Download global bacteria optimization Meta-heuristic Algorithm for Jobshop

International Journal of Operations Research and Information Systems, 1(4), 47-58, October-December 2010 47
global bacteria optimization
Meta-heuristic Algorithm
for Jobshop Scheduling
Jairo R. Montoya-Torres, Universidad de La Sabana, Colombia
Libardo S. Gómez-Vizcaíno, Fundación Centro de Investigación en Modelación Empresarial
del Caribe, Colombia
Elyn L. Solano-Charris, Universidad de La Sabana, Colombia
Carlos D. Paternina-Arboleda, Universidad del Norte, Colombia
AbStrAct
This paper examines the problem of jobshop scheduling with either makespan minimization or total tardiness
minimization, which are both known to be NP-hard. The authors propose the use of a meta-heuristic procedure
inspired from bacterial phototaxis. This procedure, called Global Bacteria Optimization (GBO), emulates the
reaction of some organisms (bacteria) to light stimulation. Computational experiments are performed using
well-known instances from literature. Results show that the algorithm equals and even outperforms previous
state-of-the-art procedures in terms of quality of solution and requires very short computational time.
Keywords:
Bacterial Phototaxis, Jobshop, Makespan, Meta-Heuristic, Scheduling, Tardiness
IntroductIon
A large number of real-life optimization problems in economics and business are complex
and difficult to solve. They cannot be solved
in an exact manner within a reasonable amount
of time (Talbi, 2009). Using approximate algorithms is the main alternative to solve this
class of problems. According to Talbi (2009),
approximate algorithms can be classified in
two classes: dedicated heuristics and meta-
DOI: 10.4018/joris.2010100103
heuristics. The former are problem-dependent
and are designed and applicable to a particular
problem. The latter are called meta-heuristics
procedures and represent more general approximate algorithms applicable to a large variety
of optimization problems. Meta-heuristics
solve instances of problems that are believed
to be hard in general, by exploring the usually
large solution search space of these instances.
These algorithms achieve this by reducing the
effective size of the space and by exploring
that space efficiently. With the improvement
of computing performance, the past 20 years
have witnessed the development of numerous
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48 International Journal of Operations Research and Information Systems, 1(4), 47-58, October-December 2010
meta-heuristic algorithms in various communities that sit at the intersection of several fields,
including artificial intelligence, computational
intelligence, soft computing, mathematical
programming, and operational research. Most
of the meta-heuristics mimic natural metaphors
to solve complex optimization problems (e.g.,
evolution of species, annealing process, ant
colony, particle swarm, immune system, bee
colony, and wasp swarm). Meta-heuristics are
more and more popular in different research
areas and industries.
Scheduling is one of the hard optimization
problems found in real industrial contexts for
which several meta-heuristic procedures have
been successfully applied (Jourdan et al., 2009).
Generally speaking, scheduling is a form of
decision-making that plays a crucial role in
manufacturing and service industries. It deals
with the allocation of resources to tasks over
given time periods and its goal is to optimize
one or more objectives (Pinedo, 2008). Among
the various types of scheduling problems, jobshop scheduling is one of the most challenging.
Except for strongly restricted special cases,
jobshop scheduling is a NP-hard optimization
problem (Garey et al., 1976), which means that
is not possible to find exact (optimal) solutions
to large-sized instances in reasonable computational time.
The objective of this paper is to present
a novel meta-heuristic procedure to solve the
jobshop scheduling problem. The proposed
meta-heuristic is inspired from biology, and in
particular from the behavior of organisms. Our
meta-heuristic, called “Global Bacteria Optimization” (GBO), is inspired from the bacterial
phototaxis, which is a kind of taxis that occurs
when an organism reacts to the light stimulation. This is advantageous for phototrophic
organisms as they can orient themselves most
efficiently to receive light for photosynthesis.
We propose to design an effective (in terms of
quality of solution) meta-heuristic algorithm to
solve the jobshop scheduling problem.
This paper is organized as follows. We first
present the problem under study and overviews
related literature. Then, the proposed GBO algorithm is presented in detail, followed by the set
of computational experiments and the analysis
of results. Finally, we present some concluding
remarks and suggest further research lines.
probleM deScrIptIon And
oVerVIew of lIterAture
As stated before, scheduling is a decisionmaking process that is used on a regular basis
in many manufacturing and services industries.
It deals with the allocation of resources (often
simply called machines) to task (jobs) over
given time periods and its goal is to optimize
one or more objectives (Pinedo, 2008). Efficient
production schedules can result in substantial
improvements in productivity and cost reductions in manufacturing and service industries.
Generating a feasible schedule that best meets
management’s objectives is a difficult task
that firms face every day (Ozgur & Brown,
1995). Among the various types of scheduling
problems, jobshop scheduling is one of the
most challenging.
Formally, the jobshop scheduling problem
can be described as follows. A set
J = { j | j = 1,…, n } of n jobs is to be processed
on a set M = {i | i = 1,…, m } of m machines.
Each job has a technological routing of processing on the machines. The processing of job j on
machine i is called the operation
Oij . Operation Oij requires an exclusive use of
machine i for a non-preemptive duration pij ,
called processing time. A schedule is a set of
starting ( Sij ) or completion (C ij ) times of each
operation that satisfies given constraints.
The challenge is to determine the optimum
sequence in which the jobs should be processed
in order to optimize an objective function.
In this paper, we first consider the wellknown objective function named the
makespan, computed as C max = max{C j } with
C j being the completion time of job j in the last
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