-

timization, a message is then routed by selecting

one of the preprocessed routes that connect the mes-

sage’s source to its destination. Alternatively, (b) so-

called componential assembly (CA) approaches en-

code an activation variable that represents the in-

clusion of each network component—e.g., a link or

a node—into the route of each message and for-

mulate constraints to ensure the assembly of valid

routes (Al Sheikh et al., 2013; Nayak et al., 2016;

Schweissguth et al., 2017; Mahfouzi et al., 2018).

The resolution of these constraints provides an as-

signment of the activation variables based on which a

valid route is constructed by assembling the activated

components.

As shown in (Graf et al., 2014), the strengths and

weaknesses of RP and CA approaches are somewhat

complimentary. CA approaches encode the usage

of each network component per message, regardless

of the network topology. This not only introduces

a high number of encoding variables—especially in

case of complex routing behaviors like multicasts

(Lukasiewycz et al., 2014) or redundant transmissions

(Smirnov et al., 2018b)—but also results in an unne-

cessarily complex description of the routing optimiza-

tion search space. RP approaches, on the other hand,

use the preprocessing phase to acquire total knowled-

ge on the network topology and provide the optimizer

with a compact description of the actual search space.

However, their need for an enumeration of all routing

possibilities limits the applicability of RP approaches

to sparsely-connected network topologies where the

number of possible routes is small, even if the net-

work itself is not small. For densely-connected net-

work topologies, the encoding overhead of CA ap-

proaches is more than compensated by their superior

scalability. Furthermore, the ﬁne-grained encoding of

routing decisions in CA approaches not only enables

the formulation of additional constraints, e.g., to re-

spect link capacity or the mutual exclusion of compo-

nents, but also results in a much better performance

when optimizing objectives which are strongly inﬂu-

enced by individual components of the routes, for in-

stance, monetary cost or reliability (Smirnov et al.,

2018b).

Contribution: Real-life communication net-

works rarely completely fall into one of the two ex-

treme connectivity categories listed above (dense or

sparse), but rather constitute a connection of several

subnetworks, each being either sparse or dense. This

holds particularly true for automotive networks: On

the one hand, safety-critical ADAS applications make

a certain degree of transmission redundancy manda-

tory. On the other hand, the high cost pressure and the

necessity to reuse network designs from previous car

generations prohibit the free practice of redundancy at

every possible point. Rather than that, it seems more

likely that redundancy is considered only for the most

critical components, e.g., links which are especially

vulnerable or important. This redundancy scheme re-

sults in network topologies in which several sparsely-

connected subnetworks are connected with each other

via densely-connected network regions.

CA and RP approaches excel when processing ei-

ther densely- or sparsely-connected networks, respec-

tively. They, however, suffer in efﬁciency or practica-

bility when applied to the compound network topolo-

gies described above. In this paper, we introduce an

optimization approach that combines the strengths of

these two strategies and proves effective for such net-

works. In the proposed approach, the given network

is partitioned into network areas of one of the two fol-

lowing types: (a) proxy areas which offer exactly one

routing possibility between each pair of nodes con-

tained within them and (b) areas with a variety of dif-

Variety-aware Routing Encoding for Efﬁcient Design Space Exploration of Automotive Communication Networks

243

III

Variety Area

Proxy Area

Figure 1: Resource network consisting of a variety area (yellow/left) and a proxy area (green/right). All differences between

the routes connecting ECU E

to ECU E

(I, II, and III) occur within the variety area.

ferent routing possibilities between each node pair,

the so-called variety areas. The proposed approach

alleviates the optimization’s computational overhead

by exploiting the fact that—since any potential for

routing optimization is based on a variety of differ-

ent routing options—excluding proxy areas from the

optimization does not limit the search space, as any

valid route can be unambiguously described by speci-

fying its route segments within the variety areas.

We exemplify this for the simple network in Fig. 1

consisting of one variety area (yellow, left) and one

proxy area (green, right). For a communication be-

tween ECU E

and ECU E

, the architecture offers

three distinct routes (I, II, and III) which differ from

each other only in their respective segment in the vari-

ety area and are identical within the proxy area. Each

and every route between E

and E

can, therefore, be

uniquely speciﬁed by its route segment in the variety

area (the segment between E

and S

As part of our contribution, we (a) present a

lightweight algorithm that identiﬁes proxy and vari-

ety areas of the given network, and (b) propose two

approaches to integrate the proxy concept into any

existing CA route optimization approach. The hereby

obtained encoding of the routing search space is tai-

lored to the given network topology, combines the ef-

ﬁciency of RP route optimization approaches with the

scalability and extensibility of CA approaches, and

can be applied to any application and any network.

