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J Heuristics (2014) 20:235–259
DOI 10.1007/s10732-014-9239-0
Solving a robotic assembly line balancing problem using
efficient hybrid methods
Slim Daoud · Hicham Chehade · Farouk Yalaoui ·
Lionel Amodeo
Received: 20 July 2012 / Revised: 31 May 2013 / Accepted: 17 February 2014 /
Published online: 9 March 2014
© Springer Science+Business Media New York 2014
Abstract In this paper we are studying a robotic assembly line balancing problem. The
goal is to maximize the efficiency of the line and to balance the different tasks between
the robots by defining the suitable tasks and components to assign to each robot. We are
interested in a robotic line which consists of seizing the products on a moving conveyor
and placing them on different location points. The performances evaluations of the
system are done using a discret event simulation model. This latter has been developed
with C++ language. As in our industrial application we are bounded by the execution
time, we propose some resolution methods which define the suitable component and
point positions in order to define the strategy of pick and place for each robot. These
methods are based on the ant colony optimization, particle swarm optimization and
genetic algorithms. To enhance the quality of the developed algorithms and to avoid
local optima, we have coupled these algorithms with guided local search. After that, an
exact method based on full enumeration is also developed to assess the quality of the
developed methods. Then, we try to select the best algorithm which is able to get the
best solutions with a small execution time. This is the main advantage of our methods
compared to exact methods. This fact represents a great interest taking in consideration
that the selected methods are used to manage the functioning of real industrial robotic
assembly lines. Numerical results show that the selected algorithm performs optimally
for the tested instances in a reasonable computation time and satisfies the industrial
constraint.
S. Daoud · H. Chehade · F. Yalaoui · L. Amodeo
ARIES Packaging, Technopole de l’Aube en Champagne, Rosires, France
e-mail: slim.daoud@utt.fr
S. Daoud · H. Chehade (B) · F. Yalaoui · L. Amodeo
ICD, LOSI, Troyes University of Technology, UMR 6281, CNRS,
Troyes, France
e-mail: hicham.chehade@utt.fr
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236
Keywords
S. Daoud et al.
Robotic assembly line balancing · Metaheuristics · Guided local search
1 Introduction
Using robots, the flexibility and the automation of assembly lines can be enhanced. The
robotic assembly line balancing (RALB) problem is based on a balanced distribution
of work between robots with an attempt for optimal assignments task. In this paper,
we present an industrial application of robotic assembly line balancing.
The contribution of our work is to develop a system which is able to manage the
functioning of a real robotic system in which we are supposed to balance the tasks
between the robots and to maximize the efficiency of line. The efficiency is defined as
the number of seized components of products by each robot. As we have an industrial
constraint that arose out of the execution time, we are unable to apply an exact method
that requires a large execution time for this system. Metaheuristics were thus the
relevant solution. In one hand, we present some search techniques based on ACO,
PSO and GA and in the second one we enhance the performances of the algorithms by
coupling them with a guided local search to our RALB in order to escape from local
optimal solutions.
The motivation of this work is first based on an industrial request to find the best
and balanced distribution of components and location points for each robot in order
to maximize the efficiency of the line. The second motivation is based of the lack of
works deal with the robotic assembly line balancing for maximizing the efficiency.
The remainder of this paper is organized as follows. The second section presents the
problem description which is the type E of robotic assembly line balancing problems
and the problem formulation. The different search techniques and the guided local
search are presented in the third section. Computational experiments and numerical
results are presented in the fourth section before ending the paper by a conclusion and
perspectives for future works.
2 State of the art
As mentioned before, we are interested in a robotic assembly system which consists
of seizing components of products and assembling them on different location points
on a moving conveyor belt by pick and place robots.
In this literature review, we discuss about many topics such as: multi-robot assembly
cell using pick and place robots, robotic assembly line balancing problem and the
application of the developed resolution techniques in robotic systems.
First, many researches were interested with the multi-robot assembly cells using
pick and place robots. These kinds of robots have been widely applied in automated
equipments and press fabrication industries as they could satisfy some special performances requirements. There are different types of robots. Huang et al. (2007) have
studied the time-minimum trajectory planning problem of the diamond robot. For scara
robot, Taylan Das and Canan Dlger (2005) have proposed a mathematical modeling
and a dynamic simulation referring to the experiment data available. Kelaiaiaa et al.
