Linked Data as Stigmergic Medium for Decentralized Coordination

Torsten Spieldenner

1,2

and Melvin Chelli

German Research Center for Artiﬁcial Intelligence (DFKI), Saarland Informatics Campus D3 2,

66123 Saarbr

ucken, Germany

Saarbr

ucken Graduate School of Computer Science, Campus E1 3, 66123 Saarbr

ucken, Germany

Keywords:

Stigmergy, Stigmergic Medium, Coordination, Multi-Agent Systems, Linked Data, Semantic Web,

Nature-inspired Algorithm.

Abstract:

Algorithms inspired by nature have gained focus in research as a solution to classic coordination and optimiza-

tion problems. A certain type of these algorithms employs principles of stigmergy: in stigmergic systems,

coordination arises from agents leaving traces of their actions in the environment, or medium, that they work

on. Other agents instinctively adapt their behavior based on the traces, by which, in the end, the fulﬁllment of

a higher goal emerges from elementary actions of many, rather than thorough planning of complex actions of a

few. Despite the perceivable uptake of stigmergic algorithms for coordination in various domains, a common

clear understanding of a suitable digital stigmergic medium is lacking. It should however be assumed that a

well-deﬁned, properly modelled, and technically sound digital medium provides a crucial basis for correct,

efﬁcient and transferable stigmergic algorithms. In this paper, we motivate read-write Linked Data as generic

medium for decentralized stigmergic coordination algorithms. We show how Linked Data fulﬁlls a set of core

requirements that we derived for stigmergic media from relevant literature, provide an application example

from the domain of digital manufacturing, and ﬁnally provide a working example algorithm for stigmergic

decentralized coordination.

1 INTRODUCTION

Coordination of tasks or resources is an ever preva-

lent topic of research in various domains, for example

in trafﬁc and public transport (Kanamori et al., 2014;

Alfeo et al., 2018), or industrial production (Schraud-

ner and Charpenay, 2020; Cicirello and Smith, 2004).

Among research that focuses on improving appli-

cation of classic AI agent-based planning and opti-

mization techniques, there is a speciﬁc trend that em-

ploys nature inspired algorithms to solve coordination

and optimization problems (Chiong, 2009; Tzane-

tos et al., 2020). A re-occurring element from this

class of algorithms is the use of concepts of stig-

mergy (Heylighen, 2015), a behavior observed, for

example, in insect swarms: In a stigmergic system,

participants of a process leave traces in their envi-

ronment that inﬂuence subsequent behavior of other

members of the swarm, such that a community be-

havior emerges that leads the swarm closer towards a

common goal. Such nature inspired algorithms have

been found a promising approach for more ﬂexible,

fault-tolerant, and scalable coordination of complex

systems in above mentioned domains (Krieger et al.,

2000; Ricci et al., 2007; Jevti

c et al., 2012; De Nicola

et al., 2020).

However, the majority of stigmergic systems in

literature are highly use-case speciﬁc, or even imple-

mentation speciﬁc. It is in particular noticeable, that

while focusing on speciﬁc algorithms and their imple-

mentations, existing work marginalizes or ignores the

importance of a proper medium. The medium is the

environment in which agents leave traces by perform-

ing actions, i.e., where stigmergic effects emerge,

and it is considered the ”the mediating function that

underlies the true power of stigmergy” (Heylighen,

2006). The question of what a proper medium con-

stitutes is particularly interesting in the world of AI

optimization and coordination, where the medium has

no tangible physical manifestation, but where agents

operate entirely in an environment that is completely

digital, while having only abstract correspondences to

real world entities.

We believe that both research and application

of stigmergic coordination algorithms can beneﬁt

greatly from a concise common understanding of a

digital stigmergic medium. This medium should be

provided by employing widely accepted open stan-

Spieldenner, T. and Chelli, M.

Linked Data as Stigmergic Medium for Decentralized Coordination.

DOI: 10.5220/0010518003470357

In Proceedings of the 16th International Conference on Software Technologies (ICSOFT 2021), pages 347-357

ISBN: 978-989-758-523-4

347

dards to be independent of speciﬁc use-cases, do-

mains, or technologies that implement the algorithm.

It should be based on a well-deﬁned, thoroughly

formalized and established foundation to allow for

soundly deﬁned, general, transferable solutions.

Such a set of standardized and well-deﬁned tools

comes from the world of the Semantic Web (Berners-

Lee et al., 2001). Based on the notion of Linked

Data (Bizer et al., 2008) and typically modeled

in terms of the Resource Description Framework

(RDF) (Lassila et al., 1998)

, the Semantic Web is

commonly promoted as a generic integration layer for

applications from various domains.

With the Internet, being the maybe largest dig-

ital medium that relies on a wide variation of stig-

mergic effects (Dipple, 2011), and being built around

technologies and principles closely related to those

of the Semantic Web, one may expect that a ma-

chine readable and writable Linked Data layer (read-

write Linked Data) in the Semantic Web may as well

provide a widely standardized, established, domain-

independent interactive medium for stigmergy-based

coordination (Dipple et al., 2013; Privat, 2012). To

this end, this paper makes the following contributions:

We derive from relevant literature a set of require-

ments towards digital media to serve as proper stig-

mergic medium; we establish read-write Linked Data

as suitable medium for stigmergic systems; and we

demonstrate the application of read-write Linked data

as stigmergic medium with an example from the do-

main of virtual manufacturing.

