Optimal Decision Making in Agent-based Autonomous Groupage Trafﬁc

Stefan Edelkamp and Max Gath

Center for Computing and Communication Technologies, Institute for Artiﬁcial Intelligence,

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

Keywords:

Operations Research, Decision Making, Multiagent Simulation, Asymmetric TSP, Logistic Processes.

Abstract:

The dynamics and complexity of planning and scheduling processes in groupage trafﬁc require efﬁcient, proac-

tive, and reactive system behavior to improve the service quality while ensuring time and cost efﬁcient trans-

portation. We implemented a multiagent-system to emerge an adequate system behavior and focus on the

decision making processes of agents that is based on the Traveling Salesman Problem (TSP) with aspects like

contract time windows, individual restricted capacities of trucks, premium services and varying priorities of

dynamically incoming orders. We present an optimal depth-ﬁrst branch-and-bound asymmetric TSP solver

with constraints on tour feasibility and depot reachability at any step of the process. To evaluate our approach,

we use established benchmarks as well as its inclusion in a real-life multiagent-based simulation. Simulated

scenarios are based on real customer orders of our industrial partner Hellmann Worldwide Logistics GmbH &

Co. KG and are applied on real world infrastructures. The results reveal that efﬁcient optimal decision making

in multiagent systems increases the service quality and meets the requirements and challenges in logistics.

1 INTRODUCTION

In this paper we present an approach to optimize the

planning and controlling processes in groupage traf-

ﬁc to improve the service quality while ensuring cost-

and time-efﬁcient transport processes. To meet the

high requirements on complexity and dynamics, we

implemented a multiagent system to ensure a ﬂexible

system behavior and developed efﬁcient, optimal de-

cision making algorithms for participating agents.

In transport logistics the decision making often re-

lies on efﬁcient solutions to the Traveling Salesman

Problem (TSP), a touchstone for many general ap-

proaches in combinatorial optimization. In our ap-

plication of a forwarding agency, the TSPs are gen-

erated via shortest paths reductions of route networks

between pickup or delivery stops. Each order to be

served corresponds to one city in the TSP. Symmet-

ric TSPs (STSPs), for which edges cost are the same

in both directions, are usually optimally solved with

algorithms relying on the quality of the Held-Karp

lower bound (Johnson et al., 1996).

Due to one-way streets in this paper we consider

Asymmetric TSPs (ATSPs), where other bounds ap-

ply (Miller and Pekny, 1991; Karp and Steele, 1990).

Most of them consider the solution of the according

Assignment Problem (AP), which can be solved by the

Hungarian algorithm or reﬁned approaches (Jonker

and Volgenant, 1986), followed by some tour patch-

ing strategies. ATSPs can be converted into STSPs,

but this requires doubling the number of cities. Em-

pirical TSP exploration results often partially refer to

the 8th DIMACS Challenge. As an example, depth-

ﬁrst branch-and-bound (DFBnB) has been reﬁned for

the TSP (Zhang, 2000).

Many additional constraints apply in practice. Be-

sides capacity and time constraints we have a cer-

tain mix of pick-up and backhaul and premium ser-

vices constraints to be served in the tour, while oth-

ers non-premium services are optional (but should

be maximized). We also consider TSPs with de-

livery and backhauls (Gendreau et al., 1996); not

to be mixed with delivery and pick-up (Anily and

Mosheiov, 1994). For the TSP with release and due

time window constraints (TSPTW), exact dynamic-

programming algorithms exploit elimination tests to

reduce the state space (Dumas et al., 1995). Vari-

ants can also be applied to TSPTW problems with

precedence constraints. Frequently, branch-and-cut

algorithms are the method of choice (Ascheuer et al.,

2001). Introducing capacities constraints links to con-

straint solving. With the mix of premium and non-

premium tasks we generate a preference problem that

includes a combination of hard and soft constraints.

Determining the optimal solution for the vehicle rout-

ing problems (Baldacci et al., 2012) with capacity,

248

Edelkamp S. and Gath M..

Optimal Decision Making in Agent-based Autonomous Groupage Trafﬁc.