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Solving a robotic assembly line balancing problem
237
(2012) have presented a methodology of dimensional design of parallel delta robots
based on the genetic algorithm SPEA-II.
May et al. (1989) have proposed a flexible architecture for the control system
of multiple robots coordination. Bozma and Kalalioglu (2012) have studied the mutirobot coordination in pick and place operations. This problem is similar to our research
work which arose out of a real time factory automation problem where there are
multiple robots working in parallel. The goal is to define a multi-robot coordination
strategy. For that reason, they have proposed an approach on non cooperative game
theory where the robot decides its tasks based on the local observation of the conveyor
belt and the decision of the robot neighbor. Lee and Lee (2002) have developed a several
automata modeling for the supervisory control logic for a multi-robot assembly cell.
Ho and Ji (2009) have presented a mathematical model and a heuristic for a scheduling
problem of PCB components on a sequential pick and place machines.
Another important feature taken in consideration our paper is the robotic assembly line balancing. Rubinovitz and Bukchin (1991) were the first to introduce the
robotic assembly line balancing (RALB). They have suggested a branch and bound
method to solve SALB which aims to balance the workload of different robots. Kim
and Park (1995) have proposed an integer programming formulation and a cutting
plane algorithm for the robotic assembly line balancing. Tsai and Yao (1993) have
presented an approach which provides the number and the type of robot for robotic
assembly lines. This approach is based on an integrated capacity planning procedure.
Khouja et al. (2000) have developed two-stage methodology to perform robotic assembly cells. Nicosia et al. (2002) have proposed a dynamic programming algorithm in
order to minimize the cost of the workstation. Their problem aims to assign all tasks to
non identical workstations subject to precedence constraints. Bukchin and Rabinowitch (2006) have generalized this approach by developing an optimal solution based
on a back traking branch and bound algorithm. Levitin et al. (2006) have dealt with the
type II of robotic assembly line balancing (RALB-II) problem and proposed a genetic
algorithm GA which aims to assign tasks to workstations and to select the best robot
type for each workstation. Yoosefelahi et al. (2012) have presented a new formulation
of the robotic assembly line balancing problem type II. This latter aims to minimize
the cycle time, the robot setup costs and the robot costs. The authors have developed
three versions of multi-objective evolution strategies to solve this problem.
Since, our problem is bounded by the industrial constraint related to the execution
time, we should develop an approach which is able to solve the problem in a short
computational times. We opt to metaheuristics taking in consideration that those latter
have proved their efficiency in solving, in short computational times, different kinds
of combinatorial optimization problems. These metaheuristics are based on ACO, GA
and PS. Then, guided local search is developed to enhance the search ability of the
developed algorithms.
The first method is based on ant colony optimization. Ant colony optimization
(ACO) has been defined by Dorigo (1992). This algorithm is based on the behavior
of ants while searching for food source. In fact, ants deposit a chemical substance
on their ways. This chemical substance is called pheromone and it aims to guide
the ants while looking for the optimal solutions. Nowadays, scientists are applying
ant colony algorithms to solve assembly line balancing problems and also RALB
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S. Daoud et al.
problems. Ze-qiang et al. (2007) have presented an improved ant colony optimization
to solve type 1 of the simple assembly line balancing problem. Simaria and Vilarinho
(2009) have studied Two-sided assembly lines in which workers perform assembly
tasks in both sides of the line. They have proposed a mathematical model and an
ant colony optimization to solve the problem. The main goal of the problem is to
minimize the number of workstations. Yagmahan (2011) has dealt with the mixedmodel assembly line balancing problem. He has developed a multi-objective ant colony
optimization in order to minimize the number of stations for a given cycle time. For
robotic assembly lines, Sharma et al. (2008) have used the ACO for the generation of
optimized robotic assembly sequences by minimizing the energy function. Liang et
al. (2012) have developed an ant colony optimization for on-line scheduling and due
date determination.