The remainder of the paper is structured as fol-

lows: We review relevant related literature in Sec-

tion 2. In Section 3, we recapture core concepts

of Linked Data architectures, as well as stigmergic

systems. In Section 4, we derive requirements to-

wards digital stigmergic media and discuss Linked

Data as suitable choice. We demonstrate by exam-

ple how to model a digital environment for stigmergic

coordination in Section 5, and present a prototypical

stigmergy-based coordination algorithm in 6. We dis-

cuss how by our chosen medium, the presented algo-

rithm indeed achieves beneﬁts of stigmergic systems

in Section 7, and conclude our work and provide an

outlook upon future challenges in section 8.

2 RELATED WORK

Stigmergic systems have been thoroughly described

and analyzed (Heylighen, 2015; Dipple et al., 2013),

RDF 1.1 Primer document (Jan. 2021):

https://www.w3.org/TR/rdf11-primer/

and also been discussed with respect to applicability

in Web-based environments (Dipple et al., 2014; Pri-

vat, 2012).

Agents in digital stigmergic systems communicate

indirectly by reading from and writing to a shared data

space, and by this can be considered to follow a gen-

erative communication paradigm. (Gelernter, 1985;

Ciancarini et al., 1997). Practical implementations of

this paradigm were, among others, realized in the Sys-

tem Linda, based on Tuple Spaces (Gelernter, 1985).

Stigmergy has been applied in various domains as

a means for realizing coordination, for example in the

ﬁeld of robotics (Matari

c et al., 2003; Krieger et al.,

2000; Jevti

c et al., 2012), or generally, distributed co-

ordination in cyber-physical manufacturing (Cicirello

and Smith, 2004; Schraudner and Charpenay, 2020).

In the ﬁeld of telecommunications (Bonabeau et al.,

1998), concepts of evaporation rate and refresh rate

from the ant world were applied for managing the dy-

namic requirements of a network. In the ﬁeld of trafﬁc

and public transport, data acquired from large num-

bers of vehicles or passengers is used to predict hot-

spots and usage preference, and from this, plan more

optimal routes for individuals based on the current sit-

uation (Kanamori et al., 2014; Alfeo et al., 2018).

Ant inspired optimization techniques have been in

focus of research since the early 1990s, and various

variations have been developed ever since (Dorigo

and Blum, 2005; Heylighen, 2015). It has been shown

that bio-inspired algorithms, such as stigmergy, per-

form generally well on decentralized decision mak-

ing (Jevti

c et al., 2012) as well as peer-recruitment

and coordination for task accomplishments (Krieger

et al., 2000). (Koro

sec et al., 2012) have shown a

stigmergic approach for high dimensional numerical

optimization (Differential Ant-stigmergy Algorithm,

DASA). (Chopra et al., 2017) presented a distributed

variant of the Hungarian Method for solving the Lin-

ear Sum Assignment Problem (LSAP), with multiple

agents cooperating and ﬁnding an optimal solution

for the LSAP without a central coordinator or shared

memory. In recent years, the ﬁeld of Multi-Agent

Systems (MAS) has generally seen a growing inter-

est in the concept of stigmergy (Yu and Cheng, 2020;

Ricci et al., 2007; De Nicola et al., 2020; Cicirello

and Smith, 2004).

In all the bio/insect-inspired works that have been

discussed in this section, there has been no particu-

lar emphasis given to the medium to the extent that

it is described by (Heylighen, 2015). Its fundamen-

tal meaning as a shared environment that agents use

to leave traces, sense its state and act on it, has been

largely overlooked. Some of the presented works (e.g.

from the domain of trafﬁc and transport) bypass the

ICSOFT 2021 - 16th International Conference on Software Technologies

348

medium, and rely on direct agent-to-agent communi-

cation.

The fact that often the environment (or medium)

is reduced to very basic representations, while agents

lack cognitive abilities to make better use of a poten-

tially more complex environment, has already been

observed (Ricci et al., 2007). There is moreover an

awareness of both the need for a common understand-

ing of such an environment (Charpenay et al., 2020),

and the difﬁculty to properly correspond concepts

from the real-world scenarios to concepts in nature in

order to properly employ those algorithms (Valcke-

naers et al., 2007). In this paper is, we discuss and

present with appropriate examples, that read-write

Linked Data layer is a suitable general stigmergic

medium for said purposes.

3 BACKGROUND

3.1 Resource-Oriented Architectures

A Resource Oriented Architecture (ROA) is built

around the notion of a Resource as common repre-

sentation for and kind of virtual or real-world enti-

ties. (Fielding and Taylor, 2000; Lucchi et al., 2008).

A resource is typically characterized by a name (iden-

tiﬁer), its representation and links between resource

representations (Lucchi et al., 2008). As deﬁned by

Fielding, a representation is a sequence of bytes and

metadata to describe those bytes. A resource may

be described by more than one representation at any

given time i.e., provide the same content for example

in different serializations formats. More detailed con-

siderations of this architecture can be found in (Field-

ing and Taylor, 2000).

3.2 Linked Data Systems

Linked Data

is a way to share and structure informa-

tion using links. It is a design principle that imple-

ments a Resource Oriented Architecture, and is built

on the HyperText Transfer Protocol (HTTP) and HA-

TEOAS (Hypermedia as the Engine of Application

State) principles. That means that Linked Data en-

ables software user-agents or applications to derive all

necessary information to understand data, or how to

interact with it, by following links as provided by the

server (Fielding and Taylor, 2000). This understand-

ing is supported by semantic annotations that describe

to a data consumer the meaning of a particular ﬁeld of

data, or APIs that provide this data, thus leading to a

https://www.w3.org/standards/semanticweb/data

uniform understanding of the data by different appli-

cations (Verborgh et al., 2011; Mayer et al., 2016).