DOI: 10.5220/0004256702480254

In Proceedings of the 5th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2013), pages 248-254

ISBN: 978-989-8565-38-9

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

time and premium services constraints, backhauling

and dynamic change becomes practically intractable.

2 DISPATCHING IN GROUPAGE

TRAFFIC

In groupage trafﬁc, several orders to different desti-

nations with less-than-truckload (LTL) shipments are

served by the same truck to decrease total cost. In

pickup tours, trucks transport loads from their origin

to a local depot where the shipments are consolidated

to build economical loads. Through LTL networks the

load is transported to a depot in the destination area

where each good is delivered to its ﬁnal destination.

The process planning complexity is even increased by

individual qualities of shipments like weight, volume,

priority, and value. Handling the complexity is ag-

gregated by the high degree of dynamics that result

also from unexpected events, such as an exact amount

and properties of incoming shipments are not known

in advance.

Quality of service is an important factor to suc-

ceed the economic objectives. The transportation of

so-called premium services must be guaranteed with

respect to their time windows while considering other

hard constraints, e.g., the capacity of vehicles. In or-

der to increase service quality through short transit

times and reliable deliveries it is mandatory to handle

the high degree of dynamics and complexity of logis-

tic processes with adaptive, reactive system behavior.

By delegating the planning and controlling pro-

cesses from central decision making systems to de-

centralized entities, e.g., agents that represent vehi-

cles, the overall problem is split into smaller problem

instances that can be solved optimally. Regarding the

dispatching processes each vehicle has to ﬁnd a tour

with minimum costs, such that each pickup and deliv-

ery stop is visited exactly once and the tour returns to

a central depot. This problem can be described by a

TSP with stops i, i ∈ {1,2,.. .,n}. All distances be-

tween two stops i and j given by c

i, j

∈ R with c

i,i

= 0

for 1 ≤ i, j ≤ n. Feasible solutions are permutations

of (1,2,. .., n) with the additional constraint that the

ﬁrst city to visit is the current position of the truck and

the last city is the depot. Real transport infrastructures

are commonly represented by directed graphs, so that

we search an optimal tour for an ATSP.

In logistic transport networks participating for-

warding agencies have to pay high amounts of penalty

if they are not fulﬁlling the agreed commitments.

Therefore, we distinguish hard premium service con-

strains that must be delivered on date of receipt and

soft non-premium services constraints that can be de-

layed by up to 2 days.

Deﬁnition 1. Pickup and delivery of premium ser-

vices is mandatory and deﬁned by



1, if i is a premium stop

0, otherwise

(1)

Hence, the priority of premium stops is higher

than visiting other stops.

Deﬁnition 2. The optimal tour of the asymmetric TSP

must be feasible and fulﬁll the following requirements

ordered by their priorities for the variables

i, j



1, if (i, j) is part of the tour

0, else

(2)

1. Maximize the number of transported premium ser-

vices: max

∑

i=1

∑

j=1

· x

i, j

2. Maximize the number of visited stops:

max

∑

i=1

∑

j=1

i, j

3. Minimize the total cost of the path:

min

∑

j=1

∑

i=1

i, j

· x

i, j

subject to

(a)

∑

i=1

i, j

= 1 for all j ∈ {1,... ,n}

(b)

∑

j=1

i, j

= 1 for all i ∈ {1,. .., n}

i, j

{

0,1

}

for all j,i ∈ {1,... ,n}

(d)

∑

j∈S

∑

i∈S

i, j

≤ |S| −1 for all S ≤

{

1,.. .,n

}

We assume that all premium stops have to be tra-

versed such that we have to ﬁnd the tour with min-

imum costs that includes all premium services and

the maximum number of stops while satisfying all

time and capacity constraints. Therefore, the problem

changed into a maximizing-minimizing problem.

