Integrating Memory-Based Perturbation Operators into a Tabu Search

Algorithm for Real-World Production Scheduling Problems

Manuel Schlenkrich

1,2

, Michael B

ogl

, Anna Gattinger

, Ionela Knospe

and Sophie N. Parragh

Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria

RISC Software GmbH, Softwarepark 32a, 4232 Hagenberg im M

uhlkreis, Austria

Keywords:

Real-World Production Scheduling, Tabu Search, Perturbation, Destroy and Repair Operator, Elite Solutions.

Abstract:

Production scheduling problems, arising in real-world use cases, are characterized by a very large number

of operations and complex constraints. In order to handle such problems, practical solution approaches need

to be generic enough, to capture all relevant restrictions, while being able to calculate good solutions in a

short amount of time. Metaheuristic methods, especially combinations of trajectory and population-based

approaches, are promising techniques to meet this criterion. In this work, we develop a framework for de-

riving and integrating memory-based perturbation operators into a highly ﬂexible Tabu Search algorithm for

scheduling problems, in order to enhance its overall performance. The perturbation operators are inspired

by evolutionary algorithms and collect valuable solution information during the Tabu Search procedure via

an elite solution pool. This information is used in a destroy-and-repair step integrated into the Tabu Search

procedure, aiming to preserve promising solution structures. We investigate several parameters and perform

computational experiments on job-shop benchmark instances from literature, as well as on a real-world indus-

try use case. Integrating the developed memory-based perturbation operators into the Tabu Search algorithm

leads to signiﬁcant performance improvements on the real-world problem. The benchmark evaluations demon-

strate the robustness of the approach, when dealing with sensitive parameters.

1 INTRODUCTION

The rise of Industry 4.0 across companies in vari-

ous sectors, accompanied by the introduction of dig-

ital twins and automated decision making, has cre-

ated a number of challenging planning problems and

increased the need for practical solution approaches.

Among those planning problems, scheduling of com-

plex production systems, as they occur in semicon-

ductor manufacturing, textile processing or the chem-

ical industry, is one of the most demanding ones.

In the literature several different approaches to

tackle production scheduling problems are avail-

able, such as the use of mixed integer linear pro-

gramming, constraint programming, machine learn-

ing techniques or metaheuristic methods, to name the

most popular choices. Even though a broad range of

solution methods exists, the availability of approaches

for problems of practical size and complexity is lim-

ited (Schlenkrich and Parragh, 2023). While some

methods are rather restricted in the size of the prob-

lems, that they can solve in reasonable time, meta-

heuristic solution methods are often able to capture

complicated constraints arising in real-world settings

and can provide good solutions in a short amount of

time.

In their work on real-life scheduling problems

with rich constraints and dynamic properties, B

ogl

et al. (2021) give a profound overview of the most

important aspects, that need to be considered when

developing scheduling tools for real industry cases.

They present a Tabu Search (TS) framework, mak-

ing use of an activity list-based representation of the

schedule, following the approach of Moumene and

Ferland (2009). The TS framework is embedded in

the production planning and execution software envi-

ronment of our partner company and is currently used

as the scheduling tool. The algorithm allows to han-

dle very large problem instances up to tens of thou-

sands of operations on a large variety of machines.

However, with increasing problem size, also the re-

quired computation time to reach a solution of ac-

ceptable quality rises. Thus, enhancing the existing

solution method, to counteract the growing computa-

tional burden, is of utmost importance and therefore

the main goal of this work.

Schlenkrich, M., Bögl, M., Gattinger, A., Knospe, I. and Parragh, S.

Integrating Memory-Based Perturbation Operators into a Tabu Search Algorithm for Real-World Production Scheduling Problems.

DOI: 10.5220/0012271900003639

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Operations Research and Enterprise Systems (ICORES 2024), pages 213-220

ISBN: 978-989-758-681-1; ISSN: 2184-4372

213

For this purpose, we extend the TS of B

ogl et al.