These semantic descriptions are typically mod-

eled using the Resource Description Framework

(RDF) (Lassila et al., 1998), (see also footnote

RDF allows to formulate statements about re-

sources in terms of triples that follow a subject-

predicate-object structure. The subject symbolizes

the resource, the predicate describes the qualitative

aspect of the resource and/or describes the relation-

ship between a subject and an object. A set of RDF

triples constitutes a labeled graph, where the subject

and object form nodes, connected by a directed edge

(from subject to object) that is labeled via the predi-

cate.

3.3 Stigmergic Media

Relevant results of research in the ﬁeld of stigmergy-

based self-organization have been very concisely

summarized by Heylighen (Heylighen, 2015). We

discuss stigmergy based on the ﬁndings from this pa-

per exclusively. However, we would like to stress out

that by this work being a very thorough survey over

the topic that covers research from several decades,

we well include ﬁndings from many different re-

searchers with different view on the general topic.

Heylighen derives from his ﬁndings his own deﬁ-

nition of stigmergy as an:

”indirect, mediated mechanism of coordination

between actions, in which the trace of an action left

on a medium stimulates the performance of a subse-

quent action” (Heylighen, 2015, p. 5).

The deﬁnitions of the core components of stig-

mergy as described in (Heylighen, 2015) are as fol-

lows. An action is considered as a causal process that

produces a change in the world. The medium is the

part of the world that undergoes changes because of

the action, and also whose state is sensed to incite fur-

ther actions. A trace is the perceivable change made

in the medium by an action, which can trigger subse-

quent actions. A trace that stimulates agents to per-

form a speciﬁc action, i.e. affords the action, is called

Affordance. Affordances typically encode condition-

action rules, which trigger an agent to perform an ac-

tion once a certain condition is met. A trace that keeps

agents from performing a particular action, is called

Disturbance.

Heylighen further identiﬁes different variations of

stigmergy, depending how the agents interact with the

medium (pp. 19 – 27).

This includes the observation that a medium may

be worked on by either a single agent, or crowds (in-

dividual vs collective stigmergy), that agents may take

Linked Data as Stigmergic Medium for Decentralized Coordination

349

into account either mere existence of certain features

in the medium, or quantities of those (qualitative vs

quantitative stigmergy), that agents may react to di-

rect results of work in their general environment (se-

matectonic stigmergy), or to markers that were delib-

erately left by other agents (marker-based stigmergy),

that traces left by agents in the medium can stay un-

til actively being removed by other agents (persistent

traces) or over time dissipate and vanish (transient

traces), and ﬁnally, that traces in the medium may

be observable by every agent working on the medium

(Broadcast), or only to a limited number of speciﬁc

agents (Narrowcast).

For a very thorough elaboration on the various as-

pects that we covered here in a very shortened man-

ner, we refer the reader to the original paper (Hey-

lighen, 2015).

4 LINKED DATA AS DIGITAL

STIGMERGIC MEDIUM

In nature, the notions of agent and medium are de-

termined by nature itself: Ants, for example, follow

traces of pheromones left by other ants towards lucra-

tive sources of food. Here, ants are the agents, and the

ground and food are the medium. Termites use clay as

medium, steered by how the shape of their nest (made

of this very clay) has already formed. Bees use the air

as medium to guide their fellow bees to food sources

by dance patterns.

When implementing stigmergy-based algorithms

for coordination, ”agents” are usually considered to

be software AI user-agents. These agents operate on

a digital representation of the to-be-coordinated con-

cepts, which may correspond to real-world physical

artifacts (e.g. physical production machines or robots

in manufacturing scenarios, cars and trafﬁc lights

in trafﬁc). This partition between digital and real

world is common in agent-based coordination algo-

rithms (Dipple et al., 2014), with the partitions lately

labeled as Agent Space for the digital, and Artifact

Space for the physical representation space (Charpe-

nay et al., 2020).

4.1 Requirements for (Digital)

Stigmergic Media

From the notions and variations of stigmergic media

in the Section 3.3, we derive the following require-

ments that a digital medium should fulﬁll to be suited

for use in stigmergy-based systems:

R1 (Representation). The medium must be able to

represent entities of the domain in which the co-

ordination algorithm performs, and relations be-

tween them. The medium thus serves as Agent

Space. If artifacts in Artifact Space are target of

coordination, the medium must be able to provide

a representation of the physical entity in the Agent

Space, and allow access to the physical entity via

the mediums, e.g. to switch a real-world trafﬁc

light, or start a production process on a produc-

tion machine.

R2 (Accessibility). The medium must be accessible

to the agent in the meaning that an agent must be

able to enter the medium to perform actions on it.

Furthermore, the agent must be able to navigate

through the medium to the point where an action

is to be performed.

R3 (Observability). The medium must be observ-

able (readable) for the agent to recognize condi-

tions of condition-action rules to be fulﬁlled in the

medium. For this, the agent needs to be able to at

least observe the existence of effects (for qualita-

tive stigmergy). The medium should further be

suitable to provide:

R3.1 (Interpretability) of observed effects in the

medium w.r.t the domain for the agent to cor-

rectly set the observed effects into relation with

each other.

R3.2 (Quantities): The medium must be able to ex-

press quantities for coordination by quantita-

tive stigmergic effects.

R4 (Consistency). For collective stigmergy, the

medium must consistently deliver the same infor-

mation to different agents at the same point of

time. In particular, if an agent induces a change

in the medium, following this change, all other

agents must observe the changed state as actual

state of the medium.

R5 (Malleability). Agents must be able to form and

change elements in the medium as result of their

action. This includes both changing the state of

existing entities within the medium (comparable

to continuing the construction of a begun nest

by a swarm of termites), and add or remove en-

tities from the medium (comparable to leaving

pheromone markers, or dissipating markers over

time). However, changing the medium should

happen in a controlled manner, leading us to the

requirement of Stability:

R5.1 Stability: Any change to the medium must be

possible without inﬂicting unwanted effects to

resources outside the scope of a performed ac-

tion. ”Unwanted” is in this case not to be con-

ICSOFT 2021 - 16th International Conference on Software Technologies

350

fused with changes that an agent ”unintention-

ally” left as a trace, but to be understood as an

effect that changes the state of an entity beyond

what was intended by the algorithm.