Experimental results for two mainstream topologies

of automotive networks give evidence that an opti-

mization based on the proxy concept is faster by up to

two orders of magnitude, yields optimization results

of equal or higher quality compared to state-of-the-

art route optimization approaches, and, consequently,

enables an automated design optimization of systems

which are signiﬁcantly larger than what existing ap-

proaches can practicably optimize.

The remainder of this paper is outlined as follows:

Section 2 provides an overview of the related work.

The system model is presented in Section 3. Section

4 details the proxy concept and shows how it is in-

tegrated into existing encoding approaches. Experi-

mental results are presented in Section 5, while Sec-

tion 6 concludes the paper.

2 RELATED WORK

A large body of research exists on the optimization

of routings during the design of embedded systems.

An introduction to the general problem and the dif-

ferent routing algorithms is given in (Wang and Hou,

2000). The authors of (Graf et al., 2014) provide a de-

tailed performance comparison between RP and CA

approaches and show that RP approaches can outper-

form CA approaches in sufﬁciently sparse networks.

Yet, in general, RP approaches are not considered to

be a good practice, as enumerating all routing pos-

sibilities is an NP-hard problem. To overcome the

scalability problem, RP approaches often limit the

search space. For instance, authors of (Laursen et al.,

2016) consider only the K shortest routes while the

RP heuristic presented in (Gavrilut et al., 2017) is tar-

geted at reusing the already allocated links.

The majority of existing routing optimization ap-

proaches can be viewed as CA approaches. A link-

based encoding for AFDX routings is presented in

(Al Sheikh et al., 2013). The authors of (Lukasiewycz

et al., 2009) go a step further and present a constraint

set where the routing is optimized together with the

mapping and the allocation of an embedded system.

Indeed, the easy modiﬁcation to certain design goals

is an additional advantage of CA approaches. For

example, several works present constraint sets for a

joint optimization of routing and transmission sched-

ule (Nayak et al., 2016; Schweissguth et al., 2017;

Smirnov et al., 2017; Mahfouzi et al., 2018) or even

the optimization of the VLAN partitioning of an au-

tomotive network (Smirnov et al., 2018a). Yet, to the

best of our knowledge, existing CA approaches for-

mulate the constraints regardless of the topology. In

this paper, we show how each of these approaches can

be improved by restricting the exploration to the areas

which actually offer room for routing optimization.

VEHITS 2019 - 5th International Conference on Vehicle Technology and Intelligent Transport Systems

244

Figure 2: Illustrative example of a speciﬁcation.

3 SYSTEM MODEL

The strategies presented in this paper can be applied

to any routing optimization approach relying on a

CA routing encoding. Without loss of generality,

we use the system model presented in (Lukasiewycz

et al., 2014) for the explanations throughoutthe paper.

There, the entire search space of the design problem at

hand is modeled by the so-called speciﬁcation. Each

valid problem solution that is generated based on the

speciﬁcation is referred to as an implementation.

3.1 Speciﬁcation

The speciﬁcation contains the architecture graph, the

application graph, and the mapping edges in-between.

Architecture Graph. The architecture graph

, E

) consists of resource nodes N

= N

∪

, connected by bidirectional link edges l ∈ E

where each resource is either an ECU E ∈ N

or a

switch S ∈ N

Application Graph. The application graph

, E

) contains task nodes N

= N

∪ N

and

data dependencies E

, where each task is either a pro-

cess P ∈ N

or a message C ∈ N

. Each data de-

pendency is a directed edge between a message and a

process. We refer to the predecessor and the succes-

sor tasks of a message as the source and destination

tasks of the message, respectively.

Mapping Edges. Each mapping edge

m = (P, E) ∈ E

indicates an ECU E ∈ N

which process P ∈ N

can be implemented.

Example. An example of a speciﬁcation graph is

illustrated in Fig. 2. The application graph G

(left)

consists of three process tasks P

, P

, and P

which

have a data dependency, represented by their connec-

tion to the message task C

via dependency edges d

, and d

. The architecture graph G

on the right

side of the ﬁgure represents a switched ECU network

and consists of three ECUs E

, E

, and E

, connected

Figure 3: An example of an implementation that can be ge-

nerated from the speciﬁcation in Fig. 2.

by switches S

and S

and links l

–l

. The four map-

ping edges m

–m

show that P

and P

can only be

implemented on E

and E

, respectively, while P

can

be implemented on both E

and E

3.2 Implementation

An implementation represents a valid solution of the

design problem and is derived from the speciﬁcation

through a set of allocation, binding, and routing deci-

sions.

Allocation. During the allocation, a subset of the

architecture graph G

is chosen to form the allocated

architecture graph. In a valid design, only those re-

sources are allocated which are used to execute pro-

cesses or transmit messages.

