TABU SEARCH STRATEGIES IN SCHEDULING PROBLEM IN
FLEXIBLE MANUFACTURING SYSTEM
Considering tool switches and number of setups
Antonio Gabriel Rodrigues, Arthur Tórgo Gómez
Mastes in Computer Applied, Unisinos University, Av. Unisinos 950, São Leopoldo,Rio Grande do Sul, Brazil
Keywords: Tabu Search, Scheduling Problem, Flexible Man
ufacturing Systems.
Abstract: In this paper it’s investigated the impact of the Tabu List size, neighborhood generation approach and the
managing of the decision variables of the Objective Function in the quality of a Tabu Search solution to the
Scheduling Problem applied to a Flexible Manufacturing System. It was used a Part Scheduling Model,
which starts with qualitatively different initial solutions that yields experiments in which it’s observed the
Tabu List size influence in the results quality, according to the pre-defined Objective Function variables
contribution. This Model creates a schedule in a Flexible Manufacturing System, considering resident
tooling concepts, production turns, Part Selection, Machine Magazine Constraints and Due-dates. Numerical
results show relations among neighborhood strategies and the Tabu List size behavior considering initial
solutions and contribution managing of the Objective Function variables.
1 INTRODUCTION
In this paper the impact of the Tabu List size is
analyzed in the solution’s quality in the Scheduling
Problem applied to a Flexible Manufacturing System
(FMS). Its considered initials solutions approaches,
neighborhood generation and the managing of the
decision variables of a Objective Function. In order
to do so, two classic problems are studied: the Part
Selection Problem and the Scheduling Problem.
The FMS is the highest degree in automation of a
m
anufacturing system (Kaighobadi and Venkatech,
1993). Among several definitions, it can be said the
FMS possesses high degree of distributed data
processing and automated material flow, using
computer-controlled CNC/DNC machines, assembly
cells, robots and inspection machines (Dorf and
Kusiak, 1994; Kusiak, 1992).
The studied problems are solved with Cluster
A
nalysis techniques (Kusiak and Chow, 1986),
Dispatching rules (Kusiak, 1992) and Tabu Search
(Glover and Laguna, 1997).
Based in these techniques, a Part Scheduling Model
was de
veloped, with which experiments were
accomplished.
The Problems and the contemplated techniques are
p
resented in the section 2. In the section 3 it is
described the Part Scheduling Model. The
accomplished experiments are described in section 4
and the conclusions are showed section 5.
2 PROBLEMS AND TECHIQUES
CONTEMPLATED
The Part Selection Problem can be defined as a
technique in which similar parts are grouped
according to similar attributes of design and
production processes (Groover, 2001), respecting
environmental and machining constraints (Kusiak
and Chow,1986; Bedworth et al,1991). Similar parts
are grouped in Part Families, where each Part
Family possesses similar design/process
characteristics. In this work, the type of tool that
processes a part is the attribute used to generate the
Part Families (PF).
To solve this problem it’s used a Part Selection
M
odel (Rodrigues et al, 1999) which is based in the
Cluster Identification Algorithm created by Kusiak
and Chow (Gómez,1993). This model uses a binary
part-tool incidence matrix formulation to create PFs
and considers the tool sharing among PFs
(Gómez,1993). For the model’s performance
improvement, dynamic programming approach was
used.
20
Rodrigues A. and Gómez A. (2004).
TABU SEARCH STRATEGIES IN SCHEDULING PROBLEM IN FLEXIBLE MANUFACTURING SYSTEM - Considering tool switches and number of
setups.
In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 20-26
DOI: 10.5220/0001130200200026
Copyright
c
SciTePress
The Scheduling Problem (Kusiak and Chow, 1986)
can be defined in scheduling parts in processing
machines respecting its due dates. Other objectives
can be considered, such as minimizing throughput,
minimizing work in process and so on (Kusiak and
Chow, 1986). In this paper, the Scheduling Problem
approach concerns to the production batch
processing time reduction, through the minimization
of the number of machine stops for tool switching
(setup). The schedule generated should respect the
production turn time, or, it cannot have in processing
after the end of each turn.
To solve the Scheduling Problem, a Tabu Search
approach was proposed (Hertz, 1991; Glover, 1989).
This technique has been applied in combinatorial
optimisation problems, such as Travel Salesman
Problem, Time Tabling Problem, Job Shop
Scheduling Problem (Hertz, 1991; Glover, 1989;
Widmer, 1991). Tabu Search deals to find a better
solution exploring the feasible solution space.
