TEAM FORMATION FOR AGENT COOPERATION IN LOGISTICS

Protocol Design and Complexity Analysis

Arne Schuldt

Centre for Computing and Communication Technologies (TZI)

University of Bremen, Am Fallturm 1, 28359 Bremen, Germany

Keywords:

Agents, Cooperation, Team formation, Interaction protocol, Protocol design, Complexity analysis.

Abstract:

Supply network management is a challenging task due to the complexity, dynamics, and distribution of lo-

gistics processes. Delegating process control to intelligent software agents that represent logistics objects

and act on their behalf helps approach these challenges. The resulting problem decomposition reduces the

computational complexity. Dynamics can be dealt with locally. An important prerequisite for coordinated

process control is that agents can cooperate with each other. Based on requirements from logistics, this paper

presents an interaction protocol for team formation. A thorough complexity analysis for the proposed method

is conducted because the arising interaction effort is not obvious as it depends on the number of teams formed.

Therewith, agent developers can estimate the interaction effort and thus the applicability of the method in

advance. Finally, an application of the introduced protocol is outlined.

1 INTRODUCTION

Managing complex supply networks with software

systems is a challenging task. In particular, coordi-

nating logistics processes requires dealing with the

following challenges:

complexity caused by the high number of logistics

objects and their parameters,

dynamics caused, for instance, by transient customer

demands and changes in the environment, and

distribution because logistics processes often span

over multiple companies and even continents.

These properties prevent the application of centralis-

tic and monolithic software systems. Generating op-

timal plans centrally consumes a lot of time. Often,

the dynamics therefore renders these plans outdated

already in the moment their generation is ﬁnished.

Moreover, the physical distribution prevents relevant

information from being available centrally.

Consequently, the paradigm of autonomous con-

trol in logistics (Windt and Hülsmann, 2007) dele-

gates decision-making to the participating entities. In

contrast to other approaches (Chaib-draa and Müller,

2006), not only companies or departments, but ac-

tually individual logistics objects are considered au-

tonomous. For instance, shipping containers are

themselves responsible for planning and scheduling

their way through the logistics network. The com-

putational complexity is reduced because each entity

only considers its own parameters and those of co-

operating entities (Schuldt, 2010). This increases re-

activity and robustness of process control because ex-

ceptions can be dealt with locally. Autonomous logis-

tics can be implemented with intelligent agents being

representatives for logistics objects.

An important ﬁnding is that individual agents can

frequently not satisfy their logistics objectives on

their own (Schuldt and Werner, 2007). As a conse-

quence, they must cooperate with other agents. The

formal model for cooperation of intelligent agents

(Wooldridge and Jennings, 1999) distinguishes four

consecutive steps of the cooperative problem-solving

process (Figure 1). As a prerequisite, agents must

recognise a potential for cooperation because joint ac-

tion is not reasonable without. Having identiﬁed this

potential, agents can form a team. Subsequently, they

collaboratively elaborate a plan. Finally, the team ac-

tion step deals with joint execution of this plan.

This paper focuses on the team formation step.

There is a demand for a particular interaction proto-

col for team formation in logistics because interaction

schemes are underspeciﬁed in the original model for

cooperation. This paper has two contributions:

1. Protocol design

2. Complexity analysis

398

Schuldt A..

TEAM FORMATION FOR AGENT COOPERATION IN LOGISTICS - Protocol Design and Complexity Analysis.

DOI: 10.5220/0003164703980405

In Proceedings of the 3rd International Conference on Agents and Artiﬁcial Intelligence (ICAART-2011), pages 398-405

ISBN: 978-989-8425-41-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

Plan FormationTeam FormationRecognition Team Action

Figure 1: The four steps of the model for cooperation (Wooldridge and Jennings, 1999). As a precondition, agents must

recognise a potential for cooperation. Subsequently, agents form both a team and a joint plan before they actually act jointly.

The protocol design is documented in Section 2. Rel-

evant requirements for team formation in autonomous

logistics are derived and contrasted to existing ap-

proaches. Based on this analysis, an interaction

scheme for team formation is introduced. In order

to estimate the applicability of the new protocol, the

approach is thoroughly analysed with respect to its in-

teraction effort in Sections 3 and 4. Section 5 outlines

an application of the introduced protocol.

