A Meta-heuristic based Multi-Agent Approach for Last Mile Delivery

Problem

Maram Hasan and Rajdeep Niyogi

Department of Computer Science and Engineering, Indian Institute of Technology Roorkee, Uttarakhand, India

Keywords:

Horizontal Collaboration, Multi-Agent System, Logistics, Last Mile Delivery Problem, Egalitarianism.

Abstract:

e-Commerce has become a primary part of any country’s economy, and seeking maximum efﬁciency and level

of service is an essential concern for any corporation in order to stay in business. Logistics has a signiﬁcant

impact on the efﬁciency of online transactions, especially with the increasingly competitive domain with min-

imal proﬁt margin-left. Thus, the collaboration between many logistics service providers (LSPs) at different

levels has become a desirable approach to reduce the overall costs and increase the utilization level of their

resources. In this work, we propose a domain-independent multi-agent framework that allows different LSPs

to plan their operations jointly. The system considers the individual satisfaction of LSPs and their proﬁts in an

egalitarian manner while trying to achieve an overall beneﬁt. We use different search strategies for every agent

as the underlying solving method, and investigate to what level taking the personal interest of participants will

affect the overall shared/ common goal.

1 INTRODUCTION

e-Commerce has grown remarkably over a short pe-

riod of time and become an essential part of the in-

dustry (Chatterjee et al., 2016). In order to guarantee

the success of an enterprise, companies need to pre-

serve their reputation and trust of their customers and

increase the quality of service they provide. In this

matter logistics, or what is called the Last Mile Deliv-

ery LMD, plays the most signiﬁcant role as it refers to

the last step in the supply chain (Holdorf and Haasis,

2014), in which the items are carried from the ful-

ﬁllment centers to the customers within the speciﬁed

delivery period. It forms the most important stage in

the purchase process as it adds up nearly to 30% of

the total cost. Thus, making this stage most effective

is a critical issue in e-commerce transactions (Chinh

et al., 2016).

Recently, all aspects of what is expected from lo-

gistics have changed, the competition became high,

and proﬁt margins declined to a deﬁcient level. This

urged many companies and carriers to collaborate

on different levels and form partnerships in order to

manage the transportation of their goods effectively

(Ouhader and El Kyal, 2017); horizontal collabora-

tion is a form of collaboration between parties that

belong to the same level of the supply chain (all car-

riers or all suppliers). Collaborative routing helps to

reduce the overall transport costs and to increase the

customer satisfaction and utilization level of the lo-

gistics and human resources. Hence, it provides bet-

ter performance from an economic and environmen-

tal perspective. For example, the collaboration be-

tween different LSPs can save them millions out of

the total travel costs by sharing the logistics resources

and thereby solving the empty load problem caused

by the large number of vehicles that travel long dis-

tances underutilized (Chinh et al., 2016). This, in

turn, reduces congestion levels on the roads, the pos-

sibility of accidents and harmful emissions, respec-

tively (Ouhader and El Kyal, 2017). Figure.1a shows

an example of independent routing of two LSPs in

LMD where every LSP has one deposit. Meanwhile,

Figure.1b shows a collaborative routing that utilizes

the resources of each LSP to deliver the packages of

all collaborators. It leads to overall shorter trips and

lower costs.

As the transportation ﬁeld is dynamic, complex

and consists of many features and constraints, it

makes the agent-based paradigm a quite suitable and

exciting research method to solve famous problems

in this ﬁeld (Martin et al., 2016). Multi-agent frame-

works are powerful in modeling complex problems

of distributed nature and can efﬁciently represent the

complicated relationship among the entities in an in-

dependent and autonomous way (Czarnowski et al.,

498

Hasan, M. and Niyogi, R.

A Meta-heuristic based Multi-Agent Approach for Last Mile Delivery Problem.

DOI: 10.5220/0009349004980505

In Proceedings of the 22nd International Conference on Enterprise Information Systems (ICEIS 2020) - Volume 1, pages 498-505

ISBN: 978-989-758-423-7

(a) Individual Routing (b) Collaborative Routing

Figure 1: Last mile delivery scenario of two LSPs.

2013). A multi-agent system consists of a set of en-

tities (agents) that interact with each other in some

environment through predeﬁned means of commu-

nication in order to accomplish some given goal(s)

(Czarnowski et al., 2013). Agent-based paradigm in-

creases the computational power and speeds up the

performance as it enables parallel task executions; co-

operation among the agents allows efﬁciency, reliabil-

ity, and robustness. Thus, it is ideal for solving differ-

ent complex optimization problems such as our last

mile delivery problem.

