Bottom-up Job Shop Scheduling with Swarm Intelligence in Large

Production Plants

M. Schranz

1 a

, M. Umlauft

and W. Elmenreich

2 b

Lakeside Labs GmbH, Klagenfurt, Austria

Institute of Networked and Embedded Systems, University of Klagenfurt, Klagenfurt, Austria

Keywords:

Swarm Intelligence, Multi-agent Modeling, Cyber-physical Systems, Job Shop Scheduling.

Abstract:

In production plants organized by the job shop principle, the factory-wide scheduling problem is NP-hard and

can become extremely large. Traditional optimization methods like linear optimization reach their limits in

these settings due to excessive computation time. Therefore, we propose this industrial setting as a novel ﬁeld

of application for swarm intelligence using bottom-up algorithms that do not require the infeasible calculation

of an overall solution but depend only on local information. We consider the example of the semiconductor

industry producing logic and power integrated circuits where a diverse range of highly specialized but low

volume products are fabricated in the same plant. This paper shows how to select and model swarm members,

swarms, and their interactions for use in real-world production plants. There are multiple possibilities for the

modeling of the agents: a swarm member could be a single machine or a set of machines (workcenter), a

product or group of products of the same/similar type, or a more abstract agent like a process. In particular, we

consider criteria for selecting appropriate swarm members and potential candidate swarm algorithms inspired

by hormones and ants.

1 INTRODUCTION

Scheduling in production plants organized by the job

shop principle is a challenging problem in Industry

4.0. The main issues are the given constraints (e.g.,

from machines) together with the global objective in

production plants (e.g., maximizing of machine uti-

lization, throughput time, delivery reliability, or min-

imizing the work in progress (WIP)). High product

diversity together with historical growth of the indus-

trial plant increase complexity even further.

A typical example for such a highly dynamic pro-

cess is the production of integrated circuits (ICs) in

the semiconductor industry (Geng, 2018). In par-

ticular, we consider the so-called front end of line

processing where the wafers are processed to create

the ICs. For this paper, we consider the require-

ments of the leading semiconductor manufacturer In-

ﬁneon Technologies

. Between 400 and 1200 dif-

ferent stations need to be scheduled in such a pro-

duction plant (fab). Typical process steps include

lithography, doping, oxidation, etching, and measur-

https://orcid.org/0000-0002-0714-6569

https://orcid.org/0000-0001-6401-2658

https://www.inﬁneon.com

ing (Geng, 2018). They typically produce more than

1500 different products in around 300 different pro-

cess steps. These processes are characterized by a

multitude of technological and logistical boundary

conditions, like, e.g., equipment tooling, the need for

secondary resources, and constraints like time cou-

plings and batch processing. Furthermore, the chain

of necessary process steps contains loops. The job

shop scheduling problem is NP-hard (Garey et al.,

1976). Existing dispatching rules are based on heuris-

tics. Due to excessive computation time, Linear opti-

mization methods can not cope with the large, and dy-

namic search space (Lawler et al., 1993). These meth-

ods can only be used on subsets of the plant, and thus,

do not exploit the full optimization potential. There-

fore, bottlenecks cannot be prevented, and WIP waves

are generated. So far, no optimal solution for job shop

scheduling has been developed using linear optimiza-

tion that can be computed in polynomial time (Zhang

et al., 2009).

Other than using swarm intelligence as an opti-

mization algorithm (Ghumare et al., 2015), we ap-

ply a novel approach modeling the production plant

as a self-organizing system of agents that work to-

gether, each equipped with a set of local rules. A

Schranz, M., Umlauft, M. and Elmenreich, W.

Bottom-up Job Shop Scheduling with Swarm Intelligence in Large Production Plants.