Binding. The binding of processes to ECUs is

performed by choosing exactly one mapping edge

for each process. This edge then identiﬁes the ECU

where the process is executed in the implementation,

the so-called binding target of the process.

Routing. In the implementation, the route of

each message C ∈ N

is represented by the routing

graph

−→

(C), a directed acyclic subgraph of G

with directed links. Each routing graph starts at the

binding target of the source task of its message and

has the binding target(s) of the destination task(s) as

leaf(/ves), hereby fulﬁlling the data dependencies.

Example. Figure 3 illustrates an example imple-

mentation that can be generated based on the speciﬁ-

cation in Fig. 2. There, process P

is bound on ECU

, while processes P

and P

are bound on ECU E

The data dependencies between the sender process P

and its receivers P

and P

are satisﬁed by routing the

message C

from ECU E

to ECU E

over the route

consisting of links l

, l

, and l

and switches S

and

. In this case, ECU E

and links l

and l

are not

used to execute processes or route messages and are,

therefore, not allocated as part of the implementation.

Variety-aware Routing Encoding for Efﬁcient Design Space Exploration of Automotive Communication Networks

245

a) Initialization

b) Iteration 1

c) Iteration 2

d) Iteration 3

: Variance Area

: Proxy Areas

Figure 4: The proxy areas (dashed) are identiﬁed by iteratively establishing transitive proxy relations between resource pairs.

The variety area (dotted) encompasses all proxy masters (blue glow) and is reduced in each iteration.

4 VARIETY-AWARE ROUTING

ENCODING

4.1 Proxy Relations and Proxy Areas

CA routing optimization approaches encode, for each

link and each message, a decision variable to reﬂect

whether the link is used in the route of the message.

While this strategy ensures that no route is excluded

from the search space, it introduces unnecessary en-

coding variables for most networks. Consider, e.g.,

in Fig. 4a. This link connects ECU E

to the rest

of the network via switch S

. Since E

is accessible

solely through l

, one can conclude that l

is neces-

sarily used in each and every route to/from E

. Thus,

encoding a decision variable for the inclusion of l

in routes to/from E

provides no added optimization

value, as each route starting/ending at E

(referred to

as a proxy slave) can be uniquely speciﬁed using a

corresponding route starting/ending at S

(referred to

as the proxy master of E

Extending the concept of proxy (master/slave) re-

lations to larger network areas provides an even more

compact routing encoding. Consider, e.g., ECUs

–E

and switches S

, S

, and S

in Fig. 4d. In the

terminology used in this paper, we summarize these

resources and the links between them as a so-called

proxy area with S

as the proxy master of the entire

area. Between each pair of resources within a proxy

area, there exists exactly one possible route. In par-

ticular, there is exactly one possible route between

any of these resources and S

, the proxy master of

the area. Consequently, any connection between a re-

source outside the proxy area and a resource within

the area consists of an external route that connects the

outside resource to the proxy master and an internal

route connecting the proxy master to the proxy slave

inside the proxy area. Hereby, only the external route

can be established in multiple different ways (using

different sets of links) and is, therefore, relevant for

routing optimization. Contrary to that, there is only

one possible way to create the internal route. Links

within proxy areas, therefore, provide no beneﬁt for

routing optimization and can be excluded from the

routing encoding.

4.2 Identiﬁcation of Proxy Areas

We identify proxy areas within a given network us-

ing an iterative algorithm. This algorithm generates

a map of resources to their respective proxy masters

(where a proxy master is mapped to itself).

Initially, every resource is registered into a list of

potential masters. Over the course of several itera-

tions, the algorithm (I) examines every resource in the

list, (II) identiﬁes proxy slaves (resources with only

one neighbor denoted as master), (III) updates their

map entry with their sole neighbor as their proxy mas-

ter, and (IV) eliminates them from the list of masters.

Proxy relations are transitive. Thus, if R is identiﬁed

as master of

R, R automatically becomes the master

of all slave resources of

R. The algorithm terminates

when no new proxy slaves are identiﬁed during an ite-

ration.

Figure 4 illustrates the functionality of the algo-

rithm. Each subsequent iteration identiﬁes new proxy

slaves, expands the known proxy areas and shrinks the

variety area. The algorithm terminates when no new

proxy slaves are found in the fourth iteration. Except

from the proxy masters E

and S

–S

, which form the

variety area of the network, all resources are then lo-

cated inside proxy areas.

