An Artiﬁcial Hormone-based Algorithm for Production Scheduling from

the Bottom-up

Wilfried Elmenreich

, Alexander Schnabl

and Melanie Schranz

Institute of Networked and Embedded Systems, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

Lakeside Labs, Klagenfurt, Austria

Keywords:

Production Scheduling, Job-shop Scheduling, Artiﬁcial Hormone Systems, Self-organizing Systems, Swarm

Systems.

Abstract:

This paper presents a model for supporting a production scheduling system with an artiﬁcial hormone algo-

rithm. The system consists of lots that have to undergo a number of processing steps on different machines.

The processing steps for a lot are formalized in a recipe assigned to the lot type. Since the steps in the recipe

have to be processed in order, the given system allows choice only in the context of selecting a particular

machine for the next step and in changing the processing order of waiting lots at a machine. Optimization of

such a job-shop scheduling system is an NP-hard problem. In the approach proposed by this paper, artiﬁcial

hormone systems are used to express the urgency of a lot and the need for new lots at a machine type, thus pro-

viding a system using local information for optimization. Results indicate that the artiﬁcial hormone system

provides an improvement of around 5% over a First Come-First Serve approach.

1 INTRODUCTION

The production of logic and power integrated circuits

(ICs) in the semiconductor industry is a highly dy-

namic process (Geng, 2018). Unlike the high-volume

production of memory ICs, in the logic and power

sector, the wafer production has a huge product mix,

dynamic changes in the system and a high number

of processing steps and involved machines (Khatmi

et al., 2019). Weekly workloads can involve around

operations on 10

machines (Teppan, 2018). Op-

timizing such a system for WIP (work in progress)

and ﬂow factor is an NP-hard problem (Garey et al.,

1976), where existing dispatching rules and linear

optimization methods cannot cope with the NP-hard

search space (Lawler et al., 1993), and thus cannot

consider the entire system behavior due to computa-

tional complexity. Therefore, they cannot exploit the

optimization potential in job-shop scheduling in semi-

conductor production systems (Khatmi et al., 2019).

To overcome this issue, we model the production

plant as a self-organizing system of agents that in-

teract with each other in a non-linear way. There-

fore, we aim at achieving near-optimal solutions in

feasible computation time. Furthermore, such a sys-

tem is also able to adapt to changes in the environ-

ment, scale with the number of agents, and is robust

against a single point of failure, as the actions de-

pend on local interactions (Heylighen, 2001). More-

over, local rules and local interactions allow over-

coming the huge computing time of centrally per-

formed linear optimization. One possibility for a self-

organizing approach are algorithms modeled after bi-

ological hormone systems. Such artiﬁcial hormone

systems are inspired by the biological endocrine sys-

tem that is adjusting the metabolism of tissue cells

in our body (Turing, 1952; Sobe et al., 2015). It

is a class of self-organizing system with properties

like scalability, adaptability, and robustness (Prehofer

and Bettstetter, 2005) that can be used in networked

technical applications to coordinate a set of com-

plex agents interacting with each other (Elmenreich

et al., 2009; Böszörmenyi et al., 2011; Sobe, 2012).

Such algorithms are especially of interest for such

large cyber-physical systems, as, for example, in the

semiconductor industry, where traditional control or

scheduling mechanisms are at their limit.

In this paper, we describe an artiﬁcial hormone al-

gorithm that can be applied to optimize the process-

ing of lots and to balance the load between machines

of the same type. Section 2 describes the target sys-

tem problem statement that forms the basis to inte-

grate an artiﬁcial hormone-based algorithm in such a

system in Section 3. Section 4 evaluates the approach

296

Elmenreich, W., Schnabl, A. and Schranz, M.

An Artiﬁcial Hormone-based Algorithm for Production Scheduling from the Bottom-up.

DOI: 10.5220/0010243902960303

In Proceedings of the 13th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2021) - Volume 1, pages 296-303

ISBN: 978-989-758-484-8

compared to a FIFO (ﬁrst-in-ﬁrst-out) principle and

presents simulation results in Section 5. Finally, Sec-

tion 6 presents the related work to this topic and Sec-

tion 7 concludes the paper.