DOI: 10.5220/0010551603270334

In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2021), pages 327-334

ISBN: 978-989-758-528-9

327

self-organizing system is highly non-linear because

of feedback relations. Thus, it can adapt to chang-

ing environmental conditions (Heylighen, 2001), e.g.,

tool downs. We consider nature-inspired swarm al-

gorithms, since many of them are able to produce

near-optimal solutions for NP-hard problems in fea-

sible computation time. Thus, the problem is trans-

formed from ﬁnding an overall solution to deﬁning

a distributed algorithm that ﬁnds the solution from

the bottom up. The considered production plant re-

quirements match the advantages of swarm intelli-

gence: adaptivity, robustness, and scalability. In this

paper we analyze the problem setting in such a highly

complex production plant (Sec. 2), introduce how

swarm modeling could be used to address the prob-

lem (Sec. 4), show two examples of swarm algorithms

and their application in this setting (Sec. 5), and dis-

cuss our approach in comparison to the related work

in the ﬁeld (Sec. 6).

2 SEMICONDUCTOR FAB

SETTING

Semiconductor production uses an industry standard

of 25 wafers that are combined to form a lot and then

transported in so-called FOUPs

or hordes between

the individual process steps. Every lot has a transpon-

der with a unique identiﬁcation number used to track

a lot through the fab. Lots follow a speciﬁc recipe,

which prescribes which process steps to take in which

order but not the concrete machine on which to per-

form the required next process step. Machines can

be single wafer tools which work wafer by wafer, or

batch-oriented and process several lots at once. Ma-

chines are often spread across several factory build-

ings. Nevertheless, transport times between machines

are negligible while workload and waiting times be-

fore machines are the determining factor. A set of

machines which can run one or more similar pro-

cess classes form a workcenter. These sets of ma-

chines are exhaustive and disjunct. A dedication ma-

trix speciﬁes which processes are allowed on which

machines. Load in a workcenter is distributed via

a solver which calculates scheduling and local opti-

mization for the workcenter for a week in advance.

In the considered production plant about 10% of

the machines have a low utilization (e.g., 60% or

even 30%), because they are only used for some spe-

cial products. There is a difference between uti-

lization of a workcenter and the utilization of a ma-

chine. For example, for a speciﬁc machine a utiliza-

Front Opening Uniﬁed Pod

tion of 80% is very high, while for a workcenter 80%

would be quite low.

3 PROBLEM STATEMENT

Currently, optimization per workcenter works well,

but its inﬂuence on the following workcenters and

machines is unclear and does not automatically gen-

erate a global optimum. It is not understood how lo-

cal optimization affects the overall efﬁciency of the

fab or whether optimizing one workcenter will cre-

ate bottlenecks in others. Existing dispatching rules

are based on heuristics. Since job shop scheduling is

an NP-hard problem and the number of involved ma-

chines and lots is considerably large, optimization can

only be calculated for a subset of the machines in the

fab (e.g., within a workcenter). Bottlenecks arise dy-

namically due to a wide variety of reasons, e.g., tool

downs, or changed product mix. Downtimes always

cause capacity loss. Bottlenecks cannot be prevented,

and generate WIP waves.

Different machine types have different logistic re-

quirements (batch vs. single processing). Especially

after a batch process, lot arrival times vary consider-

ably (because lots leave the process in batches) while

theory suggests that for single-step processing ma-

chines high utilization is only possible when arrival

times are uniform (Stidham Jr, 2002). The main chal-

lenge is that this switch between batch and single-step

processing introduces so-called WIP waves between

machines.

Lots that traverse a loop of machines several times

can add to the challenge: how to prioritize a lot

against other lots of the same product which are one

or several cycles ahead? If only the lots with the near-

est due dates are processed, the lots with later due

dates might violate their time coupling requirements.

If too many of the same product with later due dates

are prioritized, the products with the nearest due dates

might violate theirs. In the current setting, lots of the

same product are spread over the week when intro-

duced into the fab to avoid WIP waves.