3 CONSTRAINT ATSP SOLVING

To apply Branch-and-bound (BnB), we extend depth-

ﬁrst search (DFS) with upper and lower bounds. To

determine lower bounds for the ATSP, we transform it

into the Assignment Problem (AP), that can be solved

with the Hungarian algorithm (Jonker and Volgenant,

1986) in O(n

). While the AP is a relaxation of the

asymmetric TSP, it can be used as heuristic function

for the ATSP. In order to solve the AP, we extend

the cost matrix with the distance from the depot to

the current node (we want to return to the central de-

pot which is not necessary the starting point). After

solving the AP, we subtract it to compute the current

lower bound. For increasing the upper bound (which

is the sum of the weights in the subgraphs) we de-

termine the minimum value to merge the subgraphs

of the AP by comparing the respective columns and

rows in the cost matrix and choosing the arcs with

minimum costs.

OptimalDecisionMakinginAgent-basedAutonomousGroupageTraffic

249

An initial upper bound can be obtained by con-

structing any solution, e.g., established by a greedy

approach. Unfortunately, for lager TSPs the branch-

ing process consumes a lot of time to determine a

greedy solution. Therefore, we additionally computed

the upper bound U at each node by applying Karp-

Steel patching (Karp and Steele, 1990). As with stan-

dard DFS, the ﬁrst solution obtained might not be op-

timal. With depth-ﬁrst BnB (DFBnB), however, the

solution quality improves over time together with the

global value U until eventually the lower bound L(u)

at some node u is equal to U. In this case an optimal

solution has been found, and the search terminates.

A Constraint ATSP is an ATSP in which addi-

tional state constraints are applied. As states are only

discarded from the search that do not fulﬁll the con-

straints. This weakens but does not invalidate the

lower bound. For example time and capacity con-

straints as well as priorities have to be satisﬁed.

For time constraints, the due date d

for latest

pickup (or delivery) at each stop i ∈ {1, ... ,n} has to

be met. Each stop may require additional individual

processing time δ

(e.g., for loading), which can be

compiled away (the solution value then changes by

∑

i=1

). In some cases, release date r

, i ∈ {1,. .., n}

are given, at which the order at stop i becomes issued.

If the arrival is too early, we have to wait for time β

For the TSPTW we choose the next time for

traversing the edges to be minimized rather than the

total time, which, nonetheless, is progressed for adap-

tion to release and checking with due dates. The travel

time between stops π

and π

on tour π is denoted by

i, j

, i, j ∈ {1,. .., n}. Additional capacity constraints

for the vehicle yield a Capacitated TSP (CTSP).

Deﬁnition 3. Let w

be the freight weight at stop i

and ∆

be the max. weight of the vehicle. A tour π

with stops

{

,.. .,π

}

and depot d is feasible for the

CTSPTW if for all i = 1,2,. .., n we have

∑

l=1

(α

i−1,i

) ≤ d

∑

l=1

≤ ∆

, and d = π

The pseudo-code is shown in Alg. 1. The proce-

dure is invoked with the number of cities n the depot

d, cost 0 and upper bound U set to some reasonable

estimate (U can obtained using some heuristics; the

lower it is, the better the pruning, but in case no upper

bound is known, it is safe to set U to ∞). The tour

is maintained globally and updated during backtrack-

ing. Another global variable best keeps track of the

actual solution path. DFBnB sorts the set of succes-

sors according to increasing L-values is an optional

reﬁnement to the algorithm that often aids in acceler-

ating the search for ﬁnding an early solution.

Release and due dates in TSPTWs induce a prece-

dence relationship at each city. The relationship im-

plies a partial ordering, so that a city can be selected

Algorithm 1: DFBnB for Constraint TSPs.

DFBnB(n,u,g,U)

tour

depth(u)

← u

if (depth(u) = n − 1)

if (g + c

u,d

< U)

best ← tour; U ← g + c

u,d

else

for each v

in nextcities(u)

if Constraint(v

)

if (g + h(v

) < U)

call DFSBnB(n,v

,g + c

u,v

,U)

as a successor of city only if it does not violate the

imposed ordering. Given a bitvector of cities visited

so far the subsumption check for precedence can be

executed by native Boolean operations in O(1). Simi-

larly, premium services are checked on the word level.

Theorem 1. Alg. 1 is optimal for admissible lower

bounds, and the above pruning rules.