2 PROBLEM STATEMENT

A production plant has a number of machines, each

being able to perform a speciﬁc process. Additionally,

there can be multiple instances of a machine type. It

is guaranteed that there exits at least one machine for

each process step. Based on real semiconductor facto-

ries the processing time at a machine ranges between

20 minutes and 2 hours. Table 1 depicts the parame-

ters of the system model. The notation N represents

a Normal distributed random variable, while U repre-

sents a uniformly distributed random value. Random

values are calculated once for each instance and re-

main unchanged for the duration of a simulation. The

processing time for each machine type will be set to

the outcome of a random variable X ∼ N (1.16,0.32)

at the beginning of a simulation. This corresponds

to a Normal distribution with 99% of values being

between 0.33 and 2 hours. For a simulation, a vir-

tual production plant comprising a random set of ma-

chines is generated. As it is common in the semicon-

ductor industry, wafers are combined in groups of 25

pieces forming a so-called lot. Each lot is assigned a

unique identiﬁcation number and follows a respective

recipe deﬁning an ordered list of process steps the lot

has to undergo at different machines. In our simulated

problem set, lots are instantiated according to one out

of 100 recipes. Based on the Raw Process Time (RPT)

each individual lot gets a Planned Cycle Time (PCT)

that is between 2 and 10 times higher than the RPT.

Half of the machines employ batch processing, where

lots are processed in parallel batches of U(2,8).

3 ARTIFICIAL HORMONE

ALGORITHM

The artiﬁcial hormone algorithm is engineered in a

bottom-up approach to express the urgency of a lot

and the need for incoming lots by machines. There-

fore, artiﬁcial hormones are produced at machines

which can diffuse through the production system

along with the processing steps of lots. The lots act as

swarm members that can be attracted by the hormone

level of a machine. The algorithm is based upon ﬁve

parameters, which are described with their respective

mechanisms in the following. Table 2 depicts an ad-

Table 1: Parameters used in the simulation model.

Parameter Value

Process types 100

Machines per process type U(2,10)

Machines with batch pro-

cessing

Batch size U(2,8)

Processing time per produc-

tion step

X ∼ N (1.16, 0.32)

Number of recipes (lot

types)

100

Recipe length U(90,110)

Lots per type U(2,10)

PCT U(2,10)× RPT

Total number of operations ≈ 60 000

hoc deﬁnition of parameter values, which will be used

in ﬁrst simulations. The algorithm describes the cal-

culations and decision mechanisms that affect the pro-

cessing of lots. There are several degrees of freedom

for a particular implementation in the ﬁeld. For exam-

ple, the hormone-related computing could take either

at the machines or within a layer of a networked mon-

itoring and control system.

3.1 Hormone Model

For each processing step, a corresponding hormone

type exists. Hormones can be at any machine, also

different hormone types can be at the same machine.

Every simulation tick, hormones degrade exponen-

tially at a given rate α.

hormone_amount = hormone_amount · (1 − α) (1)

An evaporation rate of 0 means that hormones do

not degrade. The maximum value is 1, where hor-

mones degrade immediately.

3.2 Machines Produce Hormone to

Attract Lots

Each machine generates a hormone of its process

type. Machines that perform the same process type

issue the same hormone. If a machine would be able

to handle multiple process types, it would issue, in

equal parts, the respective multiple hormones instead.

The goal of machines is to maximize their working

time. Therefore, a machine would aim for pulling a

sufﬁcient number of lots into its queue. The amount

of hormone produced by one machine is therefore cal-

culated by

hormone_output =

lots_in_queue + β

, (2)

where β is a smoothing factor > 0.

An Artiﬁcial Hormone-based Algorithm for Production Scheduling from the Bottom-up

297

Table 2: Suggested algorithm parameters.

Parameter Value

α .3

β 1

γ .5

δ .2

ε .8

3.3 Machines Are Linked

A machine A is upstream-linked to a machine B if

there exists a recipe that has a process of machine

B and a process of machine A in subsequent steps.

If each machine has exactly one process, the link-

ing strength from this recipe is 1, otherwise, the link

strength is 2 divided by the number of supported pro-

cesses. If the same sequence appears in other recipes,

the link strength adds up.

3.4 Hormone Diffuses Upstream

If upstream links exist, a part γ of the hormone at a

given machine diffuses upstream:

upstream_hormone = hormone_amount · γ (3)

hormone_amount =

hormone_amount − upstream_hormone (4)

For each machine connected upstream a propor-

tional part of the upstream hormone is added:

added_hormone =

upstream_hormone

link_strength

∑

link_strengths

, (5)

where link_strength refers to the upstream link

strength for the given hormone between the respec-

tive machines and

∑

link_strengths refers to the sum

of all upstream link strengths for the given hormone

that emerge from the sending machine.