R6 (Scopes). The medium must be able to limit visi-

bility of entities and effects in terms of scopes to

allow Narrowcast of stigmergic effects.

4.2 Linked Data as Stigmergic Medium

We in the following show that read-write Linked Data

fulﬁlls all requirements towards a digital stigmergic

medium.

Representation is achieved by the notion of represen-

tation space of resources (see Sections 3.1 and 3.2):

Read-write Linked Data being built around resource

oriented architectures provides both the tools and best

practices of how to represent both real-world and vir-

tual entities in terms of addressable resources. Con-

nections to physical artifacts is established by hav-

ing callable HTTP endpoints represented as resources

within the medium.

Accessibility is achieved by building Linked Data

around HATEOAS principles. Agents can access re-

sources and read information from them by HTTP

GET requests. All information needed to interact

with a resource is provided by the server that man-

ages the resource. Furthermore, Linked Data deﬁnes

query interfaces as a common interaction method with

linked data graphs. By employing graph query en-

gines like SPARQL

, agents can identify relevant re-

sources as a result of the queries. Moreover, by fol-

lowing links between related resources, agents may

explore Linked Data graphs autonomously. It is not

required to host the medium being hosted on a sin-

gle physical server instance to ensure accessibility.

In fact, Linked Data principles state that resolution

of URIs should happen transparent, and agents do

not need to make assumptions where the actual data

is hosted. This allows the medium to be hosted on

distributed servers. For queries, SPARQL supports

the integration of data from different distributed end-

points via federated queries using the SERVICE key-

word.

Observability: ”Existence” of an effect is manifested

in Linked Data by existence of a respective triple pat-

tern in the Linked Data graph. By this, the existence

of an effect as precondition for an action can be ver-

iﬁed by matching expected triple patterns against the

W3C SPARQL 1.1 Query Language Recommendation

(Apr. 2021): https://www.w3.org/TR/sparql11-query/

SPARQL Federated Queries: (Apr.2021): https://www.

w3.org/TR/sparql11-federated-query/

Linked Data graph via SPARQL queries. The state-

ments encoded by triples are moreover semantically

interpretable by software agents, as commonly estab-

lished for Linked Data graphs.

Quantities can be modelled in Linked Data graphs

either by using respective literal nodes that express

a quantity in terms of a ﬁtting datatype directly, or

by the number of triples rendered to a respective re-

source.

Consistency is achieved by the notion of state and

representation of resources in a Linked Data system as

outlined in Sections 3.1 and 3.2. Access to resources,

the represented concept, and modes of interaction are

managed by the Linked Data server and provided to

clients following HATEOAS principles. By the com-

munication between clients and server being stateless

(by following REST and HATEOAS principles), the

state of the resource as communicated by the server

towards clients is independent of particular clients,

and by this, consistent among all clients.

Malleability is achieved by write-capabilites of read-

write Linked Data. On resource-level, agents may

change the state of a resource by PUT / POST /

DELETE requests. On graph level, linked data pro-

vides possibilities to change elements in the medium

using SPARQL UPDATE requests with INSERT and

DELETE statements. The WHERE body of these

states moreover allows to take into account pre-

conditions that need to be fulﬁlled when performing

the update.

Stability during updates is achieved by unambigu-

ous identiﬁcation of relevant resources via IRIs. By

default, operations on resources do not have side-

effects on other resources, and by this, will not inﬂict

undesired changes to resources other than those that

the action was performed on. On RDF graph level,

stability during write operations is ensured by that

adding triple statements to a resource does not inter-

fere with triples already present: by adding triples,

statements about a resource may only become more

speciﬁc, but never eliminate statements that were

present before new triples were added.

Scope can be expressed in read-write Linked Data

either by speciﬁc triple statements on resources by

which agents can ﬁlter for speciﬁc resources, or by

using mechanics of Linked Data datasets and named

graphs.

Different scopes, i.e. named graphs, are

then accessed by agents for example by using FROM

and FROM NAMED clauses in the respective SPARQL

queries.

By ﬁnding all requirements R1 – R6 fulﬁlled by

and materialized via concepts of read-write Linked

Data systems, we derive that read-write Linked

https://www.w3.org/TR/rdf-sparql-query/#rdfDataset

Linked Data as Stigmergic Medium for Decentralized Coordination

351

Data is without limitations a suitable generic digital

medium for stigmergy-based coordination.

5 APPLICATION EXAMPLE

Following, we show how to employ a read-write

Linked Data layer as stigmergic medium in Agent

Space by an application example from the domain of

digital manufacturing. The example is loosely based

on the use case presented in (Schraudner and Charpe-

nay, 2020): A (simulated) factory receives orders for

simple IoT modules on a ”batch size 1” production

line as commonly envisioned in Industry 4.0 (Lasi

et al., 2014; Mrugalska and Wyrwicka, 2017). Once

an order is received, it is carried out by employing ma-

chines which provide the capabilities to perform man-

ufacturing steps necessary for particular steps during

the production process, e.g. providing plastic casts for

casings, soldering electric circuits, or ﬁxing the ﬁnal

model (see Figure 1).

Figure 1: Process of IoT module production used as exam-

ple.

Orders are executed by AI agents. The need for

coordination arises as machines are shared between

simultaneously executed orders.