Since most researches on horizontal collaboration

focused solely on utilitarianism, which mainly gives

importance to overall beneﬁt (Cruijssen et al., 2007),

(Lahyani et al., 2015), and since real-life collabo-

rators mostly care about their proﬁts and interests

rather than the overall goal, our main contribution is

to consider the satisfaction of individual participants

in an equal manner and to investigate how this affects

the global goal of reducing costs. For this purpose,

we propose a domain-independent multi-agent frame-

work in which each LSP agent represents a collabo-

rator and manages a different search strategy to solve

the LMD problem from its perspective while cooper-

ating with other agents to combine and improve solu-

tions of all agents. This paper is organized as follows;

Section II presents a literature review of collabora-

tive and multi-agent approaches to the problem of last

mile delivery. Section III presents problem formation

while Section IV explains the proposed framework.

Section V discusses the results obtained; Section VI

states the conclusion reached.

2 LITERATURE REVIEW

LMD can be considered as a Vehicle Routing Prob-

lem (VRP), which is a signiﬁcant NP-hard that was

ﬁrst introduced in 1959 (Lahyani et al., 2015). It is

concerned with ﬁnding the most cost-effective set of

routes starting from a single distribution center to dif-

ferent customers spreading on a large geographic area

while satisfying constraints (Kumar and Panneersel-

vam, 2012). Different versions of the problem were

proposed in the literature under various complexities

and constraints; (Kumar and Panneerselvam, 2012)

and (Lahyani et al., 2015) present helpful surveys.

Various methods have been proposed by researchers

to solve the problem, starting with exact methods

(Mingozzi et al., 2013), and heuristics and meta-

heuristics that ﬁnd near-optimal solutions (Clarke and

Wright, 1964) to hybrid meta-heuristics such as hy-

bridized genetic algorithm (Cattaruzza et al., 2014).

2.1 Horizontal Collaboration

With the increasing market demands and high cus-

tomer expectations, horizontal collaborative routing

has been studied to provide efﬁcient routing with

lower total operational costs (Chinh et al., 2016). Dif-

ferent methods were presented through time starting

with centralized approaches where a centralized en-

tity solves the optimization problem on behalf of col-

laborating LSPs with different levels of coordination

(Chinh et al., 2016). However, in most cases, there

is less willing of different participants to share their

full customers’ details with a central authority; thus

decentralized approach was presented in the litera-

ture to provide more compatibility with these privacy

concerns such as request exchange and auction-based

methods. The work (Wang and Kopfer, 2015) pro-

posed two distributed request exchange mechanisms

to solve the dynamic routing problems to provided

stable performance. While in (Wang and Kopfer,

2014), a route-based exchange mechanism between

collaborating LSPs that do their own planning in-

dependently and then send the planned routs to a

groupage system (GS) which regenerates routes to

reduce the overall costs. Meanwhile, auction-based

trading is presented in (Dai and Chen, 2011) to al-

A Meta-heuristic based Multi-Agent Approach for Last Mile Delivery Problem

499

low the participating LSPs to negotiate and express

their preference and the proﬁt margin in a multi-round

fashion. Another auction-based clustering method

was proposed in (Schwind et al., 2009), where a re-

quest is exported based on its cost-reduction prob-

ability using a convex hull method with a distance-

based cost estimator. Meanwhile, our proposed

method is decentralized and allows LSPs to jointly

plan their pre-deﬁned outsourcing requests and con-

tinuously exchange existing solutions between com-

puting agents to improve the ﬁnal solution.

As the works mentioned above considered achieving

a global goal of reducing overall cost, other work

in (Zhou et al., 2013) focuses on load balancing in

terms of the tour distance among the moving vehicle

as a global goal; wherein (Schwarze and Voß, 2013),

they examined effective resource utilization using a

minmax model to minimize the maximal vehicle trip

length. In our work, we consider the satisfaction of in-

dividual participants in an equal manner while achiev-

ing total cost reduction.