(2021), by deriving and integrating memory-based

perturbation (MBP) operators to foster diversiﬁcation

within the trajectory-based metaheuristic method. We

introduce a framework for deducing perturbation op-

erators that modify solution candidates on the basis

of a set of elite solutions. Promising solution pat-

terns, that are shared among the elite solutions, are

conserved, while the remaining part of the solution

candidate is largely modiﬁed, in order to diversify the

investigated solutions in the search space.

The main inspiration for our approach is com-

ing from other available works, that investigate diver-

siﬁcation strategies in different metaheuristic proce-

dures, such as Adaptive Large Neighborhood Search

(ALNS) (Ropke and Pisinger, 2006). It is an exten-

sion of Large Neighborhood Search (LNS) (Shaw,

1997). LNS and ALNS respectively, use large mod-

iﬁcations that can rearrange a solution candidate by

up to 30% or 40% to explore various regions of the

search space. A similar core idea is used in Iterated

Local Search (ILS), see e.g., Braune et al. (2007) for

an application in the scheduling context. ILS is a

trajectory-based metaheuristic method, that alternates

intensiﬁcation and diversiﬁcation phases, via small

and large step modiﬁcations respectively. The large

modiﬁcations are reached by performing perturbation

steps, that oftentimes rely on random destroy and re-

pair operators.

While both approaches, ALNS and ILS, perform

intensiﬁcation and diversiﬁcation steps iteratively,

there also exist procedures that aim to foster these

principles in two consecutive phases. In the work of

Lunardi et al. (2021), four metaheurstics are tailored

to a complex scheduling problem. The authors pro-

pose to combine different methods in order to create

more powerful approaches and use the solution of one

method as the starting point for a second one.

In our work we make use of the destroy and re-

pair concept similar to ALNS and ILS. In contrast to

ALNS however, we do not perform several large mod-

iﬁcations of the solution candidate in a row, but use it

as a one-time perturbation operator, if the Tabu Search

procedure seems to be trapped in a local minimum. In

contrast to ILS, we do not randomly destroy parts of

the solution, but aim at preserving promising parts of

the solution candidate, by collecting structural infor-

mation on the best solutions found so far during the

TS.

In the following, we ﬁrst present the investigated

scheduling problem in Section 2. Then, in Section

3 we describe our solution approach and Section 4

summarizes the numerical experiments. Finally, in

Section 5 we conclude our work and provide future

research directions.

2 PROBLEM DESCRIPTION

Within this section we describe the investigated pro-

duction scheduling problem, which has also been ad-

dressed by B

ogl et al. (2021). Since we propose an

extension to their approach, we tackle the same un-

derlying problem.

The task is to schedule a set of n jobs on a set

of k machines, such that a given objective function

is optimized. Each job j

consists of ˆn

operations

, . . . , o

i ˆn

}. While machines have different at-

tributes concerning their availability to process one or

more operations at each given time, also operation-

speciﬁc restrictions need to be considered.

For each operation to be scheduled, the following

data is available: An operation cannot be scheduled

before its associated earliest start time. It can ﬁnish

later than its latest ﬁnish time, but this might inﬂu-

ence the objective function value, in the case that ac-

tivity tardiness is considered. Each operation must

be assigned to a machine out of the set of compatible

machines. For each of the compatible machines the

consumed capacity, production duration and produc-

tion costs are deﬁned. After production the teardown

duration for each activity needs to be respected. Setup

times for activities are both machine- and sequence-

dependent and need to be considered. For each pro-

duction setup there is a machine dependent setup cost.

Any operation has a set of predecessors, which must

be ﬁnished before the activity itself can start, and a

set of successors, which can only start after the ac-

tivity itself is ﬁnished. These sets are not restricted

to a single predecessor and successor, but can contain

multiple ones. Also, these sets may contain opera-

tions that belong to other jobs than the activity itself.

For activities that have a direct precedence relation, an

overlap can be deﬁned. Waiting times have to be con-

sidered after an operation is ﬁnished, however without

occupying the assigned machines. Also, transporta-

tion times arise, when operations are transferred to

another machine. Transportation times are machine

dependent and are provided in a transportation time

matrix. Additional machines might be needed in or-

der to perform an operation. In this case an additional

operation is created that needs to be scheduled simul-

taneously. In case that a partial schedule is already un-

der execution, current start and end times of execution

can be speciﬁed. Finally, several objective functions

can be deﬁned. Popular choices are minimizing the

makespan, total weighted tardiness on activity level

(TWT) or total weighted order tardiness (TWOT).