Proof. If no pruning was taking place, every pos-

sible solution would be generated, so that the optimal

solution would eventually be found. Sorting of chil-

dren according to the L-values has no inﬂuence on the

algorithm’s completeness. The condition L(v

) < U

conﬁrms that the node’s lower bound is smaller than

the global upper bound. Otherwise, the search tree is

pruned, as for admissible weight functions exploring

the subtree cannot lead to better solutions than the one

stored with U. All further pruning rules (like prece-

dence or premium service pruning), cut off infeasible

branches from the search tree so that the solution will

be optimal for the TSP. Precedence pruning retains

optimality for the TSPTW, while capacity pruning re-

tains optimal for CTSP, etc. 

With h

we deﬁne the heuristic that is derived

from solving AP. The Hungarian algorithm for com-

puting the solution as well as lower bound off-

sets based on the tour being Hamiltonian takes time

O(n

). It can be incrementally be computed in O(n

but bookkeeping becomes involved. With h

we de-

ﬁne the heuristic that is deﬁned as the sum of the

column minima in the distance matrix. If cities are

visited, column minima are subtracted from the sum.

The travel distance back to the depot is added on top.

We compute h

incrementally in O(1) time and space.

Let u be the successor of v, and m

be the precom-

puted minima of columns i, i = {1,.. .,n} in distance

matrix D. Moreover, let the heuristic value of the de-

pot d be deﬁned as h

(d) =

∑

i=1

d,i

. For each ex-

panded node u we compute h

= h(u) − m

if u = d,

and h

= h(u) − c

u,d

, otherwise. For each generated

successor v of u we have h

(v) = h

− m

+ c

v,d

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

250

An advantage of the tree structure is that the con-

straints are checked in constant time and space. The

current time, capacity and premium service informa-

tion are stored at each node. Considering the time

efﬁciency of the algorithm, bit-vectors are realized

by one computer word: we have bit-vectors for the

visited cities, the relative ordering among them im-

posed by the time window, and the priority service

constraints. All bit-vector operations (setting, clear-

ing of bits, check for subsumption) run in O(1).

Theorem 2. Let w be the word width of the computer.

The incremental solver for the asymmetric TSP with

time windows, capacity, and premium service con-

straints and heuristic h

runs in O(n/w) per node.

It allocates O((n/w) · n

) space in its initialization

phase and no more memory during the search.

Proof. The space consumed for the distance ma-

trices as well as their compression and copies is

O(n

). The matrices for successor reordering and ﬁl-

tering take O(n

) and each state on the stack requires

O(n/w) space. As the stack is limited by the depth

times the number of successor, its memory needs

are also bounded by O((n/w) · n

). All other struc-

tures (tour covers, interval sizes, row and column cov-

ers and minima, partial ordering bitvectors, successor

sets, and visited ﬂags) take at most O(n) space. 

To determine the optimal solution for a TSP with

premium services we have to extend the algorithm.

All premium stops must be traversed so that we have

to ﬁnd the tour with min. costs that includes all pre-

mium services and the max. number of stops while

satisfying all time and capacity constraints. There-

fore, the problem changed into a max.-min. prob-

lem and branching is not applicable by comparing

the costs to the lower bound L. We have to ﬁnd a

feasible solution that includes all premium services

within max. search tree depth and the shortest dis-

tance within that depth.

To speed up search for a ﬁrst solution in depth

n − 1, the computation of lower bounds is disabled

and a subtree is cut if the current tour is not a fea-

sible tour. The following rule prunes the tree using

bitvectors and Boolean operations. Before starting the

search, the premium services are sorted by their ca-

pacities. The number of premium services included

in the best solution is saved and updated if a bet-

ter solution is found. Next, we compute the differ-

ence ∆ between the number of currently included pre-

mium services and the amount of premium services

in the best-known solution. Afterwards, the weight of

∆ lightest not considered premium services is accu-

mulated and we check if they exceed the maximum

capacity of the truck. The solution remains optimal

and complete because a feasible solution with more

premium services exists. The pruning rule is applied

to regular orders accordingly if all premium services

are included within the tour. The application of this

pruning rule is optional, because it is done in O(∆)

time (for summing up the weight of not considered

orders). Nevertheless, it speeds up the algorithm if

good solutions are known in advance, the maximum

capacity of the truck is reached, and no more orders

can be operated. In this case big subtrees are pruned

early. If we ﬁnd a ﬁrst feasible complete tour objec-

tives 1. and 2. in Def. 2 are fulﬁlled. The remaining

objective is to reduce the total cost and the problem

has changed to a classical TSP with constraints. As

a result, the computation of lower and upper bounds

described above is activated. In this case, less nodes

are expanded because the searching process is goal-

directed. If heuristic h

instead of h

is activated, the

efforts at each node are higher.