The purpose of the presented coordination algo-

rithm is to ﬁnd a suitable distribution of machines be-

tween agents working on different orders, with the

goal to complete each order in the shortest possible

time.

5.1 Domain Model

The domain model for our application example is

shown in Figure 2: An order requests a certain prod-

uct to be produced. How a product can be assem-

bled is described in recipes. These recipes spec-

ify what other products are needed as prerequisite,

and which manufacturing step is necessary to assem-

ble supply products to a higher level product. Man-

ufacturing steps are provided by units on the shop

ﬂoor, and can be executed by network interaction end-

points. As common in models for automated produc-

tion, and also assumed in (Charpenay et al., 2020)

and (Schraudner and Charpenay, 2020), we assume

production units to have callable network endpoints

by which their particular production step can be exe-

cuted. Affordance- and disturbance markers are used

to encourage or discourage the use of a certain inter-

action endpoint.

Figure 2: Domain model of the chosen application example.

Listing 1: Example of a production recipe using schema and

steps vocabularies.

1 re ci pe s : mai n - modul e rd f : ty pe s ch em a : Ho wT o ;

2 sc he ma : abo ut ma in bo ar d : p ro du ct ;

3 sc he ma : ste p st eps : so ld er ;

4 sc he ma : sup pl y [

5 rdf: typ e schema : Ho wT oSu pp ly ;

6 sche ma : ite m cpu: pr od uc t ] ,

7 [ rd f : type s chema : HowTo Su pp ly ;

8 sche ma : ite m ram: pr od uc t ] .

A recipe speciﬁes the produced artifact by

the schema:about predicate, the required supply

from which the product is created (indicated the

schema:supply predicate), and the production step

that needs to be performed to combine the speciﬁed

supplies to the resulting product via the schema:step

predicate (see Listing 1). schema: denotes the

namespace of the schema.org ontology

. We assume

a set of supply materials to be provided to the factory

without the need for speciﬁc production. These sup-

ply materials will be provided by dispenser units, and

do not require any additional supplies.

Products are described in terms of an RDF class,

e.g. (<#product>, rdf:type, cpu:product).

Dispenser and production units spec-

ify their (callable) execution endpoint as

td:InteractionPattern in a set of triples that is

referenced via td:providesInteractionPattern.

The Interaction Pattern speciﬁes the step carried out

by the respective unit (see also Listing 2). Dispensers

https://schema.org/

ICSOFT 2021 - 16th International Conference on Software Technologies

352

refer to the class of dispensed products via a triple

(<#unit>, schema:yield, <#productClass>),

with <#productClass> referring to the RDF class of

the produced product. Dispenser units can dispense

more than one class of products. Production units

do not specify particular products that are produced

at the unit to allow for various products that are

produced with the same step to be produced at the

same machine. Instead, they provide information

about the type of provided production step via a

triple (<#unit>, schema:step, steps:<type>).

An example of a simple soldering unit is shown in

Listing 2.

Interaction Patterns on machines describe par-

ticular actions that agents may perform by to trig-

ger the execution of the respective production step

on the physical machine. This is done by resolv-

ing the URI that is provided by the respective re-

source, and that is identiﬁed by the property path

td:isAccessibleThrough/td:href, with td: de-

noting the namespace of the Web Thing Description

ontology

Listing 2: Example of a simple description of a worksta-

tion that performs a soldering step. The soldering action is

executed by calling the respective referenced URI.

1 s o l : s t a t i o n −1 a t d : Thing ;

2 t d : thi ngNa me ” S o l d e r i n g S t a t i o n 1 ” ˆ ˆ x s d :

s t r i n g ;

3 t d : p r o v i d e s I n t e r a c t i o n P a t t e r n s o l : s o l d e r i n g .

5 s o l : s o l d e r i n g a t d : I n t e r a c t i o n P a t t e r n ;

6 t d : i nt e r a c t i o nN a m e ” s o l d e r ” ˆ ˆ xsd : s t r i n g ;

7 schema : s t e p s t e p s : s o l d e r ;

8 t d : i s A c c es s i b l e T h r o u g h [

9 t d : h r e f <h t t p : / / 1 0 . 2 . 1 0 0 . 1 7 / s o l d e r />

10 ] .

5.1.1 Affordances and Disturbances

Listing 3: Example of an affordance marker resource that

advertises a steps:soldering interaction as relevant for

the current order.

1 < ur n : uu id : a52 6 >

2 a s ti gm ergy : ma rk er lef ;

3 s ti gm er gy : ma rked so l : so lderi ng ;

4 s ti gm er gy : scope order : mo dule ;

5 sche ma : su pply cp u : pro duct ,

6 ram: pr od uc t ;

7 sche ma : yield mm : pro du ct .

Affordances will advertise

td:InteractionPattern resources as callable

endpoint to some executing agent. Affordances are

markers that are left on a td:InteractionPattern.

Listing 3 shows an example of such a marker:

The marker gives information about which Interac-

tion Pattern it marked (via stigmergy:marked), for

https://www.w3.org/2019/wot/td

which order the respective pattern needs to be exe-

cuted (via stigmergy:scope), whether or not the re-

spective step needs particular supplies to be present

to be executed (schema:supply), and ﬁnally, which

product will be the result of calling the respective In-

teractionPattern resource (schema:yield). A marker

can link to one or more interaction patterns. If more

than one interaction pattern is marked, it is up to an

executing agent to choose which of the endpoints to

call.

Disturbance markers will discourage agents from

visiting a marked resource. If an affordance marker

links to several resource endpoints, an executing

agent will decide for an endpoint that is the least in-

ﬂuenced by disturbance markers. The complete algo-

rithm will be detailed out in Section 6.