2 PROTOCOL DESIGN

Team formation is an important prerequisite for coop-

eration of autonomous logistics entities. Section 2.1

motivates the demand for cooperation by identifying

the potential for cooperation. In particular, relevant

requirements for team formation mechanisms in au-

tonomous logistics are derived. Section 2.2 contrasts

these requirements to existing approaches. Finally,

Section 2.3 presents an agent interaction protocol that

satisﬁes the identiﬁed requirements.

2.1 Motivation and Requirements

As a prerequisite for cooperation among intelli-

gent agents, the model for cooperation demands

that a group of agents can jointly achieve a goal

(Wooldridge and Jennings, 1999). Reasons for acting

collaboratively are twofold. On the one hand, an indi-

vidual agent may not be capable of achieving its goal

in isolation. On the other hand, the agent may have a

goal conﬂict for all of its respective own actions.

In the ﬁrst case, agents with complementing ca-

pabilities should form teams in order to jointly ac-

complish their task. In autonomous logistics, also

the second case occurs quite frequently (Schuldt and

Werner, 2007). Think, for instance, of an intelligent

package that intends to be transported from a ware-

house to a distribution centre. In principle, the pack-

age could achieve this objective on its own by nego-

tiating with a truck, also represented by an intelligent

agent, that takes over the transport. However, trans-

porting an individual package by truck is frequently

not cost-efﬁcient. Instead, it is desirable that multiple

packages with the same origin and destination jointly

employ a truck in order to prevent a goal conﬂict re-

garding their cost-efﬁciency. Therefore, the important

task for autonomous logistics entities is to establish

teams based on joint properties such as a common lo-

cation and destination.

Apart from general interaction design principles

(Rosenschein and Zlotkin, 1994; Sandholm, 1999),

the requirements for team formation in this area of

application are as follows:

1. Unique teams

2. Flexible teams

3. Genericness

4. No prior knowledge

5. Decentralisation

6. Efﬁciency

The demand for unique teams means that only one

team should exist for each instantiation of a team

property. In terms of the above example, there should

only be one team of packages for each pair of ori-

gin and destination. This ensures the highest re-

source utilisation of the trucks employed. Of course,

each team can intentionally employ multiple trucks

if necessary. In other words, the requirement for

unique teams means that agents group themselves by

an equivalence relation with respect to one property.

Nevertheless, different properties and thus teams may

exist for different purposes, e.g., transport and stor-

age service allocation.

Furthermore, teams should be ﬂexible in the sense

that additional members can join after the initial for-

mation. The method should be generic in that it is

not restricted to speciﬁc descriptors of properties. The

team formation mechanism should not make or only

make few requirements regarding prior knowledge

participants must have about the structure of the mul-

tiagent system and other participants. The approach

should be decentralised in order to prevent bottle-

necks, thereby still being efﬁcient.

2.2 Related Work

Previous work on team formation focused on formal-

ising organisations of agents (Ferber and Gutknecht,

1998; Hannoun et al., 2000; Fischer et al., 2003)

as well as the internal states of agents during team

formation (Wooldridge and Jennings, 1999; Dignum

et al., 2000). Less effort has been spent on agent

interaction protocols for team formation. Previous

TEAM FORMATION FOR AGENT COOPERATION IN LOGISTICS - Protocol Design and Complexity Analysis

399

:Participant :Directory :TeamManager

m≤n

l=n-m

request-search-teams

inform-team-list

request-register

inform-registered

request-team-match

inform-team-match

failure-team-match

request-deregister

inform-deregistered

request-join-team

inform-team-joined

Optimistic-TeamFormationByDirectory-Protocol

Figure 2: Agent interaction protocol for team formation based on a directory service. Participating agents are optimistic in

that they initially assume that they can form a new team before possibly joining an existing one.

clustering algorithms such as k-means (MacQueen,

1967) take a centralised perspective on the data to be

clustered. This perspective, however, is usually not

available in the distributed setting of multiagent sys-

tems in general and autonomous logistics in particu-

lar. Hence, they cannot be applied.