3.5 Incoming Lots Diffuse Hormone

In addition to the mechanism above, incoming lots

cause a part δ of the respective hormone at a given

machine to diffuse upstream.

upstream_hormone = hormone_amount · δ (6)

hormone_amount =

hormone_amount − upstream_hormone (7)

The machine where the lot came from receives the

upstream hormone, this way a ﬂow of lots can self-

stabilize.

added_hormone = upstream_hormone (8)

3.6 Lots Are Prioritized by Their

Timing

A lot has a base priority calculated from its remaining

RPT and its remaining PCT:

base_priority =

remaining_RPT/remaining_PCT (9)

3.7 Lots Are Attracted by Hormone

The priority of a lot is modiﬁed by hormones that are

present at the machine where the lot is currently wait-

ing

attraction =

∑

i=0

· ε

, (10)

where h

is the hormone of the process that is i steps

ahead in the lot’s recipe. Therefore, h

is the hor-

mone of the current process. ε is a factor indicating

the strength of a hormone’s inﬂuence.

The priority of a lot is then calculated with:

priority = base_priority · attraction (11)

At a machine, lots are processed based on their

priority. If a machine has batch processing, all lots

that ﬁt are accepted for one batch.

4 EVALUATION

4.1 Evaluation Environment

The simulation was constructed in a NetLogo en-

vironment. NetLogo is an agent-based modeling

software which includes the NetLogo programming

language and an integrated development environ-

ment (Wilensky and Rand, 2015). An agent-based

model is used to simulate the interactions of au-

tonomous agents while also keeping track of the

whole simulated system. Every autonomous agent

makes decisions on its own based on predeﬁned rules

which later impact the outcome of the simulation. In

the case of the problem statement, the agents are ma-

chines and lots. Before the simulation can start, the

parameters have to be set. This can be achieved via

the GUI in NetLogo or, for larger quantities, with con-

ﬁguration ﬁles. Then, the Setup function is called to

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

298

initialize the model. It uses the speciﬁed parameters

or parses the given conﬁguration ﬁles to generate the

agents. After the machines and lots have been placed

in the production plant, the lots are introduced into

production as shown in Figure 1. In it the machines

are shown as squares, batch machines are being visu-

alized with additional lines. The lots are numbered

based on their product type and the most recent path

they took is marked with a line.

4.2 NetLogo Model

After the initialization of all entities is ﬁnished, the

production starts. A production step runs as follows:

Every lot moves to the queue of the production type

speciﬁed in its recipe. It only does so if it is currently

not being processed by a machine. The algorithm then

updates the hormones and sorts the queues based on

the priority of the lots as described in Section 3. List-

ing 1 shows a simpliﬁed version of the step function

and Listing 2 and 3 outline two exemplary hormone

functions.

Figure 1: Screenshot from the Netlogo simulation: After

initialization the lots start being processed and move to the

queues speciﬁed in their recipes.

Listing 1: NetLogo process step.

to step

ask lots [

if not processing? [ move−to−queue ]

]

ask machines [

produce−hormones self

decay−hormones self

]

sort−queues

ask machines [

pick−lots−from−queue

do−processing

]

end

Listing 2: NetLogo hormone production function.

to produce−hormones [ m ]

let q (item ([m.machine_type] of machine m − 1)

queue_list)

let q_len length [q.lotlist] of q

ask machine m [ set m.hormone_amount

m.hormone_amount + (1 / ( q_len + BETA))

]

end

Listing 3: NetLogo hormone decay function.

to decay−hormones [ m ]

ask machine m [ set m.hormone_amount

m.hormone_amount

(1 − ALPHA) ]

end

After the calculations are done, the machines pick

the lots with the highest priority from their queue to

be processed. When a lot ﬁnishes its recipe it leaves

the production plant and writes its ProductionTime,

RPT and PCT to a ﬁle. This sequence is repeated un-

til there are no more lots left in the production plant.

4.3 Headless Implementation

Using the technique speciﬁed above it is possible to

gather large amounts of data by running multiple in-

stances of the simulation simultaneously without a

GUI in headless mode. The headless controller soft-

ware was written in Python using the NL4Py pack-

age

. This package was chosen instead of other

NetLogo controller software or the NetLogo Be-

haviourSpace because the algorithm has a very high

time complexity and as soon as it gets to simulating

larger quantities of machines, lots, etc. there is a sig-

niﬁcant improvement in performance. Through the

threading module multiple simulations can be exe-

cuted at the same time. The Python code was aug-

mented with an automated conﬁguration ﬁle genera-

tor. It creates new ﬁles for each simulation run using

randomly chosen values within the limits speciﬁed in

Table 3. Listing 4 shows an example workspace for

multi-threading.