4.3 Adaptation of Existing Constraint

Systems

Exploiting the concept of proxy relations reduces the

number of encoding variables and improves the opti-

mization efﬁciency by excluding network areas with-

out routing variety. Following the steps presented in

this subsection, this concept can be integrated into

any routing optimization approach based on the en-

coding of individual network components. We ﬁrst

detail how existing constraint sets can be adapted to

only encode route segments within variety areas. The

second part of this subsection then proposes two ap-

VEHITS 2019 - 5th International Conference on Vehicle Technology and Intelligent Transport Systems

246

proaches to create the internal routes within proxy ar-

eas.

4.3.1 Routing Encoding in Variety Areas

CA encodings built on the assumption of ﬁx source

and destination resources that are known prior to the

constraint formulation, e.g., (Al Sheikh et al., 2013)

or (Mahfouzi et al., 2018), do not require any adap-

tation of the constraints. The impact area of these

encodings can be limited by using the proxy mas-

ters over which the message enters/leaves the vari-

ety area—instead of the proxy slaves actually send-

ing/receiving the message—as the start/end points of

the encoded route.

Approaches where the source and the destination

of the message transmission are not known during the

constraint formulation—such as (Lukasiewycz et al.,

2014) or (Smirnov et al., 2018b), in which routing and

task mapping are optimized jointly—require an adap-

tation of the constraints. Such approaches implicitly

encode the transmission end points of a message as

the binding targets of the source/destination tasks of

that message. For these cases, we propose to encode

variables that indicate the start and the end points of

the encoded route within variety areas as follows.

We introduce variables

and

to encode the

end points of a route within the variety area. Vari-

able

reﬂects that resource R is the route start point

of message C in the variety area. Similarly, variable

reﬂects that resource R is the route end point of

message C in the variety area. We introduce new con-

straints to encode the activation of

and

accor-

ding to the binding of the source/destination tasks of

C and the proxy relations computed by the algorithm

presented in Section 4.2. The constraints state that

a proxy master R is the route start point for message

C (thus,

= 1) if the source task of C is bound ei-

ther onto R or onto one of its proxy slaves and is not

the start point (thus,

= 0) otherwise, encoded by

constraints (1) and (2), respectively. The constraints

that encode the activation of

are generated anal-

ogously. Given these variables, existing routing en-

codings can be adapted by inserting these end-point

variables into any routing constraint that relates to the

start or the end point of the route of the respective

message.

∀C ∈ N

P ∈ N

−

(C),

R ∈ N

, em = (

R) ∈

, R = M (

R) ∈ N

emem

em−

≤ 0 (1)

− (

∑

emem

em) ≤ 0 (2)

In the formulation above, N

−

note predecessor and successor tasks of message C,

respectively. N

designates all proxy masters. Func-

tion M : N

→N

returns the proxy master of a re-

source, as determined by the algorithm from Section

4.2. Throughout this paper, all encoding variables

are differentiated from the components of the system

model (detailed in Section 3) by a bold font. For ex-

ample,

m denotes the encoding variable that is set to

1 iff mapping m is activated.

4.3.2 Route Creation in Proxy Areas

We propose two different approaches to create the

routes within proxy areas.

Exclusive Approach. In the ﬁrst approach, referred

to as the exclusive approach, proxy areas are not

considered in the encoding of routing constraints.

Therefore, the resolution of the routing constraints—

adapted as detailed in Section 4.3.1—yields only the

route segments that connect the proxy masters of

the network (within variety areas). Then, in a post-

processing step, we extend the yielded route segments

with the unique internal routes (within the proxy ar-

eas) that connect proxy masters to the actual source

and destination resources to construct the complete

message route, which is used for the evaluation of de-

sign objectives such as cost, timing, or reliability.

Compact Approach. The exclusive approach of-

fers the biggest reduction of encoding variables and

the maximal optimization speedup. For certain prob-

lems, however, ignoring proxy areas may reduce the

optimization effectiveness, as it limits the ability to

formulate additional constraints regarding, e.g., the

capacity of the links within these parts of the network.

We address these cases with a second approach for

the creation of route segments within proxy areas. In

this so-called compact approach, the activation of in-

ternal links is encoded with a constraint set tailored

to the conditions found within proxy areas. By ex-

ploiting the fact that neither routing cycles nor redun-

dant route segments are possible within proxy areas,

the compact approach requires only a small number

of constraints that are formulated based on—already

existing—variables that describe task mapping and

component activation.