4 AGENT-BASED DISPATCHING

AND SIMULATION

To cope with the dynamics and complexity of lo-

gistic processes, we are implementing autonomous

groupage trafﬁc with agent technologies. The agent

system induces a proactive, reactive, and adaptive sys-

tem behavior. Agent-based commercial systems are

used within the planning and controlling processes

of containerized freight (Dorer and Calisti, 2005).

Team formation and interaction protocols have been

designed for efﬁcient resource allocation (Schuldt,

2011). Agent-based systems have optimized plan-

ning and controlling processes within dynamic envi-

ronments (Fischer et al., 1995). Other ranges of appli-

cation have been provided for industrial logistic pro-

cesses (Skobelev, 2011).

In our setting agents represent trucks and orders.

Whenever a new transport request has to be aced

upon, a new agent is created that represents an or-

der. The goal of the agent is to ﬁnd a proper transport

service provider to pickup or deliver the shipments

with respect to the time windows and premium ser-

vice constraints. The agent starts the contract-net pro-

tocol for negotiating with available transport service

providers. All operating trucks are represented by an

agent as well. The truck agents evaluate the propos-

als by determining its additional costs for transport-

ing. This is done by solving the TSP optimally that is

speciﬁed in Def. 2 while considering time and capac-

ity constraints with the algorithm described in Sec. 3.

In order to schedule new orders also while transport-

ing other shipments, the truck has to consider its cur-

rent capacity constraints and position. For example,

OptimalDecisionMakinginAgent-basedAutonomousGroupageTraffic

251

picked up shipments reduce the capacities and the po-

sition of the vehicle affects the determination of short-

est ways and tours. Consequently, we link the plan-

ning and decision making processes of the agents di-

rectly with their execution behaviors and consider all

relevant observed changes of the environment as well

as the internal state of the agent within the decision

making and tour planning. On the other hand, new

plans can effect the executed actions of the agents.

Therefore, the truck agent checks during driving, if

the next stop has changed and if necessary he adapts

the tour. In real processes as well as in the simula-

tion the handing processes (boarding and deboarding

of shipments) must not be interrupted. This require-

ment is satisﬁed by not adopting plans that manipu-

lates the running handling processes.

To transport a premium service instead of conven-

tional orders or another premium service by driving a

shorter distance, already accepted orders may not be

included in the new plan. If these orders have not been

boarded the truck agent sends a message to the agent

that acts on behalf of the corresponding order. Af-

terwards, the order agent negotiates with other trans-

port service providers again. Potentially, this results

in a series of computation and communication inten-

sive negotiations between agents to achieve small im-

provements. To weaken this effect (especially if sev-

eral shipments are processed consecutively within a

short time window and the global allocation changes

signiﬁcantly) the agent waits for a certain period of

time before it starts the negotiation procedure. For op-

timal decision making agents have to solve a TSP for

each proposal. Consequently, numerous TSPs have to

be solved in the planning and controlling processes.

Applying simulation for evaluating multiagent

systems before their deployment in real applica-

tions is an accurate cost and time reducing method.