2.2 Agent-based Approaches

Agent-based systems have contributed to collabora-

tive routing solving because of its autonomous, dis-

tributed characteristics and its native support for a dy-

namic environment (Czarnowski et al., 2013). Several

domain-speciﬁc multi-agent architectures were pro-

posed in the literature, such as in (Baykaso

glu and

Kaplano

glu, 2015), where the architecture of three

types of agents (order, truck, dispatcher) was pro-

posed to obtain effective scheduling under dynamic

environment’s conditions through negotiation. Also,

in (Kalina et al., 2015), they provided a multi-agent

system consists of a set of customer agents, route

agents, and a central planner. The planner used a lo-

cal heuristic search to solve the routing problem with

time windows. In contraction, our work will not be

dedicated only to LMD domain as our agents will

be optimizing agents that able to work on any opti-

mization problem. An example of earlier population-

based, cooperative multi-agent system was proposed

in (Barbucha, 2014); where a multi-phase execution

is carried out and different search meta-heuristics

are executed at each phase simultaneously while ex-

changing information about the agents’ states and per-

formance at the end of each phase. In (Martin et al.,

2016), they proposed a general multi-agent approach

where agents periodically exchange parts of their so-

lutions that have potentials to be good edges to guide

the search of other agents in a valuable direction.

Also, the work (Chatterjee et al., 2016) included pub-

lic transportation system in their multi-agent frame-

work to plan small-size orders delivery in aim to re-

duce costs and co

emissions.

The work in (Barbucha, 2012) used different syn-

chronization modes in their proposed multi-agent sys-

tem, and used a learning mechanism to adapt the be-

havior of the agents to new states of the environment

while solving the optimization problem. Meanwhile,

the work (Souza et al., 2012) used particle swarm op-

timization (PSO), where each particle is considered

as autonomous agents and represented as a solution

in the search space. Otherwise, our proposed multi-

agent framework consists of a group of optimization

agents exploring different areas of the search space

simultaneously, producing a higher level of diversity

and mature solutions.

Although collaborative routing has been studied

in past years, there are fewer studies in the literature

as far as we know that use a multi-agent paradigm

to solve a multi-deposit VRP version that considers

the personal interests of participants in an equal man-

ner along with a global goal. The main contributions

are as follows; we implement a multi-agent frame-

work that supports the collaboration between differ-

ent LSPs to serve their customers jointly. Our frame-

work is domain-independent, which can be used to

solve any optimization problem in contrast to (Bayka-

glu and Kaplano

glu, 2015), (Kalina et al., 2015).

Agents will regularly exchange the best solutions

among themselves to combine and improve the solu-

tions.

3 PROBLEM DEFINITION

Last Mile Delivery Problem can be presented as a ve-

hicle routing problem. It aims to create a set of paths

to satisfy the delivery of n packages, from distribu-

tion center (s) to speciﬁed delivery locations satis-

fying some constraints ex. capacity and time, while

minimizing a cost function. Each Logistic Service

Provider LSP has a set of distribution centers DCs

which contains numerous different-size packages to

be distributed to many geographically scattered cus-

tomers within a city. Each package has a weight de-

mand Dem

. A distribution center has a set of vehi-

cles V used to complete the delivery tasks, each of

these vehicles v ∈ V has a capacity Q

that specify the

maximum load a vehicle can carry at once.

Here we present the notations of the problem;

given a undirected graph G=< V,E >, the set of ver-

tices V represents the customers, and the set of edges

E determines the existence of a direct road between

the adjacent customers; D: set of distribution cen-

ters D = {1, 2,3,... ,m}; C: set of customers C =

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{1,2, 3,. .., n}; K is the total count of vehicles exist-

ing in all of the distribution center.

sets of vehicles presented in the distri-

bution center DC.

i j

euclidean distance between customer i

& j.

MaxDis

maximum length of a tour a vehicle

can do.

i j

current weight of vehicle k while

traversing from customer i to j.

i j

time consumed by the vehicle k to tra-

verse from customer i to j.

[ET

,LT

] : time window of package i.

earliest time at which a package i can

be delivered to its owner.

latest time at which a package i is al-

lowed to be delivered to its owner.

service time needed to deliver the

package to the customer i by the ve-

hicle k.

: arrival time to customer i.

: leaving time from the customer i.

: ﬁxed cost of the vehicle v.

VarC

variable cost of a vehicle v within a

distance unit (ex: power supply cost).

i j

represent a decision variable.

i j











1, if a vehicle m of a distribution center k

can travel directly from i to j.

0, otherwise

(1)

3.1 The Objective Function

1. Minimize the cost of the tour

∑

k∈V

∑

j∈D∪C

∑

i∈D∪C

∗ x

i j

∑

k∈V

∑

j∈D∪C

∑

i∈D∪C

i j

∗ x

i j

∗VarC

(2)

Subject to these constraints:

(a) Maximum Distance Constraint: the length of

the tour taken by a vehicle can not exceed the

maximum length tour that is speciﬁed for it

(due to the fuel or energy supply)

∑

j∈D∪C

∑

i∈D∪C

i j

∗ x

i j

≤ MaxDis

(k ∈ V

,m ∈ D)

(3)

(b) Capacity Constraints:

the load of any vehicle k traversing from a cus-

tomer i to j can not exceed the maximum capac-

ity of that vehicle.