4 SWARM MODELING OF THE

PROBLEM

To model the production plant as a swarm, we con-

sider a set of potential swarm members and their char-

acteristics. In this consideration, the swarm can be

homogeneous (agents of the same type, e.g., lots),

or heterogeneous (agents of different types, e.g., lots

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

328

and machines). Furthermore, we identify several cri-

teria to determine whether an entity is eligible to be

a swarm member in the fab according to the related

work (see Sec. 6 for more details). A swarm member

should be able to work in a swarm per se, thus, a rea-

sonable number of other swarm members should exist

(e.g., the lithography workcenter only exists once in

the fab and on its own would not represent a good

swarm member), show a suitable level of abstraction

to be modeled, detect dynamic information from the

(local) environment, react to information from the lo-

cal neighborhood (e.g., take decisions), and be plausi-

ble and understandable to enable trust in the proposed

solution.

4.1 Challenges

When considering the introduction of a swarm-based

algorithm in a production plant, the following chal-

lenges arise:

What Should be Modeled as Agents and what is the

Right Level of Abstraction? A swarm consists of

agents that interact with each other. In our case, a

swarm member could be a machine, a lot or a process

representing an abstract entity. Modelling a swarm

algorithm requires an early decision on what entity

should be used as a swarm member. As described in

the beginning of Sec. 4 we consider several criteria.

Nevertheless, the level of abstraction is not always

clear. For example, if we consider machines as

agents, we could also map a higher abstraction level

and consider workcenters as agents, or we map an

abstraction level lower and use process steps as

agents.

How to Deal with Inhomogeneities among Entities?

Intrinsically, machines are heterogeneous by them-

selves. There is no uniﬁed type of a speciﬁc machine,

and even on nearly identical machines there is the

possibility of deﬁning different processes. Thus,

each machine has a set of different parameters that

inﬂuence its operation. The same holds for lots,

as they have different recipes and thus, different

requirements in their route through the fab.

How to Implement the Necessary Swarm

Communication Paradigms in the Setting of the

Production Plant? Swarm algorithms typically

implement one of two communication paradigms—

direct communication where agents send messages

or indirect communication (stigmergy), where agents

leave information in the environment. The entities

of the fab are already represented as digital twins in

the central fab computer system. Therefore, agent

communication can easily be implemented as local

messages within the computer system or in local

memory for stigmergy. As a result, it is not necessary

to equip machines or lots with additional computa-

tional intelligence or communication devices.

How to Implement a Solution on Top of a Working

Environment? Current fab mechanisms include a

number of different priority classes (e.g., hot lots,

developer lots). Generally, lots with priority class

“hot” will sometimes be single processed due to

time constraints, and developer lots will be single

processed because new recipes/processes are tried out

on them. Nearly 20% of lots are developer lots. They

are used for research and development, machine

control, and maintenance. Thus, it might not be

possible to combine them with others into a swarm.

The majority of these priority classes is historically

driven. To model the lots as swarm members, the

priority class is an important parameter. Nevertheless,

by the introduction of swarm-based local rules and

interactions, the priority classes could be reduced to a

single one: the due date. This would free the system

from reserving time for hot lots, but the question is

if the treatment of hot lots is still satisfactory under

such an approach. Another important consideration

are time-coupled lots: if these can not be processed

by the next machine within a certain time frame, the

lots would be damaged and need to be discarded. To

take this into account, the urgency for time-couple

lots needs to be additionally considered.

How to Validate the Approach? Testing and predict-

ing the performance of a given algorithm is difﬁcult.

Although historical data exists for each lot (e.g., the

logical transactions from machines including move-

in and move-out operations), it is hard to get WIP

and dedication matrix data that would allow predic-

tions for new rules. Furthermore, the performance of

the manufacturing process is also dependent on exter-

nal factors like machine downs, operator sickness, or

even weather conditions like lightning strikes.