Distributed clustering is, for instance, applied

in wireless sensor networks (Akyildiz et al., 2002).

However, these approachesare not applicable because

they focus on spatial data and thus make implicit

assumptions on the environment (Heinzelman et al.,

2000) that do usually not hold in autonomous logis-

tics. In particular, this contradicts the requirement for

generic descriptors.

Peer-to-peer approaches (Ogston and Vassiliadis,

2001) provide each agent with an arbitrarily cho-

sen set of other agents it is initially connected with.

Agents inform their peers about each other so that

they can exchange their direct partners by others

that are more similar. Unfortunately, this setting

is purely artiﬁcial for autonomous logistics because

autonomous logistics entities do not have any prior

knowledge about other agents in the systems. Conse-

quently, there is no natural choice for initial peers.

Often, the contract net (Smith, 1977) interaction

protocol is applied to implement team formation.

However, it only ﬁts the case (Section 2.1) that an

agent aims at ﬁnding others that supplement its own

capabilities. In particular, the requirements for unique

and ﬂexible teams are not met. It cannot be pre-

vented that teams with similar properties are estab-

lished. This is particularly because members cannot

join after a team has been established. This would re-

quire that team managers continuously advertise their

team to potential new members. The question, how-

ever, remains open what might be an appropriate fre-

quency for such announcements.

2.3 Team Formation Protocol

To summarise the discussion in Sections 2.1 and 2.2,

there is a demand for a new method for team forma-

tion. Figure 2 depicts an agent interaction protocol

that reﬂects the identiﬁed requirements. The proto-

col is based on a previous one (Schuldt and Werner,

2007). A comparison follows below.

The involved agent roles comprise the initiating

participant, the existing team managers, as well as a

directory service that administers the list of current

team managers. When an agent decides to participate

in the team formation process, it initially registers it-

self as a new team manager with the directory. This

behaviour is optimistic in that the participant assumes

that there is currently no team manager matching its

respective properties for team formation. In order to

check whether this assumption is actually true, it re-

quests the list of all current team managers from the

directory. Afterwards, it provides all team managers

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

400

with its own properties so that the managers can de-

termine whether their properties are matching. This

communication is done in parallel to be time-efﬁcient.

The check conducted by the team managers has

three possible outcomes. Firstly, the match process

may fail for all team managers, i.e., no team matches

the properties of the new participant. In that case,

the initial assumption was right and the new partic-

ipant actually becomes a new team manager. Sec-

ondly, one team manager may determine a match. In

that case, the optimistic assumption turns out to be

wrong. Hence, the new participant deregisters from

the directory and joins the matching team instead. Fi-

nally, it might also occur that multiple team managers

determine a match. This is the case whenever mul-

tiple agents have concurrently registered with the di-

rectory with same properties. To resolve this problem

of redundant teams, each team manager is assigned an

individual timestamp when registering with the direc-

tory. Based on this timestamp, all agents including the

superﬂuous team managers can join the initial team.

As an alternative to the optimistic behaviour, it

would also be possible to act conservatively as it is

done in the ancestor of the protocol (Schuldt and

Werner, 2007). In the conservative case, new par-

ticipants would ﬁrst contact all existing team man-

agers before registering themselves with the directory

service. Due to concurrency, however, still multiple

agents with same properties might register as team

managers. After the registration process, it would

therefore be necessary to contact the existing team

managers again in order to resolve redundancy. The

advantage of the optimistic procedure is thus that

team managers only have to be contacted once.

The requirements derived in Section 2.1 are re-

ﬂected as follows. The proposed interaction proto-

col ensures that the resulting teams are unique. If

teams with identical properties are established, e. g.,

due to concurrency, this can be resolved by the pro-

tocol. Team formation is ﬂexible because the partici-

pants and not the team managers initiate team forma-

tion, i. e., participants can join teams after initial es-

tablishment. The protocol is generic because it does

not restrict the possible descriptors for team proper-

ties. Furthermore, only few prior knowledge about

the system is required because participants can re-

trieve the list of existing team managers from the di-

rectory. The approach is decentralised in that all deci-

sions are made autonomously by the participants and

team managers. The only central entity and thus a po-

tential bottleneck is the directory. But the directory

service is not necessarily provided by only one agent.