0 ≤ y

i j

≤ Q

(k ∈ V

,m ∈ D,i, j ∈ C) (4)

usually attached with a time window [ET

,LT

]

that specify the time period in which the cus-

tomer i is expecting to receive his package, not

before the earliest time ET

or after the latest

time LT

. We can conclude with it the follow-

ing information The arrival time A

to customer

j from i.

= D

i j

(5)

The departure time D

from customer i

= A

+ S

(6)

We should attain the following constraints

≤ A

≤ LT

∀(i ∈ C,k ∈ V

)

≤ S

+ A

≤ LT

∀(i ∈ C,k ∈ V

)

≤ LT

+ S

∀( j ∈ C,k ∈ V

) (7)

(d) Precedence Constraints: in case of multi de-

posit scenarios, we need to guarantee that a cus-

tomer will not be visited before his provider:

≤ D

(s ∈ D,d ∈ C) (8)

(e) Each customer can be served by single vehicle

only

∑

m∈D

∑

k∈V

∑

i∈D∪C

i j

= 1 ∀ j ∈ C (9)

(f) The tour of each vehicle must start from a dis-

tribution center and ﬁnish at the same center.

∑

i∈D∪C

i j

= 1 ∀ ( j,m ∈ C,k ∈ V

) (10)

(g) Path Contentiousness: every vehicle must leave

a customer location only after reaching and

serving that customer.

∑

i∈D∪C

∑

j∈D∪C

q j

∀ ( q ∈ D∪C, m ∈ D,

k ∈ V

) (11)

2. Penalty for the Undelivered Packages: it is re-

quired that all packages get delivered, we use a

penalty for undelivered packages. We express the

penalty through the package’s priority prio(m).

∑

prio(m) ∀ (m not delivered successfully )

(12)

So, the ﬁnal objective function is to minimize

α ∗

∑

k∈V

∑

j∈D∪C

∑

i∈D∪C

∗ x

i j

∑

k∈V

∑

j∈D∪C

∑

i∈D∪C

i j

∗ x

i j

∗VarC

+ β ∗

∑

prio(m) ∀ (m not delivered ) (13)

Where α, β, are weight constants to weightage the

function’s value are in the overall objective func-

tion.

A Meta-heuristic based Multi-Agent Approach for Last Mile Delivery Problem

501

4 PROPOSED MULTI-AGENT

FRAMEWORK

Multi-agent approach provides speedup and compu-

tation efﬁciency as it supports exploring different

areas of the search space simultaneously, produc-

ing a higher level of diversity and mature solutions

(Czarnowski et al., 2013).

One of the important multi-agent paradigms is A-

Team (Asynchronous Team) that was ﬁrst proposed

in (Talukdar et al., 2003) that describes a set of asyn-

chronous independent software agents that communi-

cate to jointly solve complex problems that can not be

solved by single agent alone. A central memory stores

a population of initial solutions that will be continu-

ously modiﬁed by the software agents.

We will build the proposed distributed framework

based on A-Team architecture. It consists of two

types of agents, computing agents, each of which

represents a logistic service provider and can run

on any machine, and a coordinator agent, which

is responsible for maintaining the central memory,

and managing the communication between comput-

ing agents. Figure.2 shows the architecture of our

proposed framework. Now we discuss the types of

agents included.

4.1 Types of Agents

1. The Coordinator Agent:

It is a single agent in the proposed architecture

that manages a pool of initial valid solutions to the

collaborative problem. It receives requests from

every participating LSP agent to send it a subset

of the available solutions to use it as initial solu-

tions in its computation method. The coordinator

agent is considered a synchronizing entity in the

Figure 2: A-Team based multi-agent framework for LMD

problem.

system since it manages the communication be-

tween different LSPs agents and is kept up to date

about their latest status through message passing.