Listing 4: Python headless workspace.

d e f s t a r t _ w o r k s p a c e ( c o n f i g _ f i l e ,

p a r a m e t e r s ) :

wo r k s p a c e = n l 4 p y .

newNe t L o g oHead l e s s Works p a c e ( )

wo r k s p a c e . openModel ( model )

wo r k s p a c e . command ( " S e t u p " )

. . .

https://pypi.org/project/NL4Py/

An Artiﬁcial Hormone-based Algorithm for Production Scheduling from the Bottom-up

299

wo r k s p a c e . command ( " h e a d l e s s −go " )

w h i l e ( p r o c e s s i n g == 0 ) :

t i m e . s l e e p ( 2 0 )

p r o c e s s i n g = w o r k s p a c e . r e p o r t ( "

IS_FINISHED " )

t i c k s = s t r ( wo r k s pa c e . r e p o r t ( "

t i c k s " ) )

p r i n t ( " Ti c k s : " + t i c k s )

4.4 Parameter Optimization

Another implementation of the algorithm was devel-

oped in Java so as to achieve a better way of ﬁnd-

ing optimal parameter values for the algorithm. This

had various reasons such as performance and adapt-

ability for future work. With the possibilities of

object-oriented programming, the created simulation

environment matching the problem statement is only

based on 3 functions and it is now possible to sim-

ply exchange the algorithm of a production plant to

compare different approaches with one another. The

creation of new algorithms is also fairly easy and for

data comparison, a simple ﬁrst come, ﬁrst served al-

gorithm was also used.

5 SIMULATION RESULTS

The simulation results of the NetLogo model are eval-

uated based on average ﬂow factor and tardiness of

the lots. Table 3 details the used evaluation parame-

ters.

ﬂow factor = production_time/RPT

tardiness = production_time − RPT

Table 3: Evaluation parameters.

Parameter Value

Initial RNG seed 58008

Number of simulation runs 100

The hormone algorithm was tested using the parame-

ters outlined in Table 1, Table 2 and Table 3. Results

are depicted in Table 4.

Table 4: Hormone algorithm average simulation results.

Average Value

Time to produce all lots 173 h

RPT 59 h

PCT 348 h

Tardiness 114h

Flow Factor 2.93

A FCFS (ﬁrst come, ﬁrst served) algorithm was used

to contrast the results. It ran with exactly the same

test set and resulted in the values depicted in Table 5.

Table 5: FCFS algorithm average simulation results.

Average Value

Time to produce all lots 184 h

RPT 60 h

PCT 331 h

Tardiness 124 h

Flow Factor 3.05

With the used parameters the hormone-based pro-

duction approach seems to perform slightly better

than an FCFS algorithm; however, considering the al-

gorithm parameters in Table 2 are ad-hoc values, there

is a chance of improving the efﬁciency of the hormone

algorithm by optimizing the parameters, which was

done with the implementation in Java. While the Net-

Logo simulation ran on multiple randomly generated

sample sets to gather a better general understanding

of the speed of the algorithm, the Java version used

the same conﬁguration of machines, lots and prod-

ucts and just the parameters were altered. Table 6 and

Table 7 show the fastest and the slowest simulation

results and parameter values of the Java hormone al-

gorithm. The algorithm with the optimized parameter

set performs 9% better than the reference algorithm,

however, it has to be noted that the optimization was

done for a single test case. More importantly, while

the two tables depict a potential for optimization of

parameters, they also show that even with a bad pa-

rameter set the algorithm works slightly better than

the FCFS algorithm. For reference, Table 8 shows the

outcomes of the FCFS algorithm.

Table 6: Hormone algorithm parameters yielding the fastest

result for the tested sample set.

Name Value

α 0.2

β 3.0

γ 0.6

δ 0.3

ε 0.7

Time to produce all lots 152 h

Table 7: Hormone algorithm parameters yielding the slow-

est result for the tested sample set.

Name Value

α 0.3

β 3.0

γ 0.5

δ 0.1

ε 1.0

Time to produce all lots 164 h

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300

Table 8: FCFS Algorithm for the tested sample set.

Name Value

Time to produce all lots 165 h

6 RELATED WORK

In a dynamic job shop, currently applied dispatching

rules are based on heuristics with the disadvantage of

not optimizing lot sequences. Although linear opti-

mization methods are used to strengthen the schedul-

ing procedure, they cannot cope with the highly com-

plex, large, and dynamic search space (Lawler et al.,

1993), mostly due to the excessive and unfeasible

computation time in dynamic production plants. This

leads to bottlenecks and work in progress (WIP)

waves are generated. So far, no optimal solution for

job shop scheduling has been developed using lin-

ear optimization that can be computed in polynomial

time (Zhang et al., 2009).