Instead, it can be offered by multiple agents which co-

ordinate with each other internally (Bellifemine et al.,

2007). Regarding efﬁciency, the asymptotic interac-

tion complexity for team formation is O(mn) = O(n

)

from a coarse perspective. However, the number m of

team managers is usually only a small fraction of all

n participants, i. e., m ≪ n. A more detailed analysis

follows in the subsequent Sections 3 and 4.

3 INTERACTION COMPLEXITY

The analysis of the interaction effort for the proposed

team formation protocol is approached in two steps.

Section 3.1 examines the possible range of team con-

ﬁgurations for given sets of agents. Based on this

foundation, Section 3.2 presents the analytical exam-

ination of the team formation interaction effort.

3.1 Possible Team Conﬁgurations

As elaborated in Section 2.1, all agents in one team

are characterised by similar properties. Although

these properties may change over time, each agent has

speciﬁc properties at the time it initiates team forma-

tion. The task is thus to ﬁnd the other agents with

the same properties. There exist numerous combi-

nations how intelligent agents can be partitioned into

similar properties and accordingly teams. The distri-

bution of agents to teams can be regarded as integer

partitions (Zoghbi and Stojmenovic, 1998). As an ex-

ample, the possible integer partitions of four are:

4 = 3 + 1 = 2+ 2 = 2+ 1+ 1 = 1 + 1 + 1+ 1 (1)

Thinking of four agents, they could all pertain to the

same team. Another possibility is that there is one

team of three agents and one singleton team and so

on. The possible partitions can be written as a set of

multisets:

{{(4, 1)}, {(3, 1), (1, 1)}, {(2, 2)},

{(2, 1), (1, 2)}, {(1, 4)}} (2)

More generally, the integer partitions for arbitrary nat-

ural numbers can be deﬁned as follows:

Deﬁnition 1 (Integer Partitions). Let N ⊂ N be a set

of natural numbers, let M = (N, m) be a multiset over

N with m : N → N

deﬁning the multiplicity of the

elements of N. M = (N, m) is a partition of s ∈ N if

∑

n∈N

n· m(n) = s. The set of all partitions of s into p

summands is

partitions(s, p)

(

(N, m)



∑

n∈N

m(n) = p∧

∑

n∈N

n· m(n) = s

)

TEAM FORMATION FOR AGENT COOPERATION IN LOGISTICS - Protocol Design and Complexity Analysis

401

The total set of all partitions of i is

partitions(s)

[

p=1

partitions(s, p)

Deﬁnition 1 is the foundation for examining the

possible partitions of integers into parts (van Lint and

Wilson, 1992) and agents into teams, respectively.

Fast algorithms exist that compute all possible inte-

ger partitions (Zoghbi and Stojmenovic, 1998).

3.2 Interaction Effort Analysis

As elaborated in Section 2.3, the asymptotic inter-

action complexity of the team formation protocol is

O(mn) = O(n

) from a coarse perspective. The ac-

tual interaction effort depends on two factors:

1. The total number of team managers

2. The times at which additional participants become

team managers

Every agent that joins the multiagent system contacts

all existing team managers to ﬁnd a matching team.

To determine the interaction effort for a particular

agent, one must thus ﬁnd out how many team man-

agers exist at its creation time. The question how

many agents in the multiagent system are team man-

agers at a certain point in time can be reformulated. It

is equivalent to the question to how many teams the

agents in the multiagent system pertain. The ques-

tions are interchangeable because the ﬁrst agent of

each team is the responsible team manager.