Starting with an initial solution, Tabu Search
successively generates a set of feasible solutions by
well-defined moves approaches, in which a local
optimal is found. This local optimal becomes the
starting point for a new iteration. Among the
iterations, the best result found is stored. Each move
that leads to a local optimal is stored in a circular list
of forbidden (or tabu) moves, called Tabu List. The
stop criterion is defined as a number of interactions
without improvement occurrence in the best solution
found (nbmax) (Glover,1989; Gómez et al,2002).
3 MODEL ARCHITECTURE
The Part Scheduling Model (Gómez et al,2002)
deals to generate a schedule of a part set in a flexible
machine (Hwang e Shogan, 1987) considering
productions turns, minimizing the setup number.
The model’s representation is showed in Figure 1.
Figure 1: Part Scheduling Model architecture.
Each module in Figure 1 represents a specialized
algorithm and the flow among the modules shows
the execution sequence. The modules are described
following:
Part Generator Module: this module creates data for
experiments. These data are part-tool incidence
matrixes, which are the Part Selection Module input.
Part Selection Module: it applies the Part Selection
Algorithm (Kusiak e Chow,1986) in the parts that it
receive as input. These parts are grouped in PFs
according to the tool-type (Rodrigues and Gómez,
2000), taking in account the tool sharing among
PFs. An example of PF generation is shown in the
Figure 2;
Dispatching Rules Module: starting with a set of
parts grouped in PFs, this module generates a initial
scheduling of parts in the machine based in the
following criterions: Random, Part Family Sorting,
TABU SEARCH STRATEGIES IN SCHEDULING PROBLEM IN FLEXIBLE MANUFACTURING SYSTEM -
Considering tool switches and number of setups
21
Figure 2: Part-tool incidence Matrix and Part Selection.
Most dissimilar Resources, Most Similar Family
Resources and Larger Process-time First (Gómez et
al, 2002);
Tabu Search Module: starting with a initial solution,
the Tabu Search Algorithm generates a schedule that
reduces the production time through minimizing the
number of setups and the number of tool switches.
Its considered part batching and production turn
time. The Objective Function considered is the
following:
∑∑
=
==
++=
1
1
1
11
)(min
n
i
n
i
n
i
iii
BTimeSetTSwtxf
Where:
TSwt
i
: tool switches in batch i;
Set
i
: number of setups;
BTime
i
: processing time of the batch i;
n = total of batches;
The neighborhood generation approaches
considered are batch swap (where the two batches
are shifted from its turns) and batch insertion (where
a batch is removed from its turn and inserted into
another) (Rodrigues and Gómez, 2001). The Tabu
Search Algorithm implemented is shown following.
Begin
Initialise TList empty;
Initialise niter;
Initialise biter;
Initialise nbmax;
Load Initial Solution s;
Upload bs with init;
While (niter – biter < nbmax) do
Generate neighborhood V(s)
starting with s;
Calculate F(s) for each s
generated;
Find s* of V(s) that minimizes
F(s);
If (s* is not in TList) then
Bs = s*;
Biter = niter;
End_if
s = s*;
increment niter;
End_while;
End
Where:
TList: tabu list;
Niter: iteration counter;
Bs: best solution found;
Biter: iteration when a better solution was found;
Nbmax: number of iterations with no improvement
of bs;
F(s) parts processing time calculus;
V(s): neighborhood of solutions;
s: a solution in V;
s*: better solution in V;
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4 EXPERIMENTS
The model’s implementation was made in C++
language, using GCC compiler in a GNU-Linux
operational system. A Pentium III 833Mhz 128MB
RAM was used to perform the experiments batches.
A experiment batch consists that follows: the Part
Generator Module starts creating 10 par-tool
incidence matrixes with 90 parts versus 10 tools
dimension, respecting the 4 tools magazine
constraints. Each one of the five dispatching rules
receives as input the 10 matrixes and it generates a
set of initial solutions. All those initial solutions are
used by the Tabu Search Module, witch is executed
considering independently the two neighborhood
generation approaches and the Tabu List size
variation. The nbmax number was set in 120
iterations without improvement in the global result
and the Tabu List size were varied in 10, 50 and 100
positions. For each batch of experiments, the
analysis of the number of tool switches and the
number of setups is done separately.
In the following tables the statistics obtained with
the experiments are presented. Those statistics are
referring to the averages of setups number and tool
switches number of the initial solutions (generated
by Dispatching Rules) and final solutions (generated
by Tabu Search) and to the variation of the Tabu List
size. The tables 1,2 and 3 refer to the accomplished
experiments being considered the number of setups
and the tables 4, 5 and 6 consider the number of tool
switches.