6 EXAMPLE ALGORITHM

We now show how to realize a stigmergy-based co-

ordination algorithm based on the deﬁnition of the

Linked Data layer from the previous section.

The algorithm to execute a coordinated produc-

tion process for multiple orders is implemented in two

steps by two classes of agents. We divide agents into

marker agents and builder agents. Marker agents tra-

verse graphs in the agent space and generate produc-

tion markers as affordances on resources in the Arti-

fact space as shown in Listing 3. Builder agents are

attracted towards the respective endpoints by the af-

fordances left by the marker agents and execute those

production endpoints that were marked in the scope

of the current order, given that the production require-

ments (supplies) are met.

6.1 Marker Agents

The goal of a marker agent to identify all suitable pro-

duction units that will be involved in the process of

producing a particular order. For this, marker agents

will traverse recipe resources and leave markers on

resources as follows:

The agent maintains a list unvisited of nodes it

would like to visit, but has not yet.

1. Check for order resources that have not yet been

handled, i.e., do not carry a mark. Follow the

link via the schema:orderedItem property to the

resource that represents the class of the ordered

product and add it to unvisited. Mark the order

as handled.

2. From a resource r in unvisited, ﬁnd a respec-

tive recipe blueprint b that contains a triple (b,

Linked Data as Stigmergic Medium for Decentralized Coordination

353

schema:about, r), i.e., the recipe for the respec-

tive product.

3. Check for a schema:step link, and visit all in-

teraction patterns i matching the schema:step;

if the step is steps:dispense, ﬁnd the respec-

tive interaction patterns of dispenser units that

schema:yield r .

4. Leave a mark on each visited i (for both produc-

tion and dispenser, cf. Listing 3).

5. For each resource s in schema:supplies of b,

add s to unvisited. If no schema:supply is

speciﬁed, or resource points to an empty set

(rdf:nil), do nothing. Remove the current re-

source r from unvisited.

6. If unvisited is empty, terminate; else, go to 2.

The mark which is left by the agent in Step 4.

follows the structure of the example shown in List-

ing 3. It includes information about the order in

the scope of which it was placed, and will moreover

specify the required supplies s for this step. Mark-

ers may be scoped by order, using a triple (marker,

stig:scope, order) on the marker resource (Narrow-

cast), or unscoped and by this visible for every other

agent (Broadcast). Following the given algorithm, a

marker agent is solely driven by the structure of the

knowledge graph that is formed between product and

blueprint descriptions. Each subsequent step is solely

decided by the state of the currently visited resource.

Its behavior can by this be classiﬁed as a sematectonic

stigmergic agent.

6.2 Builder Agents

Builder agents are attracted to markers left by marker

agents and call the respective InteractionPattern

endpoints. A Builder agent for this proceeds in the

following manner:

1. Scan for all markers m left by marker agents. If

the builder agent is bound to a speciﬁc scope (i.e.

fulﬁlling a particular order), it will only follow

markers in its scope (i.e., with a matching (m,

stig:scope, order) triple present.

2. For each m, the checks, e.g. via a ﬁtting SPARQL

query, if for each supply s speciﬁed by the marker

via (m, schema:supply, s), there exists a product

p that is a product of class s, as encoded by a triple

(p, rdf:type, s).

3. For each m for which supplies are fulﬁlled,

the visit the InteractionPattern resource i that is

marked via (m, stig:marked, i) and that carries

the least amount of disturbance markers. Ex-

ecute the action endpoint that is identiﬁed via

td:isAccessibleThrough/td:href.

4. Leave a disturbance marker on the interaction pat-

tern resource, and removes the affordance marker.

By following a marker trace left by other agents,

we employ a marker-based stigmergy approach. The

supplies speciﬁed on the marker, in combination with

a reference to callable resources for execution of the

respective interaction step, encode a condition-action-

rule that the agent follows.

6.3 Correctness of the Algorithm

An order speciﬁcies the expected result of one in-

stance of the algorithm, namely the speciﬁc product

that is to be produced in the end. By marker agents

starting from the expected goal (the ordered product),

and following links backwards through the needed

supplies, it is ensured that over the total production

process, all needed supplies will be available even-

tually. Marker agents do not need to keep memory

of the goal they are following, but are guided en-

tirely by the structure of the Linked Data medium. It

can be easily shown that the marker agent’s algorithm

will terminate as soon as all dispensable supplies (leaf

nodes in the graph in Figure 1) are provided with a

marker. The builder agent’s algorithm will terminate

when the last marker is consumed. Builder agents are

not restricted to follow only markers of a speciﬁc or-

der. Consuming a marker and triggering the respec-

tive action will always result in a product that was

previously found to be a requirement by some marker

agent. Eventually, by builder agents executing end-

points for products with rising complexity as supplies

are more and more met, the ordered product will be

produced.

If several orders are executed in parallel, produc-

tion units (and dispensers) will simply receive several

independent markers. By having separate markers per

order, and having builder agents removing the marker

they followed after executing the production step, it is

ensured that for every order, every production step is

executed exactly once. The concept may be extended

for products to require more than one instance of a

supply product. In this case, a marker agent would

leave a marker per required instance of a supply.

The opportunity for coordination arises in Step

3. of the builder agent algorithm: For every recipe,

markers are left on every machine that is capable of

carrying out the needed production step. When fol-

lowing the marker trace, builder agents have a choice

which of the marked machines they actually execute.

ICSOFT 2021 - 16th International Conference on Software Technologies

354

The decision for which machine to call for to exe-

cute the step is based on the number of disturbance

markers left on the resource: The more agents visit,

means, the busier the machine already is with execut-

ing orders, the more disturbance markers are left on

the machine, and agents will be more likely to divert

to other machines to complete their order.

