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shopST: Flexible Job-Shop Scheduling with

Agent-Based Simulated Trading

Frank Yukio Nedwed1, Ingo Zinnikus2, Maxat Nukhayev2, Matthias Klusch2,

and Luca Mazzola2

1Saarland University, Saarbruecken, Germany

s9frnedw@stud.uni-saarland.de

2German Research Center for Artiﬁcial Intelligence (DFKI), Saarbruecken, Germany

{FirstName.LastName}@dfki.de

Abstract. Paradigms in modern production are shifting and pose new

demands for optimization techniques. The emergence of new, versatile,

reconﬁgurable and networked machines enables ﬂexible manufacturing

scenarios which require, in particular, planning and scheduling methods

for cyber-physical production systems to be ﬂexible, reasonably fast, and

anytime. This paper presents an approach to ﬂexible job-shop manufac-

turing scheduling with agent-based simulated trading, called shopST.

Aspects of real manufacturing scheduling problems form the basis for a

physical decomposition of the planning system into agents. The initial

schedule created by the agents in shopST through reactive negotiation

is successively improved through the exchange of resource binding con-

straints with an additional market agent. shopST is evaluated in compar-

ison to selected other diﬀerent solution approaches to ﬂexible job-shop

scheduling.

Keywords: agents, simulated trading, ﬂexible job-shop scheduling

1 Introduction

Modern production facilities are increasingly relying on networked machines for

their beneﬁts caused by increased ﬂexibility and the ability for self organization.

In order to further enhance economic factors, scheduling methods are needed,

that take advantage of these features and can cope with the rising amount of

complexity. Flexible job-shop scheduling (FJSS) is an extension of the classical

job-shop scheduling problem, which is NP-hard and among the hardest combi-

natorial optimization problems [1]. There are several diﬀerent types of solution

methods available, though most of them disregard some constraints in order to

simplify the problem or only regard a single cost function, e.g. makespan. The

combination of several criteria or additional constraints generalizes the problem

and further enhances its complexity. There is a wide range of approaches for

using multi-agent systems in manufacturing in general and for job-shop schedul-

ing in particular [20, 11, 12, 19, 17, 25, 2, 16]. In this paper, we present a novel

approach, shopST, that applies agent-based distributed simulated trading [3] to

2 Nedwed et al.

solve dynamic FJSS problems. In particular, shopST complements locally opti-

mizing reactive agent scheduling with long-term planning via simulated trading.

The results of a comparative experimental evaluation revealed that shopST is

competitive in highly ﬂexible manufacturing environments with multi-purpose

machines.

The remainder of the paper is structured as follows. Section 2 shortly introduces

the problem of ﬂexible job-shop scheduling, and gives an overview of the solu-

tion and its implementation. Section 3 presents the comparative performance

evaluation results, while related work is brieﬂy discussed in Section 4. Section 5

concludes the paper with a short summary.

2 The shopST Solution for FJSS

This section introduces the problem of ﬂexible job-shop scheduling and the ﬁrst

agent-based approach that makes use of simulated trading for this purpose.3

2.1 Flexible Job-Shop Scheduling

The problem of ﬂexible job-shop scheduling (FJSS), in general, is to ﬁnd an opti-

mal, valid job-shop schedule Sthat minimizes a cost function c(e.g. makespan)

for a given conﬁguration of jobs, operations on multi-purpose machines, and is

subject to certain constraints of processing. FJSS is an extension of the classical

job-shop scheduling problem. Classical job-shop scheduling solutions determine

a schedule for a set of jobs on a set of machines with the objective to minimize a

certain criterion subject to the constraint that each job has a speciﬁed process-

ing order through all machines, which are ﬁxed and known in advance. A more

ﬂexible job-shop scheduling allows, for example, one operation to be performed

on one machine out of a whole set of alternative machines. In the following, the

type of FJSS problems our solution approach can cope with is described in more

detail.