The compact approach is implemented by formu-

lating constraints (3)–(6) for each resource within a

proxy area. They ensure that the source process of a

message may only be mapped onto a resource inside

a proxy area if the resource is the binding target of a

Variety-aware Routing Encoding for Efﬁcient Design Space Exploration of Automotive Communication Networks

247

destination process or has at least one activated out-

link (3). An in-link of a resource may only be active

if the resource is the binding target of a destination

process or has at least one activated out-link (5). Ana-

logous constraints apply to the binding of destination

processes (4) and the activation of out-links (6). Note

that these constraints are formulated with the assump-

tion of routing optimizations like (Lukasiewycz et al.,

2014) or (Smirnov et al., 2018b), where the end points

of the routes are not ﬁxed

∀C ∈ N

, P ∈ N

(C),

P ∈ N

−

(C), m = (P, R) ∈

, em = (

P, R) ∈ E

, l = (R,

R) ∈ E

emem

em−



(

∑

m) + (

∑

l=(R,

)



≤ 0 (3)

∀C ∈ N

, P ∈ N

(C),

P ∈ N

−

(C), m = (P, R) ∈

, em = (

P, R) ∈ E

l = (

R, R) ∈ E

m−



(

∑

emem

em) + (

∑

l=(

R,R)

)



≤ 0 (4)

∀C ∈ N

, P ∈ N

(C), m = (P, R) ∈ E

l = (

R, R) ∈

, l = (R,

R) ∈ E

l=(

R,R)

−



(

∑

m) + (

∑

l=(R,

)



≤ 0 (5)

∀C ∈ N

P ∈ N

−

(C), em = (

P, R) ∈ E

l = (

R, R) ∈

, l = (R,

R) ∈ E

l=(R,

−



(

∑

emem

em) + (

∑

l=(

R,R)

)



≤ 0 (6)

5 EXPERIMENTS

We perform several experiments to evaluate the im-

pact of routing-variety awareness on the scalability

and the result quality of multi-objective routing opti-

mization approaches for two common classes of auto-

motivenetworks, namely, double-star and many-core.

In all experiments, we investigate how the scalability

and the result quality of a variety-unaware baseline

routing encoding approach is enhanced when it is ex-

tended with the exclusive or the compact implementa-

tions of the proxy concept presented in Section 4.3.2.

To evaluate the overall quality of the Pareto-

optimal system design solutions found during the op-

timization process under each investigated encoding

approach, we use the well-established ε-dominance

The constraint adaptation for the simpler case with

known route end points ((Al Sheikh et al., 2013), (Mahfouzi

et al., 2018)) is trivial and, therefore, not discussed here.

indicator (Laumanns et al., 2002) from the multi-

objective optimization domain. Broadly speaking,

this scalar measure reﬂects the distance in the multi-

dimensional objective space between a reference set

of high-quality solutions and the set of Pareto-optimal

solutions found by the evaluated approach. Thus,

for two solution sets, A and B, obtained using two

optimization approaches, the one with a lower ε-

dominance exhibits a smaller distance from the ref-

erence set, and thus, a higher quality of obtained so-

lutions. For all experiments presented in this sec-

tion, the reference set is a collection of the best solu-

tions found throughout the optimization processes of

all approaches. We plot the ε-dominance of each in-

vestigated approach versus the optimization run time.

This enables a compact representation and compari-

son of optimization speed, optimization convergence,

preprocessing time overhead, and the time required

for the constraint resolution throughout the optimiza-

tion process of each investigated approach.

We use the OPENDSE (Reimann et al., 2018)

system design optimization framework in all experi-

ments. It employs the SAT-Decoding system synthe-

sis approach (Lukasiewycz et al., 2007) which uses

the SAT4J (Le Berre and Parrain, 2010) constraint

solver and implements the broadly-used NSGA-II

(Deb et al., 2002) multi-objective genetic algorithm

to control the solution strategy used by SAT4J. Both

SAT4J and NSGA-II are integrated into the OPT4J

(Lukasiewycz et al., 2011) optimization framework

which is used by OPENDSE. Each optimization run

comprises 1, 000 generations. In each generation, 25

new solutions are generated using genetic operations

(crossover and mutation) on the previously found so-

lutions, and the population of solutions found so far

is updated accordingly. We consider a population size

of 100 solutions.

5.1 Double-star Architecture

In out ﬁrst case study, we consider a safety-critical

application and double-star network topologies. The

message routing is optimized with respect to two de-

sign objectives, namely transmission reliability and

number of allocated links

. The application tasks

exchange a total number of 64 safety-critical mes-

sages, which are transmitted in both uni- and multi-

cast fashions. Figure 6 illustrates an exemplary 24-

ECU double-star network topology composed of two

12-ECU stars. The two stars are connected over two

communication hops, with the possibility for redun-

dant transmission between the two stars. Within each

This case study is inspired by a similar case study in-

vestigated in (Smirnov et al., 2018b).