The algorithm at this point ignores transport of

products on the shop ﬂoor. A more sophisticated

heuristic may take into account also transport times

between machines between the different steps.

6.4 Implementation

We implemented the example using the Unity 3D

game engine to simulate the factory, a Fuseki triple

store to host the read-write Linked Data medium, and

the AJAN agent platform

8, 9

(Antakli et al., 2019) to

implement the behaviors of both marker and builder

agents. All related resources will be published on

GitHub:

https://github.com/BMBF-MOSAIK/

stigmergy-demo

7 DISCUSSION

In the following, we analyse the use of Linked Data

as stigmergic medium based on ﬁndings from the al-

gorithm w.r.t. beneﬁts of stigmergic systems (see also

(Heylighen, 2015, pp.13-14)):

Agents do not plan or anticipate, but only follow

links between resources in the Linked Data medium.

The condition-action-rules that determine which re-

sources to visit are generic. Agents do not need

to make per-resource decision whether following the

rule is beneﬁcial for the goal, or not. The ”goal” (pro-

duction of a speciﬁc order) is, in particular, not known

to an agent, and reaching any goal is no condition for

termination of the algorithm.

Memory-less agents are sufﬁcient by storing all

relevant information that arises during execution in

terms of resources in the medium. Same goes for

communication between agents, which is eliminated

by limiting interaction to following markers left by

other agents. Agents are moreover not aware of each

other, as their interaction is limited entirely to the

Linked Data medium. This also implies that agents

do not need to be simultaneously present.

The correct sequence of steps arises naturally by

including information about required supplies, both

https://github.com/aantakli/AJAN-service

https://github.com/aantakli/AJAN-editor

when a marker agent decides which recipe resources

to visit next, and when a builder agent decides which

marked production resource to visit next. There is no

requirement to explicitly model (and by this, impose)

sequences during execution of a particular produc-

tion in a form like ”after you have successfully vis-

ited this resource, continue with that speciﬁc resource

over there”. Instead, sequence arises implicitly from

the condition-action rules encoded in the Linked Data

medium.

Non-necessity for commitment is achieved by hav-

ing no explicit assignment of tasks to agents, but have

agents decide which resource to visit, and how to in-

teract with it (e.g., perform their competent action),

solely on the state of resources in the medium. Any

agent can pick up any task at any point in time accord-

ing to the agents’ competence.

Finally, as it is obvious from the algorithms of

both marker and builder agents, that there is no cen-

tralized coordination or control authority that agents

need to consult, or by which they are controlled.

Coordination arises solely from resource states and

markers left in the medium, as already discussed in

Section 6.3.

8 CONCLUSION AND FUTURE

WORK

In this paper, we have thoroughly analyzed read-write

Linked Data as a digital medium for stigmergy-based

coordination mechanisms. We have based this anal-

ysis on common general characteristics of stigmergic

systems in literature. By identifying direct correspon-

dences between these and central features of Linked

Data systems, we ﬁnally achieved to show that read-

write Linked Data provides a perfect digital medium

for stigmergy-based coordination algorithms. Finally,

we provided an example of how to employ these ﬁnd-

ings in a coordination algorithm for customized digi-

tal production.

Currently, the presented algorithm is to be consid-

ered a basic conceptual example to show that decen-

tralized stigmergy-based coordination works. It is not

yet intended to show improved efﬁciency and scala-

bility over existing approaches. We do plan to fur-

ther improve and evaluate the algorithm with focus

on these aspects in future work. We moreover plan

to demonstrate the applicability of Linked Data as a

stigmergic medium by more complex examples from

different domains.

For actual application in a production setting, the

algorithm as presented omits elements like location

of products and production units on the shop ﬂoor,

Linked Data as Stigmergic Medium for Decentralized Coordination

355

and by this, necessary steps and tools for transport

of products. We are working on implementing these

concepts in an extended version of the algorithm.

ACKNOWLEDGEMENTS

This work has been supported by the German Federal

Ministry for Education and Research (BMBF) as part

of the MOSAIK project (grant no. 01IS18070-C).

REFERENCES

Alfeo, A. L., Cimino, M. G., Egidi, S., Lepri, B., and

Vaglini, G. (2018). A Stigmergy-Based Analysis of

City Hotspots to Discover Trends and Anomalies in

Urban Transportation Usage. IEEE Transactions on

Intelligent Transportation Systems, 19(7):2258–2267.

Antakli, A., Spieldenner, T., K

oster, M., Groß, J., Her-

rmann, E., Rubinstein, D., Spieldenner, D., and Zin-

nikus, I. (2019). Optimized coordination and simula-

tion for industrial human robot collaborations. In In-

ternational Conference on Web Information Systems

and Technologies, pages 44–68. Springer.

Berners-Lee, T., Hendler, J., Lassila, O., et al. (2001). The

semantic web. Scientiﬁc american, 284(5):28–37.

Bizer, C., Heath, T., Idehen, K., and Berners-Lee, T. (2008).

Linked data on the web (ldow2008). In Proceedings of

the 17th international conference on World Wide Web,

pages 1265–1266.

Bonabeau, E., Henaux, F., Gu

erin, S., Snyers, D., Kuntz, P.,

and Theraulaz, G. (1998). Routing in telecommunica-

tions networks with ant-like agents. Lecture Notes in

Computer Science (including subseries Lecture Notes

in Artiﬁcial Intelligence and Lecture Notes in Bioin-

formatics), 1437(1):60–71.

Charpenay, V., Schraudner, D., Seidelmann, T., Spielden-

ner, T., Weise, J., Schubotz, R., Mostaghim, S., and

Harth, A. (2020). Mosaik: A formal model for self-

organizing manufacturing systems. IEEE Pervasive

Computing.