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

214

3 MEMORY-BASED

PERTURBATION

FRAMEWORK

TS is a trajectory-based metaheuristic method, itera-

tively evaluating solution candidates in order to ﬁnd

near-optimal solutions for optimization problems,

such as production scheduling problems. Neighbor-

hood operations, which are small modiﬁcations of the

current solution, are applied to generate new candi-

dates. The term ”tabu” in the name of the method

refers to a list of forbidden neighborhood moves,

the so called tabu list, which helps the algorithm

avoid getting trapped in local optima. Tabu Search’s

strength lies in its ability to intensify the search for

better solutions, rather than diversifying the search

space. This can be advantageous in promising areas

of the solution space, however might delay the search

procedure in the case that the algorithm is stuck in an

unfavorable area. In order to support diversiﬁcation

of trajectory based metaheuristics, several works pro-

pose combinations with population based approaches,

see e.g. Lunardi et al. (2021).

We foster this concept of combining trajectory and

population-based metaheuristics, but instead of se-

quentially performing different methods we directly

integrate principles of evolutionary algorithms into an

operator used within the TS framework. The idea is

to diversify solution candidates, as soon as the speed

of improvement falls below a certain level, meaning

that the TS is not able to make use of its strong in-

tensiﬁcation mechanism. Perturbation operators are a

common tool to diversify solution candidates. They

perform a large modiﬁcation of the current candidate,

moving to another area in the solution space, which

is possibly more promising. The problem with com-

mon perturbation operators is, however, that much

of the effort already invested by the TS algorithm is

lost, because the structure of the candidate is modi-

ﬁed randomly. To counteract this issue, we develop

a memory-based perturbation framework, that aims at

preserving promising solution structures of the cur-

rent solution, while only destroying non-promising

parts in order to reach diversiﬁcation. Information

about promising structures is extracted from an elite

solution pool, which is collected during the TS proce-

dure. The solution pool is then evaluated by means of

a conﬁgurable evaluation criterion, that detects shared

properties or structures among the elite solutions. Af-

ter that a parameterizable acceptance criterion de-

cides, which of the solution characteristics are shared

among enough of the elite solutions, in order to be

classiﬁed as promising properties, that should be con-

served for later iterations within the TS. In the fol-

lowing, the unpromising part of the candidate is re-

moved, while the promising part is preserved, using

the destroy-and-repair concept. After rearranging the

removed part, the newly generated solution candidate

is diversiﬁed, without destroying the most promising

solution patterns.

Algorithm 1 presents the TS procedure using a

ﬁrst improvement implementation. It includes the

mechanism to trigger a perturbation step, which could

be either a random perturbation or one of the proposed

MBP operators. The remainder of the work will focus

on the perturbation step, while keeping the core com-

ponents and parameters of the TS unchanged.

Data: Problem data, Tabu Search parameters,

Perturbation parameters

Result: Best found solution

initial solution s ← construction heuristic;

incumbent solution s

′

← s;

best solution s

∗

← s;

nonImprovingIterations = 0;

while termination criterion not met do

bestOb jective = ∞;

nonImprovingIterations + +;

while maxNeighborhoodSize not reached

generate next non tabu neighbor ˆs of

′

;

if ob jective( ˆs) ≤ bestOb jective then

¯s ← ˆs;

bestOb jective ← ob jective(¯s);

end

if ob jective( ˆs) ≤ ob jective(s

′

) then

nonImprovingIterations = 0;

break;

end

′

← ¯s;

update tabu list;

if ob jective(s

′

) < ob jective(s

∗

) then

∗

← s

′

;

end

if nonImprovingIterations ≥

perturbationTriggerLimit then

′

← PerturbationOperator(s

′

);

nonImprovingIterations = 0;

end

Return s

∗

as best found solution;

Algorithm 1: Tabu Search procedure in the ”ﬁrst improve-

ment” implementation including perturbation steps.