A set J={j1, . . . , jn}of n∈jobs, which corresponds to factory workpieces,

needs to be processed with a set M={m1, . . . , mp}of pmachines, while every

job jihas a number of ki≤poperations Oi={o1, . . . , oki}, which have to be

performed in order for the job to be completed. Performing a job jion a machine

mjis denoted as an operation oij , which requires the exclusive, uninterrupted

use of mjover a time period pij , called processing time. It is assumed that the

processing time can be deterministically deduced from the system in advance.

A schedule Sis a bijective assignment (S(oi)→(m, fi)) of every operation oi

to a processing machine m∈Mop

iand a completion date fi, with completion

dates fij for every operation and job j. The schedule is valid, if all time intervals,

which are assigned to a machine are free of overlaps and precedences are met

among the other additional constraints to the system. Each possible schedule S

3The source code for this project is publicly available at https://sourceforge.net/

projects/shopst/

shopST: Agent-Based Simulation Trading for FJSS 3

Fig. 1. Abstract example of a job-shop schedule for two machines M1and M2

can be evaluated by assigning a cost cto every possible state of Svia a cost

function c(S). To ﬁnd an optimal, valid schedule then requires either to compute

a valid Swith minimal costs c, or to take an existing schedule and continually

decrease its cost.

The following types of processing constraints are part of an extended ﬂexible job-

shop scheduling problem speciﬁcation. First, any operation okcan be performed

by a number of machines Mop

kand it is possible that the processing time pij

varies depending on jiand mj. We assume the constraint |Mop

k|>1, which

implies ﬂexible job-shop scheduling with multi-purpose machines. We speak of

|Mop

k|as the factory ﬂexibility for the remainder of this paper. Second, the

schedule may also have to follow a given order of precedences for the operations

to be performed. These operation precedences are encoded in a directed, acyclic

precedence graph Gprec

i= (Vi, Ei), where the number of vertices equals a subset

of the operation set Vi⊆Oi. A directed edge (o→o0)∈Eifor o, o0∈Oiis part

of the graph, if and only if operation o0has to be performed before operation o. In

contrast to classical job-shop scheduling, the non-linear precedence constraints

of the ﬂexible version allow an arbitrary order between some processing steps of

the job (e.g. drilling holes with diﬀerent machines) and other precedences that

are ﬁxed (e.g. paint job only after all drilling is completed). Inﬂexible job-shop

scheduling problems have completely linear precedence graphs. Third, possible

tool changes on a multi-purpose machines may require a certain amount of time

for it to prepare in between the processing of two operations. Such a sequence-

dependent setup time sikj is the time period in which the machine cannot process

any job, and which is dependent on the two operations oij and okj that shall

be performed in succession. In practice, these times obey the triangle inequality

sikj +skuj ≥siuj . Besides, jobs jithat enter the system at a release time ri

cannot have their operations processed before that time, and can have a due

date di> ribefore which their completion is preferable, if stated in the cost

function. Deadlines are mostly relevant for tardiness related cost functions like

maximum lateness. We assume that already started operations oij cannot be

interrupted (no preemption).

Finally, we focus on a dynamic version of FJSS with sequence dependent setup

times and multi-purpose machines: J-M P M|prec, ri, di, sdst|cin the established

α|β|γnotation for scheduling problems, whereas cdenotes an arbitrary cost

function [10]. The αﬁeld contains the overall class of the problem and the beta

4 Nedwed et al.

ﬁeld describes additional constraints in the setup. In particular, the sets J,M

and Mop of FJSS problems may dynamically change during optimization of the

schedule, since new jobs may enter the system, and changes to the operation

sequences, machine breakdowns and other unexpected events may occur at any

time. That requires the dynamic optimization to be suﬃciently robust against

such changes. Furthermore, the information exchange between networked ma-

chines and tools is required to be decentralized, that is, unlike most state-of-

the-art solution approaches [7], we assume no global information blackboard for

this purpose, as the system is decomposed by the physical constraints of the

machines and not the functional ones of the algorithm.

2.2 shopST System: Overview

The proposed FJSS optimization system, shopST, consists of two phases: In the

ﬁrst phase, agents create a valid schedule by scheduling the resource binding

constraints (operations) through standard contract net protocol based interac-

tion in a reactive manner. In the second phase, the valid schedule is improved by

the long-term schedule optimization via agent-based simulated trading. These

phases are executed in succession whenever an unanticipated event disrupts the

validity of the planning. The ﬁrst phase creates a valid solution, which is im-

proved in the second phase.