Our system PlaSMA (http://plasma.informatik.uni-

bremen.de) extends the JADE framework (Bellifem-

ine et al., 2007) and provides a discrete time sim-

ulation that ensures a correct conservative synchro-

nization with time model adequacy, causality, and

reproducibility. The transport infrastructure within

the simulation environment is modeled as a directed

graph. Nodes represent trafﬁc junctions or logis-

tic sources and sinks, while edges represent differ-

ent types of ways, e.g., roads, motorways, trails, and

waterways. To model sound planning and control-

ling processes in the logistic domain, we extended our

system to import infrastructures from OpenStreetMap

(OSM) databases. The directed graph includes infor-

mation about the real worlds speed limits, the dis-

tance as well as the type of an edge. Particularly

within large infrastructures determining the shortest

path between nodes is an essential, costly, and time-

consuming procedure within the decision making pro-

cess of an agent. However, computing the distance

matrix between cities is essential for solving the TSP

on a shortest path reduced graph. Consequently, we

implemented single-source shortest paths search (Di-

jkstra, 1959) with a memory-efﬁcient joint represen-

tation of graph and heap nodes. Computing a dis-

tance matrix requires many shortest-path queries with

a ﬁxed starting node and is time-critical. Hence, we

adapted the search procedure and saved the last vis-

ited nodes within a hash map as well as in the heap as

long as the start node has not changed. While process-

ing new search requests we check in constant time, if

the shortest path to the node was already found and

retrieve the corresponding node from the heap. Oth-

erwise, shortest path search is continuing at the last

expanded node. We extended the search with a cache.

5 EVALUATION

In the ﬁrst setting (all experiments were run on an In-

tel i7 processor with negligible RAM requirements;

see Theorem 2) we generated a fully-connected ran-

dom graph of k nodes with edge weights in [0..C].

With C = 10 our solver can handle problems with 500

cites. For C = 100, and up to 100 cities the experi-

mental outcome shows that there are rare unfortunate

cases that need hours for computation, but generally

remain tractable. For smaller values of n (the number

of cities) and more complex TSPs, our incremental

solver with constant time per node was often more ef-

fective than computing a lower bound by solving the

Assignment Problem (Jonker and Volgenant, 1986) at

each node.

Next, we extended the solver with time windows

and focus on the performance of applied heuristics.

As release and due times are more difﬁcult to gen-

erate randomly, we took an existing benchmark set

of TSPTW problems (Dumas et al., 1995). The re-

sults in Table 1 examine the search efforts for DF-

BnB with h

and h

(see Sec. 3). While the number of

nodes is substantially lower for h

, the solving time is

sometimes (but not always) larger than for h

, indicat-

ing that the more constraint the problem is, the worse

the AP approximation and the better the search with

a simpler heuristic. Note that the best results were

obtained with a combination of both heuristics, using

the more expressive one in the top part of the tree and

the less expressive one in the bottom part of the tree.

To investigate the interactions between agents we

implemented several scenarios within PlaSMA. The

transport infrastructure contains 124,462 nodes and

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

252

Table 1: Results in Dumas’ TSPTW Benchmark (Exp.

nodes and CPU time for the two heuristics are shown).

Prob. Cost E

n20w20.001 378 49 < 1s 2784766 < 1s

n20w20.002 286 97 < 1s 3234936 < 1s

n20w20.003 394 138 < 1s 4944477 < 1s

n20w20.004 396 156 < 1s 2331312 < 1s

n20w20.005 352 41 < 1s 4017260 < 1s

n20w40.001 254 38022 3s 103087541 18s

n20w40.002 333 88 < 1s 11388523 2s

n20w40.003 317 1409 < 1s 21158796 3s

n20w40.004 388 7676 1s 35117607 6s

n20w40.005 288 10287 2s 20801644 3s

n20w60.001 335 40810 14s 223904879 43s

n20w60.002 244 97144 7s 81367918 15s

n20w60.003 352 399127 27s 31292739 5s

n20w60.004 280 4055453 258s 1245195466 238s

n20w60.005 338 105393 10s 104049862 18s

n20w80.001 329 316992 35s 288653549 56s

n20w80.002 338 260552 36s 166880630 33s

n20w80.003 320 15959 3s 208526467 42s

n20w80.004 304 1258898 80s 373077547 73s

n20w80.005 264 5224435 438s 1660621704 332s

n20w100.001 237 1635101 52s 1232596799 279s

n20w100.002 222 68954 7s 2203174867 531s

n20w100.003 310 13382035 765s 2586795810 538s

n20w100.004 349 34289 2s 1213551958 266s

n20w100.005 258 688887 44s 2308713055 548s

292,521 edges. Orders and transport requests were

provided by the Bremen ofﬁce of Hellmann World-

wide Logistics GmbH & Co. KG. We started a reverse

geocoding process to map the address information to

coordinates and determined the nearest neighbor node

in the map, to link the addresses with graph nodes.