In the course of this paper, we model the produc-

tion plant as a self-organizing system of agents. Due

to its non-linearity, it is able to produce near-optimal

solutions for NP-hard problems in feasible computa-

tion times (Zhang et al., 2009; Dhiman and Kumar,

2017) by transforming the problem from ﬁnding an

overall solution to deﬁning a distributed algorithm

that ﬁnds the solution from the bottom up. The re-

lated work on the application of self-organization in

production scheduling builds upon the particle swarm

optimization (Ghumare et al., 2015), and artiﬁcial

bee colony algorithm (Zhang et al., 2013), and ant

algorithm (Udomsakdigool and Kachitvichyanukul,

2008), to name but a few. Compared to these algorith-

mic approaches, we do not create a swarm that oper-

ates in a solution space to a given job-shop scheduling

set. Instead, we derive a bottom-up approach, where

embodied agents represent physical entities in the fab,

and work with local rules from which a global behav-

ior emerges. This presents a novel approach in the

application of self-organizing principles in job-shop

scheduling.

This approach can be implemented with an arti-

ﬁcial hormone algorithm. It is a bio-inspired self-

organizing algorithm to produce near optimal solu-

tions in NP-hard, highly complex and dynamic sys-

tems based on relatively simple and local rules. The

algorithm was introduced by Sobe et al. (Sobe et al.,

2010) and describes the inspiration by the endocrine

system of higher mammals on the technical applica-

tion of sharing multimedia units. The main principle

describes virtual hormones that show their interest in

speciﬁc interest units with their concentration density.

These hormones are created, consumed or evaporated,

and forwarded by the agents in this artiﬁcial hormone

system (Szkaliczki et al., 2013). Artiﬁcial hormone

systems have been applied in technical systems such

as task allocation (Renteln et al., 2008), synthesis

of robot controller software (Hamann et al., 2010),

or content delivery in dynamic networks (Schelfthout

and Holvoet, 2003). Trumler et al. (Trumler et al.,

2006) propose an artiﬁcial hormone system as mid-

dleware for ubiquitous computing, as for example in

smart ofﬁce applications. Brinkschulte et al. present

an artiﬁcial hormone system for task allocation for

heterogeneous processing units in a processor grid

to realize self-X features (self-conﬁguration, self-

optimization, self-healing) (Brinkschulte et al., 2007;

Brinkschulte et al., 2009). Sobe et al. (Sobe et al.,

2015) build a middleware inspired by an artiﬁcial

hormone system for search and delivery of informa-

tion units. They showcase the applications of multi-

media distribution at social events, and the informa-

tion dissemination in smart electrical microgrids us-

ing tens of thousands of agents. The evaluation was

also performed on a theoretical foundation to show

that the hormone levels converge to a limit at each

agent using a set of theorems on convergence con-

ditions (Szkaliczki et al., 2016). Finally, Dong et

al. (Dong et al., 2010) successfully proposed the ar-

tiﬁcial hormone algorithm for clustering in wireless

sensor networks to prolong the lifetime of the sen-

sor nodes. Further details on the origins of the artiﬁ-

cial hormone algorithm, including the medical back-

ground of the endocrine system and its digitization,

can be found in Xu and Wang (Xu and Wang, 2011).

7 CONCLUSION

The novel contribution of this paper is the application

of an artiﬁcial hormone algorithm in the context of a

job-shop scheduling system such as a large semicon-

ductor fab from the bottom-up. The algorithm builds

upon ﬁve principles, which are (i) machines produce

hormone to attract lots, (ii) hormone diffuses process-

upstream, (iii) incoming lots diffuse hormone, (iv)

lots are prioritized by their timing, and (v) lots are at-

tracted by hormone. Via these mechanisms, machines

can balance their workload by pulling required lots

towards them. The algorithm has been implemented

and evaluated in a NetLogo simulation model. Simu-

lation results indicate that the artiﬁcial hormone sys-

tem provides an improvement of around 5% for over-

all production time and ﬂow factor.

An Artiﬁcial Hormone-based Algorithm for Production Scheduling from the Bottom-up

301

ACKNOWLEDGEMENTS

We would like to acknowledge Martina Umlauft for

her comments on the paper and the NetLogo imple-

mentation. This work was performed in the course of

project SWILT (Swarm Intelligence Layer to Control

Autonomous Agents) supported by FFG – IKT der

Zukunft under contract number 867530.

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