Integrating Memory-Based Perturbation Operators into a Tabu Search Algorithm for Real-World Production Scheduling Problems

215

Figure 1: The Memory-Based Perturbation Framework.

There are several possibilities to construct a per-

turbation operator, that serves the purpose described

above. We have developed a framework, which can be

used to derive different operators, based on four im-

portant components, namely the design of the elite so-

lution pool, choice of a suitable evaluation criterion,

deﬁnition of an acceptance level and procedure for the

destroy-and-repair phase. Figure 1 presents the devel-

oped MBP framework, which is further described in

the following sections.

Elite Solution Pool. The elite solution pool is a col-

lection of solution candidates obtained during the ex-

ecution of the TS. Since the goal is to gather infor-

mation on promising solution structures, the solution

candidates selected for the elite solution pool are sup-

posed to be of adequate quality. This could, for ex-

ample, mean that every newly best found solution is

added to the pool. Another option would be to select

all newly found incumbent solutions, which are the

solution candidates used by the TS to generate neigh-

boring solutions. On top of the initial selection crite-

rion for the elite solution pool, also a time-dependent

criterion can be deﬁned, restricting the elite solutions,

based on the TS iteration in which they have been

added to the set. This could either mean assigning

higher relevance to more recent candidates or delet-

ing earlier and therefore more outdated candidates.

Evalution Criteria. Once the relevant elite solution

pool is deﬁned, a criterion for evaluating the selected

solution candidates need to be speciﬁed. This crite-

rion determines the solution properties, that should be

compared among the elite solutions in order to deduce

promising patterns among them, meaning that several

solutions of good quality share the same characteris-

tic. There are numerous possibilities to deﬁne such

an evaluation criterion, e.g., to compare the machine

index of activities, the activity list index or the over-

lap of ranges around activity starting times. Through

the highly modular approach, this criterion can be ex-

changed effortless, leading to different MBP opera-

tors.

Overlap Acceptance Level. After evaluating the

solutions in the elite solution pool according to the

chosen evaluation criteria, an overlap acceptance level

needs to be speciﬁed. This acceptance level deter-

mines, if the chosen properties are shared among

enough elite solutions, to be deﬁned as promising so-

lution patterns. These acceptance levels can again

be deﬁned and replaced in a highly ﬂexible manner,

leading to different operators. A very strict accep-

tance level would be to categorize solution patterns

as promising, only if they are shared among all solu-

tions in the elite solution pool. This criterion could be

moderated by only demanding an overlap on a frac-

tion of the elite solutions. An approach to keep the

size of the preserved part of the solution stable, is to

always categorize a ﬁxed fraction of the solution as

promising, namely the one with the highest overlap

among the elite solutions. We will later refer to this

approach by using a so called ”destroy percentile”,

meaning that the percentile of the solution candidate

with the lowest overlap will be destroyed, while the

rest is preserved.

Destroy-and-Repair Phase. In the last phase of the

MBP, the gathered information about high quality so-

lutions and their shared promising structures is used

to preserve those structures in the current solution,

while diversifying the remaining parts. The so called

destroy phase removes all activities, that do not meet

the selected overlap acceptance criteria from the cur-

rent solution. Those removed activities are then in-

serted into the perturbated candidate, using a con-

ﬁgurable insertion mechanism, that could either be

based on activity properties or inserts randomly. The

result of the repair phase, is a new diversiﬁed solu-

tion candidate, that still contains the most promising

patterns, identiﬁed in the elite solution pool.

4 NUMERICAL STUDY

In order to evaluate the impact of the proposed ap-

proach on the performance of the TS algorithm, which

in its base version is currently used in the planning

software of the company, we derive two types of MBP

operators. The ﬁrst one uses the activity list index

evaluation criterion, meaning that elite solutions are

compared concerning the positions of each activity in

the encoded representation of the solution, namely the

activity list. The second operator uses the machine

index evaluation criterion, meaning that shared prop-

erties are evaluated by means of the position of each

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

216

activity on the machines. Both operators store the new

best found solutions within the elite solution pool and

use the destroy percentile acceptance criterion.