The use of an arbitrary short term agent-based planning system in the ﬁrst

phase enables local optimization of the machine schedules and a heterogeneous

agent system. We used a standard contract net protocol for the local short term

planning in this paper, but others can be used. The factory environment can

be highly dynamic because of machine breakdowns, or other events, such that

the plans have to be adapted immediately in order to commence production,

which requires an anytime solution. Long-term planning with simulated trading,

as ﬁrst introduced by Bachem [3], is a method to ﬁnd approximated solutions

through several rounds of hypothetical trading between trading agents and a

common market agent, followed by a consolidation round. In the following, we

focus on the application of simulated trading and required modiﬁcations to ﬁt

the planning domain. An overview of the agent interaction is given in Figure 2.

Agent mapping. The trading agents are the instances in the system, which

want to optimize their cost function. Thus, every machine in the system pro-

vides one trading agent. An additional non-physical market agent is existent in

the network. The communication in the network is enabled via common agent

technologies as described in section 2.3.

Each agent is equipped with a cost function c(m), m∈M, that on the one

hand, resembles a good evaluation of the local performance of the machine.

On the other hand, the summed local costs over all agents Pm∈Mc(m) should

be a good indicator of the overall factory performance. We experimented with

diﬀerent possibilities for such cost functions with varying complexity. Simple cost

functions like the total operation completion date (TOpC) c(m) = Pfifor all fi

that have a pair (m, fi) in the schedule Sor the total operation lateness (TOpL)

shopST: Agent-Based Simulation Trading for FJSS 5

Fig. 2. Algorithm sequence and agent system structure

seem to work well and are computationally inexpensive. shopST also oﬀers total

operation tardiness (TOpT) and slack time (TOpSL) as cost functions.

Initialization. At the beginning of the simulated trading protocol, all partic-

ipating agents are invited by the market agent to perform successive trading

steps. In each such step, called a trading level, every agent chooses either to sell

a resource binding constraint to the common market agent, or to buy such a

constraint from it. Resource binding constraints of the trading machine agents

in the planning domain are their processed operation plans. Whether to buy or

sell is determined evenly randomized. The decision, whether a certain operation

is traded or not, is not solely made in a greedy manner by local criteria, because

in this case, agents would always sell the costliest operation at the moment and

never buy because their resources are bound by this action. Because of this be-

havior, the trading is randomized and the used random distribution still depends

on the anticipated buying cost or selling gain respectively, as follows. Because

buying an operation from the market does almost always result in a deterioration

of the local cost function, buying probabilities are derived from the diﬀerence

of the cost diﬀerence the selling agent achieved, and the current buying cost. A

trading agent can only buy an operation from the market if it can process this

operation on the machine it is representing and successfully integrate it into its

current schedule. If an operation is sold, it is deleted from the local schedule

of the machine and its information is transferred to the market agent, where

other agents can see and possibly buy it in upcoming trading levels. The trading

agents decide which operation to trade by a random distribution depending on

the impact on their local cost function. This random function is designed in a

6 Nedwed et al.

way, that operations, that highly impact the cost function of the agent are more

likely to be sold. In order to avoid stagnation, every operation has a strictly

positive probability.

Trading graph. In the previous phase, it is possible for an operation to be

bought by multiple agents or that sold operations are not included in the plan

again. This means that the hypothetical schedule resulting after a certain amount

of trading levels is not necessarily valid. In order to generate a valid schedule

of lower cost, a trading graph is maintained during the execution of the trading

phase. The trading graph is a bipartite graph, its vertices are represented by

the single buy and sell actions. Edges link the actions belonging to the same

operation and are weighted with the cost diﬀerence achieved by this trade. An

exemplary trading graph is represented in Figure 3. Every node is annotated

by the number of the trading level it was performed in. This results in a unique

identiﬁcation using trading agent and trading level, as every agent trades exactly

one operation per level.