The initial solutions are shown briefly: RAN
(Random Initial Solution), FAM (Part Family Initial
Solution Based), PMSR (Part Family Most Similar
Resources), MDR (Most Dissimilar Resources) and
LPTF (Larger Process Time First).
Table abbreviations:
istn = number of tool switches of the initial solution;
fstn = number of tool swsitches of the final solution;
issn = number of setups of the initial solution;
fssn = number of setups of the final solution;
std = stander deviation;
Table 1: Average of the initial and final number of setups and number of tool switches for the dispatching rules, with Tabu
List size set in 10 position and considering only the machine setup.
Initial Solutions Batch swap Batch insertion
Istn std issn std fstn std fssn std fstn std fssn std
FAM 40,4 4,22 21,9 2,23 39,8 4,92 20,2 2,66 39,8 4,92 20,2 2,66
LPTF 198,1 13,16 82,9 2,47 53,1 7,74 21,3 2,75 51,5 6,82 20,6 2,72
MDR 214,5 15,57 86,6 1,17 50,2 6,46 21,2 3,01 49,2 8,79 19,7 3,02
PMSR 28,1 2,64 20,5 2,55 27,9 3,21 19,6 3,03 27,7 3,40 19,7 2,98
RAN 200,5 13,54 77,7 20,39 51,1 5,86 20,8 2,57 50 8,26 20,1 2,77
Table 2: Average of the initial and final number of setups and number of tool switches for the dispatching rules, with Tabu
List size set in 50 position and considering only the machine setup.
Initial Solutions Batch swap Batch insertion
Istn std issn std fstn Std fssn std fstn std fssn std
FAM 40,4 4,22 21,9 2,23 39,5 5,05 19,8 2,74 39,8 4,92 20,2 2,66
LPTF 198,1 13,16 82,9 2,47 52,4 8,22 20,8 2,90 50,8 7,21 20,4 2,59
MDR 214,5 15,57 86,6 1,17 50,1 6,38 21,1 2,96 49 8,87 19,6 3,03
PMSR 28,1 2,64 20,5 2,55 27,9 3,21 19,6 3,03 27,7 3,40 19,7 2,98
RAN 200,5 13,54 77,7 20,39 49,6 8,47 20,5 2,59 49,8 8,07 20 2,62
TABU SEARCH STRATEGIES IN SCHEDULING PROBLEM IN FLEXIBLE MANUFACTURING SYSTEM -
Considering tool switches and number of setups
23
Table 3: Average of the initial and final number of setups and number of tool switches for the dispatching rules, with Tabu
List size set in 100 position and considering only the machine setup.
Initial Solutions Batch swap Batch insertion
Istn std issn std fstn std fssn std fstn std fssn std
FAM 40,4 4,22 21,9 2,23 39,5 4,99 20 2,75 39,8 4,92 39,8 4,92
LPTF 198,1 13,16 82,9 2,47 52,4 8,13 20,7 2,83 50,8 7,21 50,8 7,21
MDR 214,5 15,57 86,6 1,17 50,1 6,38 21,1 2,96 49 8,87 49 3,03
PMSR 28,1 2,64 20,5 2,55 27,9 3,21 19,6 3,03 27,9 3,40 27,9 3,35
RAN 200,5 13,54 77,7 20,39 49,6 8,47 20,4 2,67 49,8 8,07 49,8 2,62
Table 4: Average of the initial and final number of setups and number of tool switches for the dispatching rules, with Tabu
List size set in 10 position and considering only the tool switches.
Initial Solutions Batch swap Batch insertion
istn std issn std fstn Std fssn std fstn std fssn std
FAM 40,4 4,22 21,9 2,23 34,8 3,77 20 2,79 32,7 2,31 20,1 2,69
LPTF 198,1 50,41 82,9 2,47 40,8 7,83 23,1 5,00 32,3 2,11 20,4 2,41
MDR 214,5 15,57 86,6 1,17 38,7 3,92 22,2 3,16 32,3 2,58 20,2 2,86
PMSR 28,1 2,64 20,5 2,55 26,9 3,11 19,8 2,86 26,6 2,88 19,6 3,03
RAN 200,5 13,54 84 2,21 41,1 7,02 22,5 3,72 33,6 2,55 20,2 2,82
Table 5: Average of the initial and final number of setups and number of tool switches for the dispatching rules, with Tabu
List size set in 50 position and considering only the tool switches.