We ﬁrst test the TS algorithm on job-shop

scheduling benchmark instances from the literature,

where optimal solutions are known. Note, that these

problems represent a simpliﬁed version of the real-

world scheduling problem that is described in Sec-

tion 2. See e.g., Adams et al. (1988) for more infor-

mation about the job-shop scheduling problem. It is

not our goal to compete with solution approaches and

solvers, that are tailored to the job-shop scheduling

problem, such as the CP Optimizer (Laborie et al.,

2018). For our experiments on the benchmark in-

stances, we performed optimization runs with a CPU

time limit of 15 minutes per instance, which allows at

most 10,000 to 50,000 iterations per instance, due to

the overhead of the software framework. The aim of

the experiments on the benchmark instances is to bet-

ter understand the sensitivity of the approach towards

parameters, such as the number of non-improving it-

erations before a perturbation is triggered or the size

of the destroy percentile. In order to put the obtained

results into perspective, we compare them to the re-

cent approach of Yuan et al. (2023), who use deep

reinforcement learning to learn effective policies for

job-shop scheduling problems. We have chosen a

learning-based approach as a comparison, because in

the face of the complexity of our real-world schedul-

ing problem, this technique would be a reasonable al-

ternative to the currently used algorithm. In contrast,

integrating a constraint programming solver into the

software environment of the company was not a fea-

sible option.

In a second step, we apply the TS algorithm to

a real-world industry use case, which was provided

by the partner company, in order to assess its capa-

bility to improve solution quality under realistic con-

ditions. For all following experiments we chose an

equal base setting for the TS, such as employed con-

struction heuristics and available neighborhood oper-

ators. The length of the tabu list is 100 and the maxi-

mum neighborhood size for the operators is set to 300,

to name a few of the most important parameters. All

experiments were carried out on an Intel(R) Xeon(R)

Gold 5315Y CPU @3.20GHz with 8GB RAM.

4.1 Job-Shop Benchmark Results

The job-shop benchmark instances consist of two sep-

arate test sets, with different objective functions. For

instances of the ﬁrst set, the makespan should be min-

imized, while for instances of the second test set, the

total weighted tardiness (TWT) is to be minimized.

The makespan test set consists of 153 instances and

consists of ﬁve subsets, taken from different works in

the literature, namely abz from Adams et al. (1988), la

from Lawrence (1984), orb from Applegate and Cook

(1991), swv from Storer et al. (1992) and ta from Tail-

lard (1993). The number of jobs ranges from 10 to

100, while the number of machines ranges from 5 to

20, making the largest instance have 2000 operations.

The TWT test set consists of 63 instances and is di-

vided into four subsets, namely abz, la, mt and orb,

which are all taken from Singer and Pinedo (1998).

All instances consist of 10 jobs on 10 machines, re-

sulting in 100 operations each.

As a base version we tested the TS algorithm with-

out any perturbation of the solution. In a next step,

we implemented a random perturbation operator with

a ﬁxed destroy percentile. This random operator re-

moves a randomly chosen part of the solution can-

didate and inserts it back randomly. For our exper-

iments we have chosen a destroy percentile of 30%,

which turned out to be a good choice for random per-

turbation in earlier tests. A very sensitive parame-

ter is the number of non-improving steps, after which

the perturbation operator is called. For our numerical

study we choose to investigate the settings 10 and 15

for this parameter. We have chosen these values, as

we have seen that choosing a smaller value than 10

results in a search procedure, in which the solution is

destroyed too often, and on the other hand, for val-

ues larger than 15 the solutions are very similar to the

base version, since the perturbation is rarely called.

It must be noted that the best setting for this parame-

ter very much depends on the problem instances and

that intensive parameter tuning is not always possi-

ble in practice. Perturbation operators that perform

well, even for suboptimal choices of this parameter

are therefore favorable.

In a next step we performed experiments using

the TS with implementations of the MBP operators.