Chiong, R. (2009). Nature-inspired algorithms for optimi-

sation, volume 193. Springer.

Chopra, S., Notarstefano, G., Rice, M., and Egerstedt,

M. (2017). A Distributed Version of the Hungarian

Method for Multirobot Assignment. IEEE Transac-

tions on Robotics, 33(4):932–947.

Ciancarini, P., Gorrieri, R., and Zavattaro, G. (1997). To-

wards a calculus for generative communication. In

Formal Methods for Open Object-Based Distributed

Systems, pages 283–297. Springer.

Cicirello, V. A. and Smith, S. F. (2004). Wasp-like agents

for distributed factory coordination. Autonomous

Agents and Multi-Agent Systems, 8(3):237–266.

De Nicola, R., Di Stefano, L., and Inverso, O. (2020).

Multi-agent systems with virtual stigmergy. Science

of Computer Programming, 187:102345.

Dipple, A., Raymond, K., and Docherty, M. (2013). Stig-

mergy within Web Modelling Languages : Positive

Feedback Mechanisms. eprints.qut.edu.au.

Dipple, A., Raymond, K., and Docherty, M. (2014). Gen-

eral Theory of Stigmergy: Modelling Stigma Seman-

tics. Elsevier.

Dipple, A. C. (2011). Standing on the shoulders of ants:

Stigmergy in the web. In Proceedings of the 20th

international conference companion on World wide

web, pages 355–360.

Dorigo, M. and Blum, C. (2005). Ant colony optimization

theory: A survey. Information Sciences.

Fielding, R. T. and Taylor, R. N. (2000). Architectural

styles and the design of network-based software ar-

chitectures, volume 7. University of California, Irvine

Irvine.

Gelernter, D. (1985). Generative communication in linda.

ACM Transactions on Programming Languages and

Systems (TOPLAS), 7(1):80–112.

Heylighen, F. (2006). Mediator evolution: a general sce-

nario for the origin of dynamical hierarchies. World-

views, Science and Us.(Singapore: World Scientiﬁc),

44:45–48.

Heylighen, F. (2015). Stigmergy as a universal coordina-

tion mechanism: components, varieties and applica-

tions. Human Stigmergy: Theoretical Developments

and New Applications; Springer: New York, NY, USA.

Jevti

c, A., Gutierrez,

A., Andina, D., and Jamshidi, M.

(2012). Distributed bees algorithm for task allocation

in swarm of robots. IEEE Systems Journal, 6(2):296–

304.

Kanamori, R., Takahashi, J., and Ito, T. (2014). Evalu-

ation of trafﬁc management strategies with anticipa-

tory stigmergy. Journal of Information Processing,

22(2):228–234.

Koro

sec, P.,

Silc, J., and Filipi

c, B. (2012). The differential

ant-stigmergy algorithm. Information Sciences.

Krieger, M. J., Billeter, J. B., and Keller, L. (2000). Ant-like

task allocation and recruitment in cooperative robots.

Nature, 406(6799):992–995.

Lasi, H., Fettke, P., Kemper, H.-G., Feld, T., and Hoffmann,

M. (2014). Industry 4.0. Business & information sys-

tems engineering, 6(4):239–242.

Lassila, O., Swick, R. R., et al. (1998). Resource description

framework (rdf) model and syntax speciﬁcation.

Lucchi, R., Millot, M., and Elfers, C. (2008). Resource Ori-

ented Architecture and REST. Assessment of impact

and advantages on INSPIRE, Ispra: European Com-

munities.

Matari

c, M. J., Sukhatme, G. S., and Østergaard, E. H.

(2003). Multi-robot task allocation in uncertain en-

vironments. Autonomous Robots, 14(2-3):255–263.

Mayer, S., Verborgh, R., Kovatsch, M., and Mattern, F.

(2016). Smart conﬁguration of smart environments.

IEEE Transactions on Automation Science and Engi-

neering, 13(3):1247–1255.

Mrugalska, B. and Wyrwicka, M. K. (2017). Towards lean

production in industry 4.0. Procedia engineering,

182:466–473.

ICSOFT 2021 - 16th International Conference on Software Technologies

356

Privat, G. (2012). Phenotropic and stigmergic webs: The

new reach of networks. Universal Access in the Infor-

mation Society, 11(3):323–335.

Ricci, A., Omicini, A., Viroli, M., Gardelli, L., and Oliva,

E. (2007). Cognitive stigmergy: Towards a framework

based on agents and artifacts. Lecture Notes in Com-

puter Science (including subseries Lecture Notes in

Artiﬁcial Intelligence and Lecture Notes in Bioinfor-

matics), 4389 LNAI:124–140.

Schraudner, D. and Charpenay, V. (2020). An HTTP/RDF-

Based Agent Infrastructure for Manufacturing Using

Stigmergy. (01):197–202.

Tzanetos, A., Fister Jr, I., and Dounias, G. (2020). A com-

prehensive database of nature-inspired algorithms.

Data in Brief, 31:105792.

Valckenaers, P., Hadeli, Germain, B. S., Verstraete, P.,

and Van Brussel, H. (2007). MAS coordination and

control based on stigmergy. Computers in Industry,

58(7):621–629.

Verborgh, R., Steiner, T., Deursen, D. V., d. Walle, R. V.,

and Vall

es, J. G. (2011). Efﬁcient runtime service dis-

covery and consumption with hyperlinked restdesc. In

2011 7th International Conference on Next Genera-

tion Web Services Practices, pages 373–379.

Yu, X. and Cheng, T. (2020). Research on a Stigmergy-

driven & MAS-based Method of Modeling Intelligent

System. pages 1042–1047.

Linked Data as Stigmergic Medium for Decentralized Coordination

357