The question of the number of teams can be ap-

proached in two steps. Firstly, one must determine

the probability that an agent of a particular team has

already been created. Secondly, the resulting proba-

bility must be accumulated for all teams to get the to-

tal number of different teams existing. A foundation

for this investigation is the hypergeometric distribu-

tion (Bronshtein et al., 2004). It is deﬁned as follows:

Deﬁnition 2 (Hypergeometric Distribution). Let

A ∈ N be the size of the population, let T ≤ A ∈ N

be the number of successes in the population, let a ≤

A ∈ N be the number of draws, and let t ≤ A ∈ N be

the number of successful draws. The probability for t

given a, T, and A is

P(X = t)

= h(t |a, T, A) =





A−T

a−t







Let A denote the total number of agents. All

agents are numbered by a in the order of their cre-

ation. That is, a− 1 agents have been created before

agent a with 1 ≤ a ≤ A. Let T denote the number of

agents pertaining to a particular team. Based on Def-

inition 2, the probability that at least one member of

the team is in the total number of agents examined so

far can be derived as follows:

P(X > 0)

∑

t=1

h(t|a, T, A) = 1− h(0| a, T, A) (3)

Therewith, the question of the probability that at least

one agent of a team has already been created is an-

swered. The extension to all teams follows.

The respective partitioning of agents to teams, or

to properties to be more precise, can be considered an

integer partition (Deﬁnition 1). The respective parti-

tioning of all agents A is represented by the multiset

M = (N, m) ∈ partitions(A) (4)

Summing up the probabilities for the existence of in-

dividual teams (Equation 3) for all teams (Equation 4)

in the multiagent system reveals the number of al-

ready existing teams at the creation time of agent a:

f(a, (N, m), A)

∑

n∈N

m(n) ·



1− h(0| a, n, A)



(5)

To recapitulate, the number of teams corresponds to

the number of team managers agent a has to interact

with, i.e., it speciﬁes the expected interaction effort

of agent a. The total interaction effort of the whole

system until the creation of agent a can be derived

from Equation 5 as follows:

F(a, (N, m), A)

∑

i=1

f(i, (N, m), A) (6)

∑

i=1

∑

n∈N

m(n) ·



1− h(0| i, n, A)



4 CASE STUDY

A considerably high number of possible agent parti-

tions into teams exists. Hence, following the general

analysis of the interaction effort for team formation,

this section investigates a particular conﬁguration in

more detail. Out of the variety of possible partitions,

the case in which all teams have approximately the

same size is examined. This means that those parti-

tions M = (N, m) ∈ partitions(s) with the following

numbers of s agents into p teams are considered:

N =









(7)

The multiplicity m of the numbers of agents in M is:

m =





, p− (s mod p)







, s mod p



(8)

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

402

100

200

300

400

500

600

700

800

900

1000

Teams

600

100

200

300

400

500

700

800

900

1000

Agent

200

400

600

800

1000

1200

Interactions

200

400

600

800

1000

1200

Interactions

Figure 3: The number of interaction partners for participants in the team formation interaction protocol. The number of

interactions depends on the number of predecessors in the team formation process.

For the sake of understandability, the partition can

also be written as a sum. It corresponds to the fol-

lowing equation:

s =





· (p− (s mod p)) +





· (s mod p) (9)

Note that the remainder s mod p may be zero. Then,

the right element in the sets of Equations 7 and 8

is omitted. This is in accordance with Deﬁnition 1

which demands multiplicities to be positive. In this

case, all teams have the same number of agent mem-

bers. Otherwise, it holds that all teams have approxi-

mately the same number of agents, i. e., the difference

of the number of agents does not exceed one:

∀

∈N

− n

| ≤ 1 (10)

Figure 3 depicts Equation 5 for such average

teams for all 1 ≤ a ≤ A when varying the number of

teams 1 ≤ T ≤ A for a total of A = 1, 000 agents. Fig-

ure 4 shows the overall interaction effort for the same

team partitions investigated in Figure 3. Figures 3 and

4 have a different scale. The maximum interaction ef-

fort is 1, 000 for an individual agent and about half a

million for the whole system of 1, 000 agents.

5 PROTOCOL APPLICATION

The team formation interaction protocol is currently

applied in autonomous logistics applications, such as

autonomous onward carriage (Schuldt, 2010). In on-

ward carriage, containers arriving from overseas at

container terminals have to be transported to appro-

priate warehouses. In autonomous onward carriage,

intelligent shipping containers are expected to solve

this task on their own. To this end, they haveto choose

the warehouse based on their properties. For instance,

containers with valuable goods should choose a se-

cured warehouse. After having chosen a warehouse,

the containers must organise their transport by choos-

ing a means of transport out of truck, train, and barge.