The ﬁrst derived operator uses the activity list index

evaluation criterion. We performed test runs with pa-

rameter NonImproving set to 10 and 15 in order to

compare the behavior to the random perturbation set-

ting. Since we have observed similar results for the

MBP operator in both settings, we decided to use the

slightly better performing parameter setting of 15 for

the ﬁnal experiment, which was running the TS with

the MBP operator, that uses the machine index eval-

uation criterion. For each of the derived perturbation

operators we investigate three settings for the destroy

percentile, namely 10%, 30% and 50%.

Table 1 presents the results for the makespan test

instances, displaying the percentage deviation from

the optimal makespan, averaged over the respective

Integrating Memory-Based Perturbation Operators into a Tabu Search Algorithm for Real-World Production Scheduling Problems

217

instance group. For the makespan instances we ad-

ditionally report the results obtained by Yuan et al.

(2023). Table 2 shows the results for the TWT in-

stances, reporting the absolute deviation of the opti-

mal tardiness in minutes, again averaged over the re-

spective instance group.

Integrating the MBP operators into the TS leads to

improvements on both instance sets, compared to the

base version. The average deviation from the opti-

mal makespan over all 153 test instances was reduced

from 12,7% to 10,5%. In contrast, the random per-

turbation with the NonImproving parameter set to 15

led to nearly no improvement. With this parameter

set to 10, the random perturbation even led to a worse

makespan than the base version. This indicates that

choosing the trigger level for the perturbation too low,

in combination with large uncontrolled modiﬁcations,

can harm the search procedure by jumping to another

search area, without exploiting the full potential of the

current region. Among the MBP operators, however,

we observe rather stable results, meaning that even for

a high number of perturbation calls, solution quality

stays adequate. This is a practically highly relevant

aspect, since those parameters cannot always be tuned

in a real-world setting, where time is scarce.

On the second benchmark test set the absolute de-

viation of the TWT from the optimal value averaged

over all 63 instances was reduced from 194 minutes

to 182 minutes by applying the MBP operators. Also,

for the TWT instances the results show, how sensitive

the search procedure is to the NonImproving param-

eter. For a wrong choice of the parameter, as can be

seen in the columns for a value of 10 in the random

perturbation case, the results drastically deteriorate.

Again, this can be reasoned by the fact, that solution

candidates are modiﬁed too drastically, before new

better solutions can be found by the neighborhood

operators. This test set, however, also demonstrates,

that for good choices of the NonImproving parame-

ter, even the random perturbation can lead to better

results, as it can be seen for the choice of 15.

4.2 Real-World Industry Case

Finally, we have the possibility to evaluate the pro-

posed perturbation operators on a real-world industry

case with 905 operations on 67 machines. It includes

all the aspects and constraints described in Section

2. Activity deadlines, as well as order deadlines are

available in the data, meaning that we can evaluate ac-

cording to the two objectives, that are relevant for the

company, namely total weighted tardiness (on activ-

ity level) and total weighted order tardiness (on or-

der level). For each of the two objectives we per-

form test runs, using the TS without perturbation as

the base version, with random perturbation, as well

as with MBP operators using the activity list index

and the machine index evaluation criteria. For the

perturbation operators we again test 10%, 30% and

50% destroy percentiles. We have seen, that for the

real-world use case strong diversiﬁcation after a small

number of unsuccessful iterations is even more crucial

than for the benchmark instances, due to the smaller

overall number of possible iterations. Therefore, we

evaluate the values 2 and 10 for the number of non-

improving steps before perturbation. We perform 100

iterations per approach and objective, resulting in a

runtime of approximately 1 hour for each of the ex-

periments. Tables 3 and 4 present the evaluation re-

sults on the real-world industry case for the TWT and

TWOT objective, respectively. A more detailed rep-

resentation of the search procedure and the objective

value paths, reached with the best parameter settings

for each approach, can be found in Figure 2 for the

TWT case and in Figure 3 for the TWOT case. For all

perturbation approaches the best evaluated parameter

for the destroy percentile was 10%. In the TWT case,

the best found setting for the non-improving parame-

ter was 2 for MBP with the activity list index criterion,

while it was 10 for random perturbation and MBP

with the machine index criterion. For the TWOT ob-

jective on the other hand, a value of 2 performed best

for the MBP with the machine index criterion, while

10 was superior for MBP with the activity list index

criterion. For random perturbation both 2 and 10 gave

the same result.