4.2 Swarm Member Candidates

The model for the problem consists of a produc-

tion plant with machines, queues, processes, lots, and

recipes. The production plant P contains several sets

or workcenters of machines W

= {M

, M

, . . . },

where m is the machine type. Each machine M

has a

queue Q

Every machine in a machine set/workcenter

can perform a process P

A set of lots L = {l

, l

, . . . } need to be processed

in the plant, where t is the product type. Each prod-

Bottom-up Job Shop Scheduling with Swarm Intelligence in Large Production Plants

329

uct type t is deﬁned by a recipe R

which prescribes

the sequence of processing steps necessary to manu-

facture this product. The lot l

can choose which of

the suitable machines M

to use for each necessary

process step P

Therefore, the recipes imply a directed graph G =

(V, E) of possible movements between the machines

of the plant, where the nodes V consist of all machines

and the edges E are deﬁned between two ma-

chines M

and M

if there exists a lot l

with a recipe

containing processes P

and P

in direct succes-

sion. A route R is an ordered list of machines which

can execute the corresponding processes in the recipe.

The taken routes are a sub-graph of G with G

⊆ G.

Out of this formal deﬁnition, we identiﬁed a num-

ber of possible components in a fab that can act as

swarm members. Machines M: know their processes

and their utilization. There are many different ma-

chines in the fab that could form either multiple co-

operating homogeneous swarms, or a heterogeneous

swarm with different capabilities. The neighborhood

is locally and dynamically deﬁned by the recipes of

the incoming and outgoing lots. Machines can take

decisions locally and can, e.g., re-order their queue

and thereby select which lot to process next. Further-

more, they can communicate with other machines,

and could ask for lots of a speciﬁc processing type.

Workcenters W : with W ⊂ M have attributes very

similar to single machines, because a workcenter is

simply a set of related machines. It can calculate

when lots will be processed internally and can use

makespan information (the time that elapses from the

start to the end of a lot’s production) to calculate when

the lots currently being processed will be ﬁnished.

Lots L: can also form either homogeneous (lots

of the same product type), or heterogeneous (lots of

multiple product types) swarms. Lots follow a spe-

ciﬁc recipe, which prescribes which process steps to

take in which order but not the concrete machine on

which to perform the required next process step. As

there are typically multiple machines which can per-

form the same process, lots could decide which ma-

chine to take next. The concrete path taken through

the machines of the fab is called a route. Typically,

lots of similar product types will share parts of their

recipes. Given a stable load situation in the machine

park, lots of the same product type and lots of similar

product types can therefore be expected to share parts

of their routes. Furthermore, lots could manipulate

their own prioritization.

Processes P: could be virtual swarm members.

They see all machines that they can potentially be

run on plus the current and total workload. Addition-

ally, they could forecast the workload, the times for

re-tooling, and have information on batching require-

ments.

5 CANDIDATE ALGORITHMS

In the following we present two candidate algorithms

for the job shop problem using bottom-up approaches.

They have been selected because they present an em-

bodied approach, thus, each agent in the algorithm

can be modeled from a “real” entity in the produc-

tion plant. These swarm members are already rep-

resented as digital twins. For the swarm approach

we can add supporting attributes (e.g., pheromones),

and observe the virtual, but local environment of the

selected swarm members. Thus, instead of a global

computation of the overall fab, the digital twins can

work and interact with local information.

5.1 Hormone Algorithm

In a semiconductor fab, a network for propagating an

artiﬁcial hormone can be constructed by the planned

processing steps (recipes) of lots. An artiﬁcial

hormone system can help to express the urgency of

a lot and the need for new lots at a machine type.

Artiﬁcial hormone produced at machines can diffuse

through the production system via the lot recipes.

Lots act as swarm members that are attracted by

hormone. The approach is inspired by the usage

of artiﬁcial hormones to reorganize agents (Sobe

et al., 2015) in a self-organizing systems for technical

applications (Elmenreich and de Meer, 2008; Elmen-

reich et al., 2009). For implementation, the artiﬁcial

hormone system is realized as a software layer spread

over the processing queues of all machines in a fab.