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248

0 100 200 300

0.2

0.4

0.6

0.8

Run time [s]

ε-dominance

8 ECUs

baseline

compact

exclusive

0 200 400

600

0.2

0.4

0.6

Run time [s]

24 ECUs

baseline

compact

exclusive

0 200 400

600

800

0.2

0.4

0.6

Run time [s]

40 ECUs

baseline

compact

exclusive

500

1,000

0.2

0.4

0.6

0.8

Run time [s]

56 ECUs

baseline

compact

exclusive

Figure 5: Average ε-dominance of 40 optimization runs for the double-star case study. Exploiting proxy areas results in an

optimization speedup that scales with the network size.

Figure 6: Exemplary double-star network topology with 24

ECUs connected by 3 switches.

star, the connection between each ECU and its imme-

diate switch offers no redundancy, so that each star

can be regarded as one proxy area.

For this experiment, we implemented the routing

encoding presented by the authors of (Smirnov et al.,

2018b). This encoding is used as the baseline routing

optimization approach. To implement the proposed

approaches, we reﬁne the baseline encoding by iden-

tifying proxy areas of the network and implementing

the compact and the exclusive encoding approaches

detailed in Section 4. For each optimization approach,

we perform 40 optimization runs.

The experimental results presented in the follow-

ing are an average among the 40 optimization runs for

each approach. Figure 5 illustrates the ε-dominance

of the investigated routing optimization approaches

(baseline, compact, and exclusive) versus their opti-

mization run time for four double-star networks com-

posed of different numbers of ECUs (8, 24, 40, and

56), equally distributed between the two stars.

In terms of result quality, all approaches perform

similarly well, indicated by their ε-dominance indices

at the end of the optimization. Here, the exclusive ap-

proach offers an average ﬁnal ε-dominance of 0.03,

and thereby, slightly outperforms the baseline and

compact approaches which offer an average ﬁnal ε-

dominance value of 0.052 and 0.053, respectively.

In terms of optimization run time, however, the

variety-aware approaches, i.e., compact and exclu-

sive, offer a signiﬁcant optimization speedup which

scales with the complexity of the problem. Recall

that the baseline approach encodes the activation of

every individual link in the network, even though a

big part of the network is contained within the two

proxy areas (stars) which do not offer any routing

100

150

200

250

300

Message Number

Generation time [min]

baseline

compact

exclusive

Figure 7: Excluding proxy areas from the optimization de-

cision space signiﬁcantly reduces the constraint generation

time. For a ﬁxed time budget (horizontal cut in the plot),

the exclusive approach enables the optimization of conside-

rably larger systems.

variety. The exclusion of proxy areas from the rou-

ting encoding signiﬁcantly reduces the number of en-

coded decision variables, see Table 1. As a result,

the baseline approach requires more time (a) for con-

straint formulation and preprocessing which is visi-

ble as the initial run time offset in the plots in Fig. 5

and (b) for the constraint resolution which results in a

higher overall run time. A comparison among the four

plots in Fig. 5 also revealsthat these time overheads—

just like the number of the encoded variables—scale

with the problem complexity. Note that the time re-

quired for the identiﬁcation of proxy areas for the

variety-aware approaches is negligible in comparison

to the time taken for constraint formulation, which is

reﬂected by the nearly identical run time of all ap-

proaches for the smallest network. All in all, the pro-

posed variety-aware approaches, compact and exclu-

Table 1: Number of the encoding variables for 64 messages

in different double-star topologies.

ECU Number

Variable Count

baseline exclusive

8 2, 988 2, 453

24 8, 088 3, 658

40 14, 831 4, 092

56 24, 199 4, 526

Variety-aware Routing Encoding for Efﬁcient Design Space Exploration of Automotive Communication Networks

249

sive, signiﬁcantly outperform the baseline approach,

as they offer results of similar quality at a smaller

optimization run time. Here, the compact approach

offers an optimization speedup of up to ×1.26 (and

requires 21% of the time needed by the baseline ap-

proach) with an average of ×1.14 (12%) over the four

networks, while the exclusive approach achieves an

speedup of up to ×3.06 (67 %) with an average of

×2.04 (43%).

To further investigate the scalability of the pro-

posed approaches, we measured the time required for

the generation of the routing constraints for the exem-

plary 24-ECU double-star topology depicted in Fig. 6

for different numbers of messages. The results are

illustrated in Fig. 7. Since routing constraints are ge-

nerated at design time, the time required for their ge-

neration is not subject to any hard restrictions. How-

ever, the constraint generation time scales exponen-

tially with the number of variables and may quickly

render an approach impractical. Indeed, with the

ongoing growth in the size of automotive networks

and the number of transmitted messages, the time re-

quired for the generation of routing constraints is pro-

gressively becoming the limiting factor for the appli-

cability of existing routing optimization approaches.