The real weight, premium service constraints, latest

delivery times as well as the incoming dates are at-

tached with the order. Since exact delivery times are

not available, only the date is considered during eval-

uation. As a result, we modeled the dynamics by gen-

erating new orders successively until all orders of this

day have been dispatched. In real transport processes,

vehicles with interchangeable units are sent to stops

where numerous shipments have to be handled. Con-

sequently, we did not consider orders if more than six

orders had to be picked up at the same stop. While the

dynamics of the planning and controlling processes

of delivery tours are limited due to the fact that ship-

ments have to be loaded at the depot in the morning

and cannot be changed anymore, we only consider

pickup orders and simulate the planning processes si-

multaneously to the execution of plans.

We assume that tours start at 7am at the depot and

the vehicle must return not after 4pm. Moreover, the

average velocity of a truck is set to 60 km/h, all trucks

have a maximum possible capacity of 7.5 tons and a

truck starts only one tour per day. The handling and

waiting periods at incoming goods departments is half

an hour.

Table 2: CPU time in ms for solving the TSP as well as for

shortest path searches during the matrix computations.

#Trucks #TSP time for time for

solving TSP in ms matrix computation in ms

5 6,122 199,043 4,912,094

10 11,893 324,566 16,588,955

20 22,457 604,675 56,845,930

25 26,751 972,579 75,882,546

30 31,542 2,246,511 94,921,678

40 40,759 7,979,063 144,742,544

60 56,152 79,704,147 225,749,232

Figure 1: Black/White bars show the percentage of picked

up premium/conventional services in the selected scenario.

We modeled seven scenarios. In each scenario

1,265 orders are distributed within a whole week

while the number of trucks is varying. About six per-

cent of the total amount of modeled orders are pre-

mium services. Table 2 shows the computation times

elapsed during each simulation run for computing the

distance matrix with the shortest-path algorithm as

well as the time for solving the TSP speciﬁed in Def. 2

while cons. The results reveal that more computation

time is required for the reduction of the real world in-

frastructure graph to a minimum distance matrix be-

tween relevant nodes than for optimally solving of the

TSP. Consequently, the shortest path matrix computa-

tion is the most expensive part of the decision making

process of the agent, if we are considering the com-

putational effort. Moreover, Table 2 indicates that the

amount of TSPs rises with the number of available

trucks. This is obvious, because the TSP solver is an

essential part within the decision making process of

each truck.

Fig. 1 shows the percentage of picked-up premium

and conventional orders within each scenario. Con-

sequently, the agent system serves premium services

with higher priorities. Even with 5 trucks nearly 50%

of all premium services are sill picked up, while pro-

cessing more than 90% of conventional orders are

postponed to other days. An increase of the num-

ber of available trucks leads to processing more pre-

mium services as well as more conventional orders.

If about 70% of all premium services were satisﬁed,

only transported conventional orders increased. How-

ever, not more than 70% of all premium services are

transported even if enough trucks are available. We

OptimalDecisionMakinginAgent-basedAutonomousGroupageTraffic

253

assume, this is explained by the scenario assumptions

in combination with the customer orders. For exam-

ple, if the max. velocity of trucks is set to 60 km/h,

it is not possible to pick up premium services with a

distance of more than 60 km at 8am, if the trucks start

the transporting process at 7am.

6 CONCLUSIONS AND

OUTLOOK

We developed a dispatching system matching the re-

quirements of forwarding agencies in groupage traf-

ﬁc. To face the dynamics of consecutively incoming

orders and the high complexity of logistic processes,

we implemented a reactive and proactive multiagent

system. The agents link the planning and schedul-

ing processes directly with their actions. Therefore,

changes of the environment can be considered dur-

ing runtime and induce a reactive behavior. We fo-

cused on the planning and decision making processes

of the agents and developed an efﬁcient TSP solver

that is crucial for negotiation with service customers

agents. The optimal branch-and-bound TSP solver is

time and space efﬁcient: it checks resource, time, and

premium service constraints in O(1) time and space

per generated node. Moreover, after the allocation of

O((n/w)·n

) words at initialization time for the stack

contents and other structures (including copies of the

distance matrix) no additional memory is allocated

during the search. The performance was proven on ar-

tiﬁcial graphs with test sets from benchmarks (Dumas

et al., 1995) as well as in simulated real world scenar-

ios of an entire week by computing more than 56,000

TSPs including time windows, capacities, handling

times, and priorities.