Machines are assumed to have artiﬁcial glands that

can produce hormone. The hormone algorithm for

optimizing lot processing in a semiconductor fab can

be decomposed into six mechanisms:

Production: Machines M

produce hormone h

ac-

cording to the number of lots in their processing

queue. Machine that are about to run out of lots pro-

duce more hormone. Each machine set/workcenter

has its own type of hormone.

| + β

, (1)

where H

is the hormone corresponding to workcen-

ter W

at machine M

, β is a smoothing factor and

| is the number of waiting lots in the queue for

machine M

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330

Evaporation: Hormone levels at an agent evaporate

exponentially with a given rate α:

i,t+1

= H

i,t

· (1 − α) (2)

where H

i,t+1

and H

i,t

, represent the state of hormone

at machine M

before and after a discrete evaluation

step.

Diffusion: Hormone diffuses from machine to ma-

chine based on lot’s recipes that connect the ma-

chines. Hormone diffuses upstream, i.e. from a later

machine in a recipe to a machine that comes before

that machine in the recipe. Thus, hormone diffusion

follows the transpose graph of G, G

. If there is an

edge in G

between process P

and a process P

being the predecessor of P

in a recipe R

), the

amount of hormone moving upstream from machine

is deﬁned by

∆H = H

· γ (3)

− =∆H (4)

where γ is a parameter setting the motility of hor-

mone. The link strength l

, p between two machines

and M

is equivalent to the number of recipes R

containing processes P

and P

in direct succession.

Each machine connected upstream receives a propor-

tional part of the upstream hormone:

+ =∆H

m,p

∑

m,r

, (5)

where

∑

m,r

represents the sum of all upstream links

from P

Diffusion through Lot Movement: Incoming lots

following an edge of G generate a ﬂow of hormone

back to where the lots came from via the correspond-

ing backwards edge in the transpose graph of G.

∆H = H

· δ (6)

− = δH (7)

+ = δH (8)

where ∆H deﬁnes the amount of hormone that moves

with the lot, calculated from the amount of available

hormone H

at a machine M

. The lot moved from

machine M

to M

, thus adding to H

. M

can be

also a machine from a different workcenter than W

Attraction: Lots are attracted by hormone, if those

match the machines types required for their next steps

in their recipe. The amount of attraction decreases ex-

ponentially based on the number of steps ahead. The

attraction force is applied to lots waiting in a process-

ing queue Q

and can make an attracted lot move for-

ward in the queue.

attraction =

∑

i,m

· ε

, (9)

where H

is the hormone amount at a machine that

is n edges away and ε is a factor < 1 deﬁning the

degradation of the hormone attraction over edge dis-

tance in graph G. Attraction is used to reorder wait-

ing lots, but other factors such as remaining raw pro-

cess time and remaining process cycle time also in-

ﬂuence lot urgency. The diffusion by lots is a self-

reinforcing process that is balanced by hormone pro-

duction based on the shortest processing queues. In

this way, a path through the system where lots are pro-

cessed quickly—the paths we would like to have in a

productive system—is marked with hormone. Each

mechanism comes with a parameter indicating the

strength of each part, that is evaporation rate α, hor-

mone production factor β, upstream diffusion factor γ,

hormone distribution factor δ and attraction factor ε.

A possible conﬁguration of these parameters is stated

in (Elmenreich et al., 2021). Due to the interaction

between each of the mechanisms forming feedback

control loops, the algorithm can operate with a broad

set of possible parameter settings.

5.2 Ant Algorithm

Ant algorithms are inspired by the foraging behavior

of ants which can ﬁnd near-optimal paths to food

sources without global knowledge by marking trails

with pheromones. They have been successfully ap-

plied to route optimization of the traveling salesman

problem (Caro and Dorigo, 1998; Di Caro et al.,

2005). As shown in Sec. 4.2 the plant can be seen as

a graph G = (V, E) and lot progression through the

fab as a routing problem. Lots are mapped to ants

and machines are mapped to network nodes. The

approach can then be decomposed as follows:

Trail Following: Lots choose the next machine M

probabilistically out of the set of possible machines

based on the local pheromone values for that

machine and a local heuristic of its current load (ie.

the queue length of the machine) as shown in Equa-

tion 10.

i, j

i, j,d

+ αη

i, j

1 + α(N

− 1)

(10)

with

η = 1 −

i, j

∑

(11)

the relative queue length of the machine and N

the number of possible machines. Instead of a

Bottom-up Job Shop Scheduling with Swarm Intelligence in Large Production Plants

331

“destination node” as in the original AntNet variant

of the algorithm, we use the next following step of

the recipe for the destination d. Thus, a machine with

a high amount of pheromone and a short queue length

becomes more attractive for a lot. The inﬂuence of

pheromone vs. local heuristic can be adjusted via a

parameter.

Trail Laying: Pheromone values are updated after

a lot has progressed. In distributed ant routing al-

gorithms for packet networks, this is done by send-

ing a backward ant to travel the same route in re-

verse after the original ant has reached its ﬁnal des-

tination. Backward ants update the pheromone val-

ues at each hop according to the time it took the

original ant to traverse the respective link. In our

approach, pheromone updates are triggered not by

sending a “reverse lot” but rather by communication

between machines. To facilitate the pheromone up-

date, each lot keeps a memory of the time it took

to traverse an edge—i.o.w. how long it took to wait

in the machine’s queue. Since complete production

of a lot takes weeks, backward communication and

pheromone update is performed as soon as a lot has

traversed a workcenter. For a chosen machine M

the

pheromone value is updated as follows:

x,d

← τ

x,d

+ r(1 − τ

x,d

) (12)

while for all potential machines M

which were not

chosen, the pheromone values are updated according

to Equation 13

n,d

← τ

n,d

− rτ

n,d

(13)

with reinforcement r depending on the time the lot

took to traverse this “hop” and the current congestion

status according to the local heuristic:

r ≡ r(T, M

) (14)

Evaporation: At regular time intervals, pheromone

values are evaporated with a rate p so that trails which

have gotten worse (e.g., due to machine downs) are

removed (Equation 15).

τ(t + 1) = τ(t)(1 − p) (15)

6 RELATED WORK

Production scheduling aims at arranging and control-

ling work and workloads in a production process so

that a given optimality criterion, such as minimizing

makespan, mean ﬂow time, idle machine time, or to-

tal tardiness is addressed (Blazewicz et al., 2019). It

is an NP-hard problem, thus belonging to the class

of hardest problems according to computational com-

plexity theory (Garey et al., 1976). To address large

problem sizes, various techniques are suggested in-

cluding differential evolution algorithms (Yuan and

Xu, 2013), genetic algorithms and tabu search (Li and

Gao, 2016), large-neighborhood search (Pacino and

Van Hentenryck, 2011), or a deﬁning scheduler upon

general purpose declarative problem solvers (Da Col

and Teppan, 2016). Although several approaches al-

ready exist, they typically make the calculations cen-

trally and beforehand (similar to existing linear opti-

mization approaches).

In swarm intelligence complex optimizations

problems are solved by using local rules inspired

by swarms of birds, ﬁsh, and ants (Almufti et al.,

2019; Hassanien and Emary, 2018). When modeling

a swarm, the choice of agents in the system needs to

be deﬁned carefully. The two main aspects comprise

the agent’s properties (internal and external states)