The baseline and the compact approaches are based

on the same set of variables and display similar ge-

neration times, which quickly grow with the num-

ber of messages in the system. While the exclusive

approach also displays an exponentially growing ge-

neration time, the required constraints are generated

within signiﬁcantly shorter time intervals. With a time

budget of 20 minutes, the exclusive approach, e.g.,

is able to generate constraints for systems with twice

as many messages as the other two approaches. The

exclusive approach, therefore, enables the automatic

optimization of considerably larger systems.

5.2 Many-core Architecture

Many-core architectures represent an emerging class

of architectures in the embedded computing domain

which offer the scalable computation and communi-

cation power required by modern embedded applica-

tions. A many-core architecture integrates an exten-

sive number of, oftentimes heterogeneous, processors

onto a single chip where the processors are intercon-

nected by a communication network, referred to as a

Network-on-Chip (NoC).

Over the past decade, many-core architectures

have increasingly been viewed as promising candi-

dates for emerging automotive applications, as they

offer an order of magnitude higher processing power

cost-efﬁciently and enable the implementation of the

mixed-ASIL isolation, required for ISO 26262, see,

e.g., (Fuhrman et al., 2015). The authors of (Ober-

maisser et al., 2009) propose a many-core architec-

ture which is tailored to the speciﬁc requirements in

the automotive domain. This so-called integrated au-

tomotive architecture closely resembles a tiled many-

core architecture, which integrates processor tiles

(each composed of multiple resources, e.g., proces-

sors and memories) on a chip with a 2D grid NoC

interconnection scheme and offers superior perfor-

mance scalability. A part of such an architecture is

illustrated in Fig. 9.

While these distributed heterogeneous processor

networks offer great ﬂexibility, ﬁnding the optimal

mapping of an application’s tasks onto the processors

of a tiled chip is a considerable challenge. Moreover,

recent research (Weichslgartner et al., 2014) shows

that a deterministic routing approach—such as XY-

routing, which is commonly used in the many-core

domain—may render numerous system design solu-

tions infeasible due to the violation of link capacities,

thus, limiting the number and the quality of feasible

solutions. Exploring the space of routing possibili-

ties may, therefore, signiﬁcantly increase the quality

of found solutions.

In our next case study, we investigate the impact

of the proposed approaches on the efﬁciency and sca-

lability of routing optimization in many-core automo-

tive systems. In order to optimize the non-redundant

message routes, we have implemented the approach

presented in (Lukasiewycz et al., 2014) which we

consider as the baseline routing optimization ap-

proach. We extend the baseline with the proposed

compact and exclusive variety-aware strategies which

are then compared against the baseline approach.

The goal of our system synthesis optimization is

to ﬁnd implementations of an automotive application

with 21 messages provided by the Embedded System

Synthesis Benchmarks Suite (E3S) (Dick, 2010) on

3×3- and 4×4-tiled many-core architectures, which

are optimal with respect to two design objectives,

namely energy consumption and makespan. For both

architecture sizes (3×3 and 4×4), the bandwidth of

each inter-tile link is quantized into 5 (hard) or 10

(relaxed) equal budgets, hereafter referred to as link

capacity, that can be utilized by the routed messages.

We use additional constraints to ensure that the band-

width capacity of each link is strictly respected. Since

the exclusive approach disregards links within proxy

areas, we use an additional evaluator—namely, link

capacity evaluator—to check the feasibility of found

design solutions in terms of respecting link capacities

inside proxy areas.

Figure 8 illustrates the ε-dominance of the in-

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250

0 2,000 4,000

0.2

0.4

Run time [s]

ε-dominance

3×3 relaxed

baseline

compact

exclusive

0.5

·10

0.5

Run time [s]

3×3 hard

baseline

compact

exclusive

0 1 2 3

·10

0.2

0.4

Run time [s]

4×4 relaxed

baseline

compact

exclusive

0 1 2 3

·10

0.1

0.2

0.3

Run time [s]

4×4 hard

baseline

compact

exclusive

Figure 8: Average ε-dominance of 5 optimization runs for the many-core case study. Variety-aware approaches yield design

solutions of higher quality and offer an optimization speedup that scales with the complexity of the optimization problem.

Core

...

Tile

Memory

Network

Interface

RX TX

Core

...

Tile

Memory

Network

Interface

RX TX

Core

...

Tile

Memory

Network

Interface

RX TX

Core

...

Tile

Memory

Network

Interface

RX TX

Core

...

Tile

Memory

Network

Interface

RX TX

Core

...

Tile

Memory

Network

Interface

RX TX

Core

...