The second method is based on the particle swarm optimization which was introduced by Kennedy and Eberhart (1995). This algorithm, gleams with the behavior
of swarm intelligence in nature. Jian-sha et al. (2009) have proposed a hybrid PSO
algorithm for solving type 2 of an assembly line balancing problem using PSO global
search capability. Dongyun et al. (2010) have proposed the method of linearly decreasing the inertia weight of the PSO to solve on assembly line problem. Qiu-gao (2010)
has proposed to solve the mixed-model assembly line balancing PSO and simulated
annealing algorithms. His results show that the PSO-SA algorithm is very efficient and
ensures a higher assembly line balancing ratio. Chutima and Chimklai (2012) have
presented a hybrid PSO algorithm to solve a multi-objective two-sided mixed model
assembly line balancing problem. This kind of PSO is hybridized with a negative
knowledge which employs the knowledge of the relative positions of different particles in generating new solutions. Dou et al. (2011) have presented a PSO algorithm
enhanced by the reduced variable neighborhood search which is used to perform a
local search within the neighbors of the best particle. This algorithm aims to solve the
assembly line balancing problem of type 1.
The last method developed for our problem is the genetic algorithm (GA) initially
defined by Holland (1975). Akpinar and Bayhan (2011) have proposed a hybrid genetic
algorithm to solve a mixed model assembly line balancing problem of type 1. This latter
aims to minimize the number of workstations, maximize the workload smoothness
between workstations and maximize the workload smoothness within workstations.
Gao et al. (2009) have presented a type II of robotic assembly line balancing (rALB
II) problem, in which each task has to be assigned to each workstation and each
workstation needs one available robot. They have proposed an innovative genetic
(GA) hybridized with local search based on different neighborhood structures. Chen
et al. (2012) have developed a grouping genetic algorithm for assembly line balancing
of sewing lines with different labor skill levels in garment industries. Chu and Beasley
(1998) have proposed a genetic algorithm for the mutidimensional knapsack problem.
As mentioned before, to enhance the performances of the developed algorithms,
such as ACO, PSO and GA, we have coupled these letters by a guided local search
(GLS). Voudouris and Tsang (1996) were the first to develop the GLS for combinatorial optimization problems to avoid local optima by changing the objective functions.
This is done by increasing penalties in an augmented objective function. Tseng et al.
(2007) have proposed a guided local search to improve the performance of a memetic
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Solving a robotic assembly line balancing problem
239
algorithm in order to guide it out of local minima and to solve assembly sequence planning. Chehade et al. (2009a) have developed an ant colony optimization with guided
local search for selecting machines and sizing buffers in assembly lines. Meanwhile,
guided local search was applied in many research works such as facility layout problems by Yalaoui et al. (2009) and quadratic assignment problems as described by Hani
et al. (2007).
This paper proposes a metaheuristics to solve a robotic assembly lines balancing
of type E. We have added GLS procedure to escape from the local optima and to
enhance the performances of the solutions. At our knowledge, the only paper which
investigates on real time factory automation problem is Bozma and Kalalioglu (2012).
This problem is similar to our problem. Meanwhile, we add the balancing loading
of the lines for our studies. We may note that a few work which deal with comparison of metaheuristics in pick and place robotic system or in assembly line balancing. Suren (2012) has presented an application and comparison of ACO and PSO
in manufacturing automation which uses a pick and place robot material handling
system. Faisae Rashid et al. (2011) have reviewed the most frequently soft computing approaches, (ACO, PSO and GA), for assembly sequence planning and assembly
line.
3 Problem description
The problem comes from a pick and place robotic assembly line which is composed
of a moving conveyor and robots in order to get a final assembled product. The main
objective of this work is to balance all tasks for each robot and to maximize the
line efficiency E by maximizing the gripping products. This robotic assembly line is
illustrated in Fig. 1 and it is composed of I serial pick and place robots. Theses latters,
seize the J components (on the left side of the figure) from the moving conveyor belt
and places them in specific locations (right side of the figure). This operation which
is the robot motion is called in the rest of the paper the assigned tasks. Furthermore,
the assembly of the final product requires the execution of K assigned tasks. The final
assembled product is composed of n layers and for each layer we have K 1 components
∀ α = 1, . . . , n . We note K α,β the position of the component in the final assembly
product. For the first layer, β is laying between 1 and K 1 . After that, β is between
K α+1 and K α ,(∀ α = 1, . . . , n − 1 ).