In further investigations, we will evaluate the mul-

tiagent system on multiple computer and enable par-

allel decision making. As a result, trucks have suf-

ﬁcient computational power to continue negotiating

with other trucks and improve the allocations consec-

utively. Applying the contract-net protocol in com-

bination with the optimal TSP solver, the negotia-

tions will converge in a global optimum (Shoham and

Leyton-Brown, 2009, p. 27).

ACKNOWLEDGEMENTS

The presented research was partially funded by the

German Research Foundation (DFG) within the Col-

laborative Research Centre 637 ”Autonomous Coop-

erating Logistic Processes: A Paradigm Shift and its

Limitations” (SFB 637) at the University of Bremen,

Germany. We thank the Bremen ofﬁce of Hellmann

Worldwide Logistics & Co. KG for great cooperation.

REFERENCES

Anily, S. and Mosheiov, G. (1994). The traveling salesman

problem with delivery and backhauls. Operations Re-

search Letters, 16(1):11–18.

Ascheuer, N., Fischetti, M., and Groetschel, M. (2001).

Solving the asymmetric travelling salesman problem

with time windows by branch-and-cut. Math. Pro-

gramming, 90:475–506.

Baldacci, R., Mingozzi, A., and Roberti, R. (2012). Re-

cent exact algorithms for solving the vehicle routing

problem under capacity and time window constraints.

European Journal of Op. Res., 218(1):1–6.

Bellifemine, F., Caire, G., and Greenwood, D. (2007). De-

veloping Multi-Agent Systems with JADE. John Wiley

& Sons.

Dijkstra, E. W. (1959). A note on two problems in connex-

ion with graphs. Numerische Mathematik, 1:269–271.

Dorer, K. and Calisti, M. (2005). An Adaptive Solution to

Dynamic Transport Optimization. In AAMAS, pages

45–51.

Dumas, Y., Desrosiers, J., Gelinas, E., and Solomon, M.

(1995). An optimal algorithm for the travelling sales-

man problem with time windows. Operations Re-

search, 43(2):367–371.

Fischer, K., Mueller, J. P., and Pischel, M. (1995). Cooper-

ative Transportation Scheduling: An Application Do-

main for DAI. Journal of Applied Artiﬁcial Intelli-

gence, 10:1–33.

Gendreau, M., Hertz, A., and Laporte, G. (1996). The trav-

eling salesman problem with backhauls. Comp. & Op.

Research, 23(5):501–508.

Johnson, D. S., McGeoch, L. A., and Rothberg, E. E.

(1996). Asymptotic experimental analysis for the

Held-Karp traveling salesman bound. In SODA, pages

341–350.

Jonker, R. and Volgenant, A. (1986). Improving the hungar-

ian assignment algorithm. Operations Research Let-

ters, 5:171–175.

Karp, R. M. and Steele, J. M. (1990). Probabilistic analysis

of heuristics. In The Traveling Salesman Problem, E.

Lawler et al. (eds.), 181–205.

Miller, D. L. and Pekny, J. F. (1991). Exact solution of

large asymmetric traveling salesman problems. Sci-

ence, 251:754–761.

Schuldt, A. (2011). Multiagent Coordination Enabling Au-

tonomous Logistics. Springer Verlag.

Shoham, Y. and Leyton-Brown, K. (2009). Multiagent

Systems: Algorithmic, Game-Theoretic, and Logical

Foundations. Cambridge Univ Press

Skobelev, P. (2011). Multi-agent systems for real time re-

source allocation, scheduling, optimization and con-

trolling: Industrial applications. In HOLOMAS, 1–14.

Zhang, W. (2000). Depth-ﬁrst branch-and-bound versus lo-

cal search: A case study. In AAAI, p.930–936.

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

254