Fig. 3. Trading graph example for machine agents M1 to M3. Jobs are referred to by

letters, their operations are numbered.

Trading match. In order to get to a valid schedule again, a so called trading

match has to be found. This matching is a subset of the trading graph and has

to satisfy the following conditions:

–A sold operation may only be bought by exactly one agent, this property is

equivalent to a matching graph.

–If a vertex of round iis part of the matching, then every vertex of the same

trading agent with level smaller than ihas to be part of the graph, too.

–The overall weight of the graph has to be negative, which means that if the

trading actions belonging to the graph are all executed, the overall cost of

the system is decreasing.

In Figure 4, two trading matchings with three trading levels are displayed, which

may result from the trading graph in Figure 3. Consolidation and anytime

feature. If a trading match is found, the according trading actions are com-

municated to the corresponding agents. Because of the structure of the trading

matching, the resulting schedule is valid and the overall costs decrease; this con-

cludes the trading round. As each round generates another valid schedule and

shopST: Agent-Based Simulation Trading for FJSS 7

Fig. 4. Matching graphs of the trading graph in Figure 3

costs do not deteriorate after a round, the system can take new properties of

the factory into account after each round. Algorithms that behave in such a way

belong to the class of anytime algorithms, as they can be interrupted arbitrarily

and still deliver a valid result, which is at least as good as the initial state.

Incorporated aspects of simulated annealing. A main property of sim-

ulated annealing is the acceptance of system states with higher costs [18]. In

order to avoid early stagnation of the shopST algorithm, we adopted aspects of

simulated annealing. Several simulated trading rounds are clustered into a super

round. In a single super round, the quality of the schedule may also decrease by

accepting trading matchings with positive weight up to a certain limit imposed

by the temperature. The temperature decreases from round to round, similarly

to the original simulated annealing meta-heuristic. In order to not aﬀect the

reactivity of the system, the sizes of these super rounds have to be adapted to

the frequency of disturbances of the system. For the remainder of this paper, we

will refer to the number of trading rounds in a single super round as round size.

2.3 Implementation

The shopST system has been implemented in Java. For the reactive agent plan-

ning, we used standard contract net protocol based interaction between the

agents. The agent framework was built according to FIPA standards [5] and uses

ACL messages to communicate between agents. For the transference of informa-

tion and to keep the system generic, an ontology was used, which was speciﬁcally

designed for this task. The transferred information is especially relevant for the

trading agents to compute whether they can handle a workpiece operation and

if they do, at which cost. The search for an optimal matching graph during

the consolidation phase is computationally costly and mainly contributes to the

overall runtime of the algorithm. However, its costs can be transferred into the

network by the market agent and thus, make use of convenient resources as they

are not bound to a speciﬁc physical instance.

3 Comparative Performance Evaluation

Experimental setting. The experimental evaluation of shopST was run on

a laptop with Intel Core i5-5300U CPU@2.3 GHz processor. In order to test

8 Nedwed et al.

shopST performances, we pragmatically determine some optimal values for its

main parameters ﬁrst. The main metrics used for the comparison are the quality

of the produced solutions and the eﬀects the factory ﬂexibility has on solutions.

As the criterion of solution quality, the total length of the computed schedule, i.e.

the makespan, has been taken. Regarding the testing of ﬂexibility, we adopted its

deﬁnition from [14], i.e. the average number of machines that can execute a given

operation, and the best makespan reached as a measure for diﬀerent settings of

this parameter. The solution quality of shopST was compared with that of the

most recent and successful FJSSP solving algorithms: HTSA [21], Zhang GA [33],

AIA [4], X2010 [31], MOGA [28], P-DABC [23], X2009 [30], MOPSO [13], and

HSFLA [22]. Whenever available, experimental results from the original papers

were reused. The Zhang GA had to be re-implemented due to the unavailability

of the original code, in order to run it on the same infrastructure and to support

more detailed comparisons with shopST. Every run was repeated ﬁve times on

the same instance, in order to obtain meaningful and comparable results. For

the makespan analysis, the best result was adopted, in accordance with the

general approach reported by the compared algorithms; for ﬂexibility analysis,

the results were averaged to overcome the non-deterministic nature of the shopST

algorithm.