The autonomous logistics approach has been im-

plemented with JADE (Bellifemine et al., 2007) and

validated with PlaSMA (Schuldt et al., 2008). For

evaluation purposes, real-world container data has

been provided by a major European retailer of con-

sumer products. Multiagent-based simulations with

over 11,500 shipping containers show that process

control can actually be delegated to autonomous lo-

gistics entities. In particular, it can be shown that

cooperation is advantageous in autonomous logistics

(Schuldt, 2010). Both choosing storage and trans-

port resources requires cooperation. Regarding stor-

age, containers with similar cargo should be received

in the same warehouse. This helps aggregating simi-

lar goods for subsequent distribution processes. Team

formation for this purpose requires establishing teams

based on descriptors for the articles loaded. Utilis-

ing means of mass transport requires cooperation by

shipping containers with same origin and destination.

Hence, spatial criteria have to be considered for this

purpose. This means that teams for allocating stor-

age and transport resources differ in this application

(Schuldt, 2010).

TEAM FORMATION FOR AGENT COOPERATION IN LOGISTICS - Protocol Design and Complexity Analysis

403

100000

200000

300000

400000

500000

600000

Interactions

100000

200000

300000

400000

500000

600000

Interactions

100

200

300

400

500

600

700

800

900

1000

Teams

600

100

200

300

400

500

700

800

900

1000

Agent

Figure 4: The total number of interactions for team formation. Depending on the number of teams, the interaction effort

ranges between linear and quadratic.

The simulation shows that the multiagent system

outperforms the previous approach in which humans

dispatch containers manually with support by infor-

mation systems. In particular, more relevant param-

eters can be considered, thereby increasing resource

utilisation efﬁciency for standard cases. Moreover,

being relieved from handling standard cases, human

dispatchers can solve exceptional cases which are not

covered by the multiagent systems more efﬁciently.

The thorough investigation of the interaction com-

plexity helped estimate the interaction effort even be-

fore deploying agents to an actual application. In par-

ticular, the interaction effort was estimated based on

previous container data. Therewith, it was possible to

decide that the exchanged messages can actually be

handled by the multiagent system and, thus, that au-

tonomous control is actually possible in this process.

6 CONCLUSIONS AND

OUTLOOK

This paper presents an interaction protocol for team

formation of autonomous logistics entities. The pro-

tocol satisﬁes the domain-speciﬁc requirements for

unique and ﬂexible teams, as well as genericness of

team descriptors. Furthermore, it demands only min-

imal prior knowledge about the system and is highly

decentralised. Therewith, it lays important founda-

tions for cooperation of autonomous logistics entities

which in turn increase the reactivity and robustness of

logistics process control.

The motivation for the new protocol as well as its

current application are in the ﬁeld of logistics. How-

ever, it is not restricted to logistics and can be applied

also in other areas with similar requirements. In terms

of the model for cooperation of intelligent agents, it is

particularly applicable whenever agents with similar

properties want to cooperate.

The interaction effort of the new protocol has been

derived analytically. This is an important prerequi-

site for estimating the effort and limitations for au-

tonomous control already before the actual deploy-

ment. A thorough analysis as provided in this paper is

necessary whenever the interaction effort is not obvi-

ous, e. g., if the number of participants changes over

time. Limitations of the protocol are reached when-

ever the interaction effort exceeds the capability of the

individual agents or the whole system. A solution for

such a case is to employ an interaction protocol with a

lower degree of decentralisation (Schuldt, 2010). An

alternative might be to restrict the number of partic-

ipants, for instance, based on spatial regions of rele-

vance (Gehrke, 2009).

ACKNOWLEDGEMENTS

The author should like to thank Hartmut Messer-

schmidt for helpful comments on the complexityanal-

ysis. This research is funded by the German Research

Foundation (DFG) within the Collaborative Research

Centre 637 “Autonomous Cooperating Logistic Pro-

cesses: A Paradigm Shift and its Limitations” (SFB

637) at the University of Bremen, Germany.

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

404

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