Tile

Memory

Network

Interface

RX TX

Core

...

Tile

Memory

Network

Interface

RX TX

...

Figure 9: A heterogeneous tiled many-core architecture.

vestigated routing optimization approaches (baseline,

compact, and exclusive) versus their optimization run

time, averaged over 5 optimization runs. The pro-

posed variety-aware routing optimization approaches

(compact and exclusive) outperform the baseline ap-

proach in both (a) the quality of obtained solutions

(indicated by lower ε-dominance indices at the end of

the optimization) and (b) optimization run time.

Since each processor tile can be regarded as a

proxy area, a large portion of the networks is ex-

cluded from the routing constraints of the proposed

approaches. This signiﬁcantly reduces the number of

encoding variables (see Table 2) and the time required

for constraint generation (see Fig. 10). Nonetheless,

due to the complex nature of tiled many-core architec-

tures, the complexity of the routing constraint systems

has a higher impact (compared to the sheer number of

variables) on the run time of routing optimization and

the quality of the ﬁnal solutions. Here, both the exclu-

sive approach, which completely ignores the numer-

ous proxy areas, and the compact approach, which

uses a much simpler constraint set for the routing en-

coding within proxy areas (compared to baseline), re-

quire a considerably shorter time for the constraint

resolution. Consequently, since the constraint set has

to be resolved per network design generated through-

out the exploration, the rapid constraint resolution of

the variety-aware approaches results in a reduction

of up to two orders of magnitude in the total opti-

mization run time, compared to the baseline approach.

Moreover, their simpler constraint sets make it easier

2× 2

3× 3

4× 4

5× 5

6× 6

7× 7

8× 8

9× 9

10× 10

Architecture dimensions

Generation time [min]

baseline

compact

exclusive

Figure 10: Excluding proxy areas from the formulation of

routing constraints reduces the time required for constraint

generation and enables the automatic optimization of con-

siderably larger systems.

for the optimizer to learn correlations between indi-

vidual design decisions and the design objectives, so

that both the compact and the exclusive approaches

yield solutions of signiﬁcantly higher quality com-

pared to the baseline, especially for the more complex

4×4 architecture.

On average, the baseline approach offers a ﬁnal

ε-dominance of 0.102 and is evidently outperformed

by both the compact and the exclusive approaches,

which exhibit an average ﬁnal ε-dominance of 0.067

and 0.065, respectively. Compared to the baseline,

the compact approach offers an average optimization

speedup of ×32.96. The exclusive approach offers an

even larger speedup of ×80.61 on average and a ma-

ximum speedup of ×186.4 in case of the 4×4 relaxed

architecture.

Table 2: Number of encoding variables for 21 messages in

different many-core architectures.

Architecture

Dimensions

Variable Count

baseline exclusive

2×2 4,629 984

6×6 42,397 9,888

10×10 119,135 28,040

Variety-aware Routing Encoding for Efﬁcient Design Space Exploration of Automotive Communication Networks

251

A comparison between the exclusive and the com-

pact approach offers an other interesting insight. With

a link capacity of 10 (relaxed), ﬁnding routes without

link capacity violation is relatively easy, so that the

exclusive approach can create a sufﬁciently big popu-

lation of feasible solutions and outperform the other

two approaches in both run time and result quality.

However, with a link capacity of 5 (hard), creating

feasible solutions becomes more difﬁcult. The con-

straints used in the exclusive approach cannot pre-

vent capacity violations within proxy areas, because

the links within these areas are not considered during

constraint formulation. Consequently, the exclusive

approach wastes a large share of the optimization time

creating solutions with capacity violations on links in

proxy areas, which are rejected by the capacity evalu-

ator. Contrary to that, the compact approach is aware

of every link in the architecture and offers the pos-

sibility to encode constraints that eliminate the pos-

sibility of link capacity violations in the ﬁrst place.

The compact approach, thus, explores a search space

devoid of infeasible solutions and yields optimization

results of higher quality than the exclusive approach.

6 CONCLUSIONS

In this paper, we propose a novel strategy for an auto-

mated routing optimization of automotive networks.

The proposed approach exploits the knowledge about

so-called proxy areas in a given network, i.e., regions

that do not offer any routing variety. We have pre-

sented a lightweight algorithm that identiﬁes proxy

areas in a given network, proposed two approaches to

exploit this knowledge during routing optimization,

and shown how the presented strategy can be inte-

grated into existing routing encodings. Experimen-

tal results for two types of automotive networks give

evidence that encoding approaches that are aware of

the proxy areas provide design solutions of equal or

higher quality, are up to 185 times faster, and enable

the automatic optimization of considerably larger sys-

tems than variety-unaware approaches.

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