Three popular collections of problem instances have been used for testing, namely:

1. Kacem [15]: 4 problems with total ﬂexibility and diﬀerent number of opera-

tions per job; every operation can be processed on any one of the machines.

The number of machines ranges from 5 to 10, number of operations from 12

to 56.

2. Brandimarte [6]: 10 problems, which were randomly generated using a uni-

form distribution between two given units. The number of jobs ranges from

10 to 20, number of machines from 4 to 15, number of operations per job

from 3 to 103 and number of machines per operation from 2 to 6.

3. Hurink et al.[14]: 129 test problems divided by ﬂexibility levels into sdata,

edata, rdata and vdata subsets. The number of jobs ranges from 6 to 30 and

the number of machines ranges from 5 to 15.

Based on the number of operations, machines and ﬂexibility, the problem in-

stances from Brandimarte [6] and Hurink [14] datasets were grouped as speciﬁed

in Table 1. The problems were arranged by the number of machines and opera-

tions into three groups (small, average, and large). Each group was split further

by its ﬂexibility level into two subgroups with low and high ﬂexibility. The small

size group, high ﬂexibility sub-group presents only a single instance, as only one

small highly ﬂexible problem is included in the aforementioned datasets. The

test problems were chosen to cover to a certain extent the full data space for

every deﬁned subgroup. It is worth to be noted that based on the very limited

extension of the Kacem dataset (4 problems) and its full ﬂexibility, the set con-

tains only outliers with respect to the classiﬁcation dimension and consequently

no representative of it was selected, as for Table 1.

The solving of each problem listed in Table 1 has been tested with diﬀerent

values of round size, ranging from 1 to 5000. Based on the experimental results

shopST: Agent-Based Simulation Trading for FJSS 9

Size Flexibility level Problem Operations Machines Flexibility

small

low Mk01 55 6 3

la05(vdata) 50 5 2.5

la06(rdata) 75 5 2

high Mk02 58 6 6

average

low Mk04 90 8 3

la11(rdata) 100 5 2

la25(rdata) 150 10 2

high Mk07 100 5 5

la18(vdata) 100 10 5

Mk03 150 8 5

large

low la26(rdata) 200 10 2

la36(rdata) 225 15 2

la31(rdata) 300 10 2

high la36(vdata) 225 15 7.5

la26(vdata) 200 10 5

Mk09 240 10 5

Table 1. Selected problems grouped by size and ﬂexibility from [14] and [6]

shown in Table 2, one can see that there is a direct correlation between the

problem size and the round size: larger problems require larger round sizes. A

comparison of ﬂexibility levels shows that more ﬂexible problems require more

rounds to converge, which can be explained by the higher number of trade op-

tions for the agents. The result of an example run of such complex, highly ﬂex-

ible problems from la26(vdata) is shown in Figure 5 in which, for readability

reasons, the range of round size is divided into representative discrete values

(10/100/500/1000/2500/5000).

Fig. 5. Makespan convergence of la26(vdata) problem with diﬀerent round sizes

10 Nedwed et al.

Size Flexibility level Optimal round size

small low 100

high 100-500

average low 1000-2500

high 2000-5000

large low 2500-5000

high 5000

Table 2. Optimal round size by size and ﬂexibility

Based on experiments, the other parameters of shopST have been chosen as ﬁve

trading levels, 100 super rounds and TOpC as cost function. The initial solution

for shopST has been generated by randomly assigning operations to suitable

machine agents.

Solution quality. The solution qualities produced by all tested algorithms in-

cluding shopST for diﬀerent datasets are shown in tables 3 and 4. As a result,

shopST produces a solution quality that is comparable to that of the selected

representative state-of-art solution algorithms although it has not found the best

solutions most of the time. The last rows of these tables show the relative devi-

ation with respect to shopST. The relative deviation for each problem instance

is deﬁned as

dev = [(MKcomp −M KshopS T )/MKshopST ]∗100%

where MKshopST is the makespan obtained by shopST and MKcomp is the average

makespan of all the other algorithms shopST is compared to. As a result, shopST

underperformed by an average of 13.5% (ranging from 0% to about 25%). Zhang

GA[33] found 8 out of 10 best solutions and for this reason was chosen for a

more detailed comparison with shopST. Please keep in mind that the notion of

iteration diﬀers for shopST and Zhang GA[33]: While in Zhang GA one iteration

is one evolution of the population and takes around 60 msec, in shopST one

iteration corresponds to one super round of simulated trading, which can run

from several seconds to several minutes depending on the round size.