The order in which the assigned tasks have to be performed is ensured by precedence
constraints. Figure 2 presents an example of a final assembled product and shows the
precedence constraints between all the components marked by the different layers.
The following assumptions are stated to clarify the context in which the problem
arises. These assumptions were formulated by Rubinovitz and Bukchin Rubinovitz
and Bukchin (1991) to which we have added some extra ones:
1. The precedence relationships are due to technological assembly constraints
2. The duration of an assembling task is deterministic and cannot be subdivided
3. The duration of an assembling task depends on the assigned robot and the assigned
location points
4. The robot activity (assembling task) is limited by the throughput rate
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S. Daoud et al.
Fig. 1 Robotic systems description
Fig. 2 Precedence constraints of final assembled product
5. A single robot is assigned to each station
6. One type of product is considered in this problem
4 Resolution method
This section presents the methods developed to solve the robotic assembly line balancing. The idea is to satisfy the industrial constraint about the execution time requirements in order to manage the functioning on real time the robotic systems. For this
reason, we are unable to apply an exact method that requires a large execution time.
Metaheuristics are one of the relevant solutions. We present an application of the ant
colony optimization (ACO), particle swarm optimization (PSO) and genetic algorithm
(GA) for the RALB problem. The adopted algorithms, in similar problems like SALBP,
prove their efficiency to solve this type of problems.
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Solving a robotic assembly line balancing problem
241
We present in second times the guided local search (GLS) and its application to
different metaheuristics applied to our problem. The mean advantages of the GLS are
the ability of enhancing the quality of the developed algorithms and avoiding the local
optima. As explained in Rubinovitz and Bukchin (1991), the GLS is based on the
increasing of penalties of the augmented objective function. These penalties allow to
avoid the local minima and to get the optimal solutions. After that, an exact method
based on full enumeration is also developed to assess the quality of the different
developed metaheuristics.
4.1 Proposed methodology
4.1.1 Ant colony optimization (ACO)
The first method is an ant colony optimization algorithm. Its methodology is inspired
from the ant behavior to search the way of food source. This algorithm is then
based on pheromones (chemical substances) by using matrix showing the quantity
of pheromones between the different points visited by each ant allowing then to look
for the optimal solutions.
Solution encoding: In order to apply the algorithm to our problem, we have adopted
the encoding presented in Table 1 for the robotic assembly line with K M location
points, J components and I robots. This table shows the encoding adopted for the
location points and components. Each location points might be assigned to a robot
among I robots and to a component among J components. This gleams that each
assigned components j ( j = 1, . . . , J ) is picked by robot i (i = 1, . . . , I ) and placed
on a deposit point k (k = 1, . . . , K M). As mentioned in the introduction, this robot
motion is called the assigned task. The algorithm procedure is as follows: first, each
ant is deposited randomly on a starting point corresponding to the location points to
assign to a robot and the component. Then, each ant will move from a point to another
and at the end the fitness function is computed which is related to the number of seized
components by each robot.
Tours construction: Parallel ants have been used to assign the robots and components
for each location points. An ant f i chooses to move from a point r to another point
Table 1 Encoding representations for ACO
Location points 1
Location points 2
Components number:
1
2
…
Robot number:
1
2
…
J
I
Components number:
1
2
…
J
Robot number:
1
2
…
I
.
.
.
.
.
.
.
.
.
.
.
.
Location points KM
Components number:
1
2
…
J
Robot number:
1
2
…
I
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S. Daoud et al.
s based on standard equations for tours construction. In Eq. 1, q is a random number
generated between 0 and 1, q0 is a parameter (0 ≤ q0 ≤ 1) which determines the
relative importance of exploitation against exploration. S∗ is a random variable chosen
based on a probability given by Eq. 2. ηr,s is the quantity of pheromone between …
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