First of all, we see that random perturbation is not

effective for the real-world use case. Destroying a

random part of the solution makes it difﬁcult to re-

cover quickly and can even lead to worse results than

using no perturbation at all. For the TWT objective

function, TS with MBP using the machine index crite-

rion leads to a solution that is 26% better than the base

version. TS with MBP using the activity list index cri-

terion is 29% better. Figure 2 shows that the four ap-

proaches perform equally until iteration 60. The base

approach without perturbation is from this point stuck

in a local minimum. Random perturbation cannot re-

cover from its large modiﬁcations, which destroyed a

large part of the previously achieved solution quality.

Both MBP operators, however, continue to ﬁnd new

best solutions by applying more controlled perturba-

tion steps, preserving the best solution properties.

In the TWOT case, the ranking of the two MBP

operators is switched, with the machine index crite-

rion performing best. It leads to an improvement of

40% over the base version, while TS using MBP with

activity list index leads to a slightly lower improve-

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

218

Table 1: Evaluation results for the MBP operators on the makespan test set: percentage deviation of the optimal makespan

averaged over instance group.

Perturbation None (Base) Random MBP - Activity list index MBP - Machine index DRL

NonImproving 10 15 10 15 15

Destroy percentile 30% 30% 10% 30% 50% 10% 30% 50% 10% 30% 50%

abz 13.4% 17.9% 14.0% 12.5% 11.3% 10.8% 13.0% 11.8% 13.3% 13.1% 12.6% 12.5% 14.7%

la 3.3% 7.5% 3.4% 2.6% 2.1% 2.6% 2.7% 2.1% 2.3% 2.5% 2.5% 2.8% 10.9%

orb 7.1% 11.3% 4.4% 4.4% 3.5% 3.7% 5.8% 3.6% 4.2% 4.7% 6.1% 5.0% 20.9%

swv 19.3% 21.1% 17.8% 16.0% 16.4% 17.4% 16.1 16.2% 17.6% 17.7% 17.4% 16.6% 22.4%

ta 16.2% 18.5% 16.6% 13.5% 14.1% 15.3% 14.0% 13.9% 15.1% 14.1% 14.1% 14.9% 18.3%

Average 12.7% 15.6% 12.5% 10.5% 10.6% 11.5% 10.8% 10.5% 11.4% 11.0% 11.0% 11.4% 16.8%

Yuan et al. (2023)

Destroy percentile = fraction of the solution that is destroyed in the perturbation step, DRL = Deep Reinforcement Learning, MBP = Memory-Based Perturbation, NonImprov-

ing = Number of non-improving Tabu Search steps before perturbation is triggered.

Table 2: Evaluation results for the MBP operators on the TWT test set: total difference to the optimal tardiness in minutes

averaged over instance group.

Perturbation None (Base) Random MBP - Activity list index MBP - Machine index

NonImproving 10 15 10 15 15

Destroy percentile 30% 30% 10% 30% 50% 10% 30% 50% 10% 30% 50%

abz 66.7 253.8 37.7 58.2 63.8 31.2 66.7 59.3 63.7 63.7 68.8 60.7

la 80.7 173.7 69.0 82.6 80.7 74.4 76.9 74.2 73.4 77.9 78.3 78.0

mt 165.7 197.0 185.3 175.33 162.3 175.3 153.0 175.3 175.3 175.3 168.0 175.3

orb 340.0 576.7 311.9 336.2 333.9 328.3 319.7 332.5 317.7 331.9 327.5 326.7

Average 194.6 355.2 175.7 193.4 191.5 183.9 183.6 188.3 182.1 190.1 187.9 187.6

Destroy percentile = fraction of the solution that is destroyed in the perturbation step, MBP = Memory-Based Perturbation, NonImproving = Number of

non-improving Tabu Search steps before perturbation is triggered.