Execution time. In order to compare the runtimes of shopST and Zhang GA,

both algorithms have been executed with optimal parameters on the la40(vdata)

problem instance. The experiment was run 10 times for each algorithm, and the

best results were selected. The results, as shown in Figure 6 for shopST and in

Figure 7 for Zhang GA, reveal that the execution time of shopST is three orders

of magnitude larger than that of Zhang GA and appears to be connected with

the high round size requirement for reaching an optimal solution by shopST.

Flexibility. For the second evaluation metric, the eﬀects of problem ﬂexibil-

ity on solution quality were addressed in the following experiment: shopST and

Zhang GA were executed on problems with diﬀerent degrees of ﬂexibility. In

order to simulate diﬀerent levels of ﬂexibility, an original non-ﬂexible problem

la40(sdata) from Hurink dataset was modiﬁed by the application of a new pa-

rameter P, representing the probability that a particular machine can execute

shopST: Agent-Based Simulation Trading for FJSS 11

Fig. 6. Execution time of shopST

Fig. 7. Execution time of Zhang GA [33]

12 Nedwed et al.

Algorithms Instance 1 Instance 2 Instance 3

shopST 12 713

Zhang [33] 11 7 11

HTSA [21] 11 7 11

AIA [4] - 7 11

Xing [31] 12 7 11

MOGA [28] 11 7 11

P-DABC [23] 11 7 11

MOPSO [13] 11 7 11

dev(%) -6.9 0.0 -15.4

Table 3. Makespan results for Kacem[15] data, best solutions in bold

Algorithms MK01 MK02 MK03 MK04 MK05 MK06 MK07 MK08 MK09 MK10

shopST 47 34 229 84 196 80 164 558 342 267

Zhang [33] 40 26 204 60 173 58 144 523 307 198

Xing[30] 42 28 204 68 177 75 150 523 311 227

MOGA [28] 40 26 204 66 173 62 139 523 311 214

HTSA [21] 40 26 204 61 172 65 140 523 310 214

HSFLA [22] 40 26 204 62 173 64 141 523 311 215

AIA [4] 40 26 204 60 173 63 140 523 312 214

MOPSO [13] 40 26 204 61 173 62 139 523 310 214

dev(%) -14.3 -22.7 -10.9 -25.5 -11.5 -19.8 -13.5 -6.3 -9.3 -20.0

Table 4. Makespan results for Brandimarte[6] data, best solutions in bold

a particular operation. This is to simulate ﬂexible manufacturing environments

with multi-purpose machines. The results shown in Figure 8 reveal that shopST

signiﬁcantly improves its solution quality for more ﬂexible problems, and outper-

forms Zhang GA in this regard. In particular, Zhang GA shows a decrease in its

performance with increasingly ﬂexible problems, as depicted in Figure 9. Allow-

ing more machines to execute particular operations results in an increase in the

problem search space, that increases the probability for Zhang GA to be stuck

in a local minimum, hindering its capability of converging to a globally optimal

value. ShopST, on the other hand, works solely on ﬂexible problems, because

exchanges between agents are only enabled if multiple machines can exchange

operations. As a consequence, a more ﬂexible problem enables a larger number

of exchange points and therefore the performance of shopST greatly improves

with a greater ﬂexibility of the multi-purpose machines.