and the agent’s behavior. In our example, the inter-

nal or external states would describe, e.g., the agent’s

current and next process step, process time, or uti-

lization. Through its behavior, the agent can change

states from the environment, other agents, or the in-

ternal state (Schranz et al., 2020). Furthermore, we

can differentiate between three types of agents: mo-

bile, stationary or connecting agents (Wilensky and

Rand, 2015). How to choose an agent for a swarm

is application-speciﬁc. Nevertheless, (van Ast et al.,

2008) present a swarm framework to formally de-

ﬁne dynamic agents, their neighborhood, environ-

ment, and interactions. (Schranz et al., 2018) model

a swarm member by focusing on cyber-physical sys-

tems and their local memory (e.g., the current x and

y position, available energy), behaviour, physical as-

pects, security, and human interaction interfaces us-

ing the modeling tools Modelio and FREVO (Sobe

et al., 2012) to evolve a swarm algorithm solving

it. Swarm algorithms are of high interest for the do-

main of job shop scheduling as it is well-known that

optimal solutions cannot be found in feasible time

with linear optimization (Zhang et al., 2009). Nature-

inspired algorithms have been conﬁrmed to be ex-

cellent in addressing complex optimization problems

in job shop scheduling (Gao et al., 2019). The ma-

jority of related work on the application of swarm

concepts in production scheduling build upon parti-

cle swarm optimization (Ghumare et al., 2015). Ad-

ditionally, several contributions are using the artiﬁcial

bee colony algorithm (Sharma and Pant, 2017). Dig-

ital hormone models for self-organization have been

suggested in (Shen et al., 2002) and have been ap-

plied to task allocation problems (Renteln et al., 2008;

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

332

Brinkschulte et al., 2007), synthesis of robot con-

trollers (Hamann et al., 2010; Wilson et al., 2019), or

large-scale IoT systems (Sinha and Chaczko, 2017).

Artiﬁal hormone systems have also been proposed as

the basic mechanism of middleware for distributed

systems (Sobe et al., 2015). Ant algorithms have

originally been proposed in (Dorigo et al., 1996) and

(Dorigo and Gambardella, 1997). They are a bio-

inspired meta-heuristic based on the foraging behav-

ior of ants (e.g., the Black Garden ant Lasius niger

or the Argentine ant Iridomyrmex humilis) and have

been applied successfully to the NP-hard problem of

ﬁnding the shortest path in the traveling salesman

problem (Lawler et al., 1985). A thorough introduc-

tion to ant algorithms can be found in (Dorigo and

utzle, 2004) and in (Bonabeau et al., 1999); there

exist currently over a hundred variants of these algo-

rithms. Ant algorithms have also been investigated for

use as a routing protocol in packet routing networks

in, e.g., (Caro and Dorigo, 1998) or (Di Caro et al.,

2005) where they are implemented as distributed al-

gorithms using only local information at each network

node. They have been shown to converge quickly with

reasonable overhead. Compared to the related work,

we do not create a swarm that operates in a solution

space of possible schedules as solutions to a given

job-shop scheduling set, but instead derive a bottom-

up approach, where embodied agents represent physi-

cal entities in the fab (instead of representing a single

solution in the solution space), and work with local

rules from which a global behavior emerges.

7 CONCLUSION

Job shop scheduling is an NP-hard problem which

makes it impossible to ﬁnd an optimal solution of a

large scale system in reasonable time. While previ-

ous approaches often aimed at reducing the problem

size by optimizing subsets of the system, we aim for

a bottom-up approach that uses swarm-based mod-

eling to establish local interaction rules between re-

lated parts of the system. The proposed approach is

sketched via two different algorithms, one inspired by

the natural endocrine system and the other inspired by

eusocial insects. We depicted a mapping between ma-

chines and lots in the job shop system to agents of a

swarm system.

As a next step we will elaborate on the efﬁciency

of the proposed candidate algorithms using a sim-

ulation approach based on an abstracted version of

a wafer fab. An open question remains if an im-

provement is measurable at workcenter level as ap-

proximate scheduling solvers already exist for sev-

eral workcenters. This brings up another question

that needs to be answered: how to integrate with and

where to set the boundary between currently used

solvers and the swarm approach in the running sys-

tem? One possibility would be that the swarm algo-

rithms provide local information to the solver which

takes this information into account during its calcula-

tion.

ACKNOWLEDGEMENT

This work was performed in the course of project

SWILT

(Swarm Intelligence Layer to Control Au-

tonomous Agents) supported by FFG under contract

number 867530.

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