Initial Solutions Batch swap Batch insertion
istn std issn std fstn std fssn std fstn std fssn std
FAM 40,4 4,22 21,9 2,23 34,1 3,45 20 2,79 31,5 2,59 19,9 2,69
LPTF 198,1 50,41 82,9 2,47 37,9 5,09 21,6 2,80 31,9 2,56 20,1 2,81
MDR 214,5 15,57 86,6 1,17 37,7 4,06 21,7 3,16 30,7 2,91 19,7 2,98
PMSR 28,1 2,64 20,5 2,55 26,9 3,11 19,8 2,86 26,3 2,87 19,6 3,03
RAN 200,5 13,54 84 2,21 37,8 6,11 21,3 2,75 33 2,49 20,2 2,82
Table 6: Average of the initial and final number of setups and number of tool switches for the dispatching rules, with Tabu
List size set in 100 position and considering only the tool switches.
Initial Solutions Batch swap Batch insertion
Istn std issn std fstn std fssn std fstn std fssn std
FAM 40,4 4,22 21,9 2,23 34,2 3,46 20 2,79 30,9 3,28 19,9 2,69
LPTF 198,1 50,41 82,9 2,47 37,1 3,51 21,2 2,44 31,8 2,57 20,1 2,81
MDR 214,5 15,57 86,6 1,17 37,4 4,01 21,3 3,16 31 2,49 19,8 2,82
PMSR 28,1 2,64 20,5 2,55 26,9 3,11 19,7 2,98 26,7 3,23 20,3 3,40
RAN 200,5 13,54 84 2,21 37,9 7,19 21,1 2,69 33,2 2,49 20,2 2,82
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Can be noticed in these experiments that the
approach of neighborhood generation based on
batch insertion moves promotes a better Tabu
Search performance compared to the approach batch
swap based. That is due to the fact the move type
accomplished in the batch insertion generates a
richer neighborhood than the one generated by batch
swap approach, taking to a better result. The batch
insertion approach needs a larger number of moves
to find a qualitatively superior result (according to
the number of tool switches) to the result found by
batch swap approach (Rodrigues and Gómez, 2001).
For the Dispatching rules RAN, MDR and LPTF,
which generate worse initial solutions, the increase
of the Tabu List size has positive impact in the Tabu
Search performance, therefore it extends the search
in the solutions space.
The initial solutions approaches that present better
results were the PMSR and FAM, which as it can be
seen in previous works (Gómez et al,2002). The
Tabu List size increasing did not bring significant
performance improvements in Tabu Search that have
as initial solutions those approaches, independent of
used neighborhood generation approach. Those
Dispatching Rules generate a result very close to the
better solution, so the necessary number of iterations
to find it becomes smaller. To the Dispatching rules
RAN, MDR and LPTF, which generates worse
initial schedules (faraway from the better solution),
the increase of the Tabu List has a positive impact,
therefore it extends the search, escaping from local
optima.
It is also noticed in the experiments that the
contribution of the decision variable of the Objective
Function tool switches is more significant in the
reduction of the batch processing time, generating
better results than the ones generated for the setups
number variable contribution. The variable change
of tools considers the resource sharing among PFs,
factor that relieve in the setup time reduction,
assuring better solutions.
5 CONCLUSIONS
In this paper it was developed a Part Scheduling
Model in which it was observed the Tabu List size
variation and its influence in the Tabu Search
perfomance. In the Tabu Search Algorithm, two
approaches of neighborhood generation were used:
(the batch insertion and the batch swap approaches).
The initial solutions were based in five Dispatching
rules (RAN, MDR, PMSR, FAM, LPTF). In the
accomplished experiments, the Tabu List size was
varied.
It could be observed that the batch insertion
approach promotes better Tabu Search Performance
due to generation of a richer neighborhood in
comparison to the batch swap approach. That leads
to a larger number of iterations to find the better
result. The Tabu List variation has positive impact in
the batch swap approach, doing with its performance
went as good as the one of the batch insertion
approach.
The initial solutions that more contribute to the Tabu
Search performance improvement are PMSR and
FAM, therefore these rules take into account the
resource sharing among PFs. The Tabu List size
variation has positive impact in dispatching rules
that generates worse initial solutions (RAN, MRD,
LPTF), because with the search diversification, a
larger number of solutions in the neighborhood is
visited, escaping of the local optimum.
To solve the Scheduling Problem, can be opted by
the use of a more flexible approach of neighborhood
generation (batch insertion approach), having as
initial solution a Dispatching Rule that takes into
account the resource sharing among PFs (PMSR and
FAM), which is important factor for the batch
processing time minimization. The batch swap
approach needs a larger number of iterations to
reach a better result like the one found by the batch
insertion approach. To this approach, the Tabu List
would not need to store a larger number of forbidden
moves.
In case the approach of neighborhood generation
cannot be flexible and the initial solution cannot take
into account the resource sharing, a larger Tabu List
will act diversifying the space search, leading to a
better result.
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