One main strength of shopST is that it excels in solving highly ﬂexible JJS prob-

lems with agent-based simulated trading. Besides, it natively adapts online to

dynamic events that aﬀect the problem that is currently being solved without the

need of a full restart. These advantages, however, come at the cost of a compar-

atively higher execution time. Overall, shopST can be considered as a valuable

solution for job-shop scheduling in highly ﬂexible and dynamic cyber-physical

production systems and environments, if there are no hard time constraints for

solution availability.

shopST: Agent-Based Simulation Trading for FJSS 13

Fig. 8. Results of ﬂexibility test on shopST

Fig. 9. Results of ﬂexibility test on Zhang GA [33]

14 Nedwed et al.

4 Related Work

For the comparative performance evaluation of shopST, we selected diﬀerent

types of state-of-the-art FJSS problem solving approaches including multi-agent

system based ones. The solutions qualities of shopST are close to those of these

approaches, which utilize genetic algorithm, artiﬁcial immune, knowledge-based

ant colony optimization, Pareto-based discrete artiﬁcial bee colony, modiﬁed dis-

crete particle swarm optimization, shuﬄed frog-leaping, hybrid tabu search. Of

course, there are many other agent-based approaches for dynamic and distributed

job-shop scheduling in manufacturing [20, 11, 29, 12, 19, 32, 17, 2]. For example,

[29] presents an actor-based approach to job-shop scheduling using Lagrangian

relaxation which may adapt its schedule after dynamic events quickly but no

values are given for comparison. BnB-ADOPT [32] is a memory-bounded asyn-

chronous distributed constraint optimization problem solver that uses the agent

framework of ADOPT. It performs exceptionally well in regard to runtime and

solution quality but, in contrast to shopST, the dynamic constrained optimiza-

tion problem description has to be explicitly encoded for every agent in prior.

However, to the best of our knowledge, shopST is the ﬁrst agent-based approach

with simulated trading used to solve the class of FJSS problems deﬁned above.

From the results of the comparative experimental testing of ﬂexibility it became

evident that shopST has its general strength in highly ﬂexible manufacturing

environments with multi-purpose machines.

Scheduling approaches can be characterized as constructing a schedule vs. opti-

mizing a given schedule. In the ﬁrst case an (ideally) exact solution for a given

problem is generated (cf. [24] for a thorough overview of classical approaches).

Optimization approaches improve an already existing schedule with respect to a

cost function and are in general based on heuristics or meta-heuristic procedures

and generate solutions iteratively, at the expense of non-optimal schedules [27].

A related ﬁeld is online scheduling [26], where information about the problem

domain is restricted (e.g. incoming jobs are only known when they arrive and pro-

cessing times only after a job is completed). shopST addresses the problem of the

optimization and repair of schedules in ﬂexible and dynamic manufacturing envi-

ronments with multi-purpose machines. Closely related approaches are based on

(meta-)heuristics, since standard algorithms assume complete knowledge about

the problem domain which usually implies a restart of the algorithm after a

change of the problem domain. In recent years, a number of job-shop scheduling

approaches based on meta-heuristics have been proposed for this purpose. [6]

and [14] used tabu search for solving the FJSS problem, while [8] combine ap-

proaches using tabu search with simulated annealing. Several approaches for the

JSS and FJSS based on evolutionary algorithms have also been developed (for a

survey see e.g. [9]). Genetic algorithms such as those developed by Zhang [33] or

Xing [30], for example, are an eﬃcient way for schedule optimization. However,

they have two major drawbacks: The ﬁrst is that their information structure is

functional and does not take advantage of an underlying agent encapsulation.

The other is that they lose performance and solution quality in more ﬂexible

factory layouts, a use case which gets more and more common.

shopST: Agent-Based Simulation Trading for FJSS 15

5 Conclusions

We presented a novel approach, shopST, that applies agent-based simulated

trading to solve dynamic FJSS problems. shopST complements locally optimiz-

ing reactive agent scheduling with long-term optimization of the valid schedule

via simulated trading. The results of a comparative experimental evaluation re-

vealed that shopST is particularly competitive in highly ﬂexible manufacturing

environments with multi-purpose machines. Future work includes further in-

vestigation of robustness against disruptive events and performance trade-oﬀs

compared to other negotiation-based approaches when applicable to the same

problem.

Acknowledgements. The work described in this paper was partially funded by

the German Federal Ministry of Education and Research (BMBF) in the project

INVERSIV and the European Commission in the project CREMA.

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