2. Logistic Service Provider Agent LSP:

Each logistic provider is represented in the

problem-solving process by an LSP agent that op-

erates on their behalf. The LSP agents do not in-

teract together directly; they exchange informa-

tion about their state and found solutions through

the coordinator agent. In this work, every LSP

agent runs a meta-heuristic strategy that is dif-

ferent from the other agents and solves the given

problem instance from its perspective and accord-

ing to its personal priorities and goals, such as fol-

lowing potential SLA agreement. LSP agent ﬁnds

the best solution and delivers it to the coordina-

tor agent to be evaluated and possibly added to

its pool of solutions replacing the worse existing

solutions there. The coordinator may then resend

the solution to other LSP agents in the next com-

putation round in order to redirect their search to

a potentially better region.

4.2 Communication between Agents

1. 2-way Handshake:

Before starting the computations, every LSP

agent registers itself with the coordinator to en-

able sending and receiving computation messages

from the coordinator. This process starts with a

SUBSCRIBE message sent by LSP agent to the

coordinator, indicating that it is ready to partici-

pate in the computation and start its tasks. Then,

the coordinator registers the LSP in the coali-

tion and sends back a CONFIRM message to

the LSP agent so it can be prepared to the next

phase, the message contains the expected num-

ber of computation rounds that every LSP shall

execute. Once the coordinator agent successfully

receives the SUBSCRIBE message from all ex-

pected LSPs agents, the computation rounds start.

Figure 3 shows the sequence of messages between

the agents in the handshake phase.

2. Computation Messages:

After all LSPs have registered with the coordina-

tor, the coordinator initializes a collection of ran-

dom feasible solutions to the collaborative prob-

lem. Periodically, every LSP agent sends a RE-

QUEST message to the coordinator asking for a

subset of the solutions from its pool, so the agent

uses it as initial solutions in its solving method.

The coordinator reply with an INFORM message

containing a random subset of solutions. After

receiving the initial solutions by the LSP agent,

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Figure 3: Message exchange between different agents in the

2-way Handshake stage.

it starts running its search strategy to ﬁnd the

best possible solution. When the search ends, the

LSP agent sends the best solution as an INFORM

message to the coordinator, which in turn com-

pares the solution’s quality, in terms of overall

cost-minimizing, to the existing solutions in the

pool. If its quality is better, the new solution is

added to the pool, replacing a less quality solu-

tion. Figure.4 shows messages exchange between

the agents in the computation phase.

4.3 Search Strategies

Different search strategies for every agent are carried

out in the proposed approach. Each LSP agent uses an

adaptive large neighborhood search method (ALNS)

as the underlying search method (Pisinger and Ropke,

2007). ALNS is a local search that is based on ruin

and recreate principle that was proposed in(Schrimpf

et al., 2000). It uses optimization techniques like

threshold accepting and simulated annealing to par-

tially destroy and repair the solutions. There are sev-

eral strategies for the ruin phase, namely, radial ruin,

random ruin, and cluster ruin (Pisinger and Ropke,

2007). A feasible solution is obtained by excluding a

set of customers. In the recreate phase, all excluded

customers are reintroduced to the solution wisely to

minimize their effect on the complete solution. Some

of the most widely used techniques are greedy and re-

gret insertion methods.

4.4 Gain Assignment

In real-life collaboration, participants of any coali-

tion mostly care about their proﬁts and interests rather

than the overall gain. Therefore it is crucial to esti-

mate the individual gain for every participant in the

Figure 4: Messages exchange between different agents in

the computation phase.

coalition. In this paper, we will use two gain assign-

ment methods. The ﬁrst method is the Shapley value,

which is a concept that was ﬁrst presented in coopera-

tive game theory as one way to distribute the total gain

of a coalition N among the participants in a fair man-

ner. It captures the marginal contribution made by a

participant i over all permutation S ⊆ N (Ouhader and

El Kyal, 2017).

(i) =

∑

S⊆N\{i}

k ∗ (cost(S ∪ i) − cost(S)) (14)

Another method is a proportional method, a demand-

based proportional gain assignment that depends on

the demands of the participant served by the coalition.

Let cost(s) be the cost of the best solution found by

given coalition s. Then, the proportional assignment

of the participate i is given as :

cost(i) = ϕ

∗ cost(s) (15)

where ϕ

is the demand-based factor.

We explore two collaborative scenarios. First, we

consider a full collaboration level where the goal is

to achieve the minimum cost possible.

Table 1: Characteristics of participating LSPs and the costs

of non-collaborative routing.

No.of

orders

No. of

vehicles

Dem-

ands

Individual

routing

Cost

No. of

vehicle

LSP1 82 13 3591 2469.3 9

LSP2 90 13 4478 2644.4 10

LSP3 77 13 4037 2467.6 9

Total 249 39 12106 7581.3 28

Whereas in the second scenario, personalized collabo-

ration is considered as every LSP agent works accord-

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Table 2: Cost reduction in collaborative scenarios and the satisfaction level of the participants.

