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shopST: Flexible Job-Shop Scheduling with Agent-Based Simulated Trading


Abstract and Figures

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 manufacturing 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 constraints with an additional market agent. shopST is evaluated in comparison to selected other different solution approaches to flexible job-shop scheduling.
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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
2German Research Center for Artificial Intelligence (DFKI), Saarbruecken, Germany
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
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
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
A set J={j1, . . . , jn}of njobs, which corresponds to factory workpieces,
needs to be processed with a set M={m1, . . . , mp}of pmachines, while every
job jihas a number of kipoperations 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 mMop
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
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
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 ViOi. A directed edge (oo0)Eifor o, o0Oiis 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), mM, 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 PmMc(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
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
low Mk01 55 6 3
la05(vdata) 50 5 2.5
la06(rdata) 75 5 2
high Mk02 58 6 6
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
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
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
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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Conference Paper
This proposes accuracy, granularity, and frequency as universal quality dimensions for information that should be incorporated in decision-making. These dimensions are applied within an agent-based system that is to perform integrated dynamic scheduling in a real manufacturing environment.
Full-text available
Taking resource allocation into account, flexible job shop problem (FJSP) is a class of complex scheduling problem in manufacturing system. In order to utilize the machine resources rationally, multi-objective particle swarm optimization (MOPSO) integrating with variable neighborhood search is introduced to address FJSP efficiently. Firstly, the assignment rules (AL) and dispatching rules (DR) are provided to initialize the population. And then special discrete operators are designed to produce new individuals and earliest completion machine (ECM) is adopted in the disturbance operator to escape the optima. Secondly, personal-best archives (cognitive memories) and global-best archive (social memory), which are updated by the predefined non-dominated archive update strategy, are simultaneously designed to preserve non-dominated individuals and select personal-best positions and the global-best position. Finally, three neighborhoods are provided to search the neighborhoods of global-best archive for enhancing local search ability. The proposed algorithm is evaluated by using Kacem instances and Brdata instances, and a comparison with other approaches shows the effectiveness of the proposed algorithm for FJSP.
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The Job Shop scheduling Problem (JSP) is one of the most known problems in the domain of the production task scheduling. The Job Shop scheduling Problem with Transportation resources (JSPT) is a generalization of the classical JSP consisting of two sub-problems: the job scheduling problem and the generic vehicle scheduling problem. In this paper, we make a state-of-the-art review of the different works proposed for the JSPT, where we present a new classification schema according to seven criteria such as the transportation resource number, the transportation resource type, the job complexity, the routing flexibility, the recirculation constraint, the optimization criteria and the implemented approaches.
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Conference Paper
In this paper an actor based approach to manufacturing scheduling is presented. It is based on a mathematical foundation, where the scheduling problem is formulated as an integer program. With lagrangian relaxation the problem is decomposed in independent sub-problems. The sub-problems can be solved concurrently, thus the mathematical foundation lends itself to a distributed computational architecture. The presented approach is discussed in the context of other distributed approaches in general and holonic manufacturing approaches in particular. The formal foundation and the computational architecture allowing its implementation are discussed.
This paper presents an agent-based fuzzy constraint-directed negotiation (AFCN) mechanism to solve distributed job shop scheduling problems (JSSPs). The scheduling problem is modelled as a set of fuzzy constraint satisfaction problems (FCSPs), interlinked by inter-agent constraints. Each FCSP represents the perspective of the participants and is governed by autonomous agents. The novelty of the proposed AFCN is to bring the concept of a fuzzy membership function to represent the imprecise preferences of task start time for job and resource agents. This added information sharing is crucial for the effectiveness of distributed coordination. It not only can speed up the convergence, but also enforce a global consistency through iterative exchange of offers and counter-offers. The AFCN mechanism can also flexibly adopt different negotiation strategies, such as competitive, win–win, and collaborative strategies, for different production environments. The experimental results demonstrate that the proposed model can provide not only high-quality and cost-effective job shop scheduling (i.e., comparable to that of centralized methods) but also superior performance in terms of the makespan and average flow time compared with other negotiation models for agent-based manufacturing scheduling. As a result, the proposed AFCN mechanism is flexible and useful for distributed manufacturing scheduling with unforeseen disturbances.
Most scheduling problems are complex combinatorial problems and very difficult to solve [Manage. Sci. 35 (1989) 164; F.S. Hillier, G.J. Lieberman, Introduction to Operations Research, Holden-Day, San Francisco, CA, 1967]. That is why, lots of methods focus on the optimization according to a single criterion (makespan, workloads of machines, waiting times, etc.). The combining of several criteria induces additional complexity and new problems. In this paper, we propose a Pareto approach based on the hybridization of fuzzy logic (FL) and evolutionary algorithms (EAs) to solve the flexible job-shop scheduling problem (FJSP). This hybrid approach exploits the knowledge representation capabilities of FL [Fuzzy Sets Syst. 1 (1989)] and the adaptive capabilities of EAs. The integration of these two methodologies for the multi-objective optimization has become an increasing interest. The objective considered is to minimize the overall completion time (makespan), the total workload of machines and the workload of the most loaded machine. Many examples are presented to illustrate some theoretical considerations and to show the efficiency of the suggested methodology.
Scheduling is an important tool for a manufacturing system, where it can have a major impact on the productivity of a production process. In order to find an optimal solution to scheduling problems it gives rise to complex combinatorial optimization problems. Unfortunately, most of them fall into the class of NP-hard combinatorial problems. In this paper, we focus on the design of multiobjective evolutionary algorithms (MOEAs) to solve a variety of scheduling problems. Firstly, we introduce fitness assignment mechanism and performance measures for solving multiple objective optimization problems, and introduce evolutionary representations and hybrid evolutionary operations especially for the scheduling problems. Then we apply these EAs to the different types of scheduling problems, included job shop scheduling problem (JSP), flexible JSP, Automatic Guided Vehicle (AGV) dispatching in flexible manufacturing system (FMS), and integrated process planning and scheduling (IPPS). Through a variety of numerical experiments, we demonstrate the effectiveness of these Hybrid EAs (HEAs) in the widely applications of manufacturing scheduling problems. This paper also summarizes a classification of scheduling problems, and illustrates the design way of EAs for the different types of scheduling problems. It is useful to guide how to design an effective EA for the practical manufacturing scheduling problems. As known, these practical scheduling problems are very complex, and almost is a combination of different typical scheduling problems.
In this paper, we propose a hybrid shuffled frog-leaping algorithm (HSFLA) for solving the multi-objective flexible job shop scheduling problem. Three minimization objectives – the maximum completion time (makespan), the total workload of all machines, and the workload of the critical machine are considered simultaneously. In the proposed algorithm, several approaches are presented to construct the initial population with a high level of quality. Then each frog in the population is assigned to a corresponding memeplex according to the number of individuals who dominate it and then the number of frogs who are dominated by it. In the memetic evolution process, two crossover operators are presented to share information among the best frogs and the worst frog. Meanwhile, several local search methods are embedded in the algorithm to enhance the exploitation capability. Experimental results on the well-known benchmark instances and comparisons with other recently published algorithms show the efficiency and effectiveness of the proposed algorithm.