Table 3: Evaluation results in minutes for the real-world use

case, displayed for the total weighted tardiness (TWT) after

100 iterations per approach.

NonImproving 2 10

Destroy percentile 10% 30% 50% 10% 30% 50%

No perturbation (Base) 107,572

Random perturbation 146,217 146,217 146,217 107,572 107,572 107,572

MBP-Activity list index 76,548 146,217 146,217 107,572 107,572 107,572

MBP-Machine index 102,315 82,663 146,217 79,967 107,572 107,572

Table 4: Evaluation results in minutes for the real-world

use case, displayed for the total weighted order tardiness

(TWOT) after 100 iterations per approach.

NonImproving 2 10

Destroy percentile 10% 30% 50% 10% 30% 50%

No perturbation (Base) 50,328

Random perturbation 50,328 50,328 50,328 50,328 50,328 50,328

MBP-Activity list index 45,027 50,328 50,328 31,322 50,328 50,328

MBP-Machine index 29,898 48,133 30,900 48,133 39,615 50,328

ment of 37%. As it can be seen in Figure 3, also for

this objective all approaches perform equally during

the early phases of the search procedure, however di-

verge in later iterations.

5 CONCLUSIONS

We have proposed a framework to derive perturbation

operators that preserve promising structures of solu-

tion candidates, based on an elite solution pool, col-

lected during a TS procedure. After presenting a va-

riety of possibilities to conﬁgure the parameters for

these perturbation operators, we have implemented

two variants and performed numerical experiments on

job-shop benchmark instances from the literature, as

well as on a real-world industry use case. In sev-

eral test runs, we have compared the performance

Figure 2: Objective value path over 100 Tabu Search itera-

tions for the real-world industry case with the objective to

minimize total weighted tardiness (TWT).

Figure 3: Objective value path over 100 Tabu Search itera-

tions for the real-world industry case with the objective to

minimize total weighted order tardiness (TWOT).

of the TS before and after the integration of the de-

rived perturbation operators. We see that the TS in-

cluding the proposed perturbation steps is competi-

Integrating Memory-Based Perturbation Operators into a Tabu Search Algorithm for Real-World Production Scheduling Problems

219

tive with learning-based techniques, such as deep re-

inforcement learning. Due to their ability to capture

the complexity of the problem at hand, those meth-

ods would have been an implementable alternative to

the currently used TS algorithm. However, our re-

sults support the choice for the enhancement of our

metaheuristic approach. Moreover, experiments on

benchmark instances demonstrate how sensitive ran-

dom perturbation operators react to crucial parame-

ters, such as the number of non-improving solutions

before triggering a perturbation. Concerning stability,

the MBP operators have shown a signiﬁcantly better

behavior.

Most notably, the integration of the MBP oper-

ator leads to signiﬁcant improvements on the real-

world case study. For both evaluated objective func-

tions, TWT and TWOT, the TS with MBP opera-

tor outperformed the base version without perturba-

tion steps, as well as the random perturbation ap-

proach. In the TWT case, activity tardiness was re-

duced by 29%, while in the TWOT case order tar-

diness was reduced by 40%. This shows, that espe-

cially on large instances the mechanism to preserve

promising solution structures within the perturbation

steps has the potential to increase overall solution per-

formance. Since the presented framework relies on

several different parameters that can be analyzed, we

plan to further investigate the impact of other factors

on the overall solution performance. We will in more

detail evaluate the inﬂuence of the neighborhood size,

which determines how many neighbors are evaluated

by the neighborhood operators of the TS. Also other

neighbor selection strategies, such as best improve-

ment, will be compared to the current algorithmic set-

ting. Moreover, we plan to derive additional MBP

operators from the proposed framework, investigating

other evaluation criteria, that could be based, e.g., on

activity starting times, or more sophisticated repair-

mechanisms.

ACKNOWLEDGEMENTS

The research was supported by the Austrian Research

Promotion Agency (FFG) (grant # FO999907709).

This support is gratefully acknowledged.

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