Best solution Overall reduction Individual satisfaction

Cost

No. of

vehicle

Cost

No. of

vehicle

LSP1 LSP2 LSP3

Full collaboration 4142.1 26 45.3% 7.1% 5.0 6.0 5.5

Personalized collaboration 4588.9 26 39.5% 7.1% 5.67 5.7 5.4

Table 3: The routing cost allocation of LSPs under collaborative scenarios.

Best solution Cost share / Shapley value Proportional cost

Total cost

No. of

vehicle

LSP1 LSP2 LSP3 LSP1 LSP2 LSP3

Full collaboration 4142.1 26 1312.0 1419.7 1410 1228.6 1532.1 1381.2

Personalized collaboration 4588.9 26 1465.1 1539.6 1577.5 1361.2 1697.4 1530.2

ing to its personal goals while minimizing the over-

all cost. We take, as an example of LSP’s personal

goal, its desire to serve its own packages ﬁrst before

the others. To measure the satisfaction level of every

participant, we use the average index of its packages’

delivery in the found routes. The smaller the value

is, it indicates that its packages are often delivered in

the early stage with a minimum value of 1 when its

packages are delivered ﬁrst by every vehicle.

5 EXPERIMENTS AND RESULTS

To implement our proposed architecture, we used

JADE framework (Java Agent DEvelopment), which

supports FIPA speciﬁcations. We created a system

consisting of one coordinator agent and three LSP

agents representing three different logistics service

providers in the industry. In our experiment, ALNS

algorithm is used as the primary method, along with

different ruin and recreate strategies for every LSP

agent. LSP1 agent uses ALNS with random ruin strat-

egy and regret/best insertion, LSP2 agent uses radial

ruin strategy, and regret insertion, while LSP3 uses

cluster ruin strategy and regret/best insertion. The co-

ordinator agent maintains a pool of 20 initial solutions

which will be continuously updated. We consider

a multi-depot vehicle routing problem MDVRP; we

use a dataset derived from famous Cordeau datasets

(Cordeau et al., 1997) with few adjustments to ﬁt

the collaborative scenario. We will evaluate the pro-

posed approach based on its performance in solving

this problem.

Table.1 shows the characteristics of partici-

pating LSPs and the cost and vehicles needed for

their individual routing, where every LSP uses its

resources to serve its own customers only with

no collaboration. Table.2 shows the cost of the

best solution for collaborative routing scenarios

using our proposed framework. We calculate the

overall cost reduction of collective routing as the

marginal percentage of (Total Cost

no_collaboration

−

Total Cost

collaboration

)/ Total Cost

no_collaboration

∗

100. Thus, we found that full collaboration between

LSPs reduced the total costs of a margin of 45%

with an almost varied level of satisfaction for the

participants in terms of the average index of delivered

packages since the overall cost reduction was the

only goal. In the second scenario, when considering

personal goals and interests, a decrease in total sav-

ings is observed compared to the ﬁrst scenario, along

with an increase in participants’ satisfaction levels to

almost equal value as every agent works to achieve its

personal goal ﬁrst. Table.3 shows the cost allocation

for every participant LSP in both collaboration

scenarios calculated by methods mentioned in Eq.14

and Eq.15 respectively. The overall results show that

participants’ satisfaction levels can be increased by

tolerating some loss in proﬁts.

6 CONCLUSIONS

We have presented a multi-agent framework that sup-

ports the collaboration between different LSPs in

the logistics level serving their customers jointly.

The proposed framework is domain-independent and

can be used for different cooperation scenarios in

problem-solving. Furthermore, it is computationally

efﬁcient and scales to large size problems as it ex-

ploits exploring different areas of the search space si-

multaneously, and produce diverse and mature solu-

tions. When the overall beneﬁt is prioritized, some

unintended biases to one of the participants may hap-

pen, and that will affect the trust in the coalition.

Therefore, we examined when participants work to

achieve objectives according to their preferences in-

stead of focusing on the uniﬁed objective. We no-

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ticed that collaboration could achieve a cost reduction

of near 45% compared with individual routing, along

with different satisfaction levels. However, when per-

sonalized goals are considered, the overall saving is

comparatively reduced, but better levels of satisfac-

tion are obtained. Therefore, considering the egali-

tarian approach that guarantees an equal level of ser-

vice and satisfaction may encourage different LSPs to

work towards further collaboration on several levels.

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