# Optimizing the Operation Sequence of

Authors: Yee Ming Chen; Chun-Ta Lin
Journal: Journal of Artificial Evolution and Applications
 (2008)

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## Abstract

The optimization of the nozzle selection, for sequencing component pick and place operations, is very important to the efficiency of multihead surface mounting machine (SMM). The nozzle change operation, that is, choosing the best nozzle head relative pair that is most effective for picking and placing components onto the printed circuit board (PCB), significantly adds to the overall assembly time. In this paper, as a practical application, we focus on a discrete particle swarm optimization (DPSO) algorithm for multihead SMM which is used to minimize the number of nozzle change operations and pick and place operations simultaneously. To evaluate the performance of the proposed algorithm, we test it on assembly tasks of PCBs through simulations. The results of computer experiments show that this DPSO algorithm was superior to the standard PSO algorithm.


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## Body

## 1. Introduction

The  optimization
of feeder setup and component placement sequences is very important  to the
efficiency of a surface mount machine (SMM). The increase of the number of  components
to be placed on a single board has made the reduction of assembly time probably
the most important issue to further cut down production costs and increase
productivity. The assembly of printed
circuit board (PCB) on a production line can be divided into four
process-planning subproblems: grouping (i.e., assigning PCB types to product
families and to machines), allocation (i.e., assigning nozzles to the heads),
arrangement (i.e., assigning reels to slots on the feeder rack), and sequencing
(i.e., the components' pick-and-place operations). Many publications have been
devoted to these complex optimization subproblems, and various models and
techniques have been presented, for example, by Ball and Magazine [1] and Brad et al. [2]. These subproblems
are tightly intertwined, and each of them is very difficult to solve to
optimality. For example, the quality of a component pick-and-place sequence is
dependent on the feeder setup and vice
versa [2]. Various approaches have been proposed
to improve sequence of placement points and/or feeder assignment for the PCB
assembly process [3]. Egbelu et al. [4] investigated assigning components to feeder slots
and sequencing component placement onto the PCB in order to minimize the total
assembly cycle time. They classified machines depending upon whether the PCB
table and the feeder carrier were stationary or not. They developed rules such
as the centroid rule, the proportion rule, the partition rule, and the weighted
rule to initially assign components to feeder slots. To obtain the component
insertion sequence, they modeled the problem as a traveling salesman problem
(TSP). Finally, by having the component insertion sequence and the initial
feeder setup, Egbelu et al. [4]
converted the component slot assignment into a quadratic assignment problem
(QAP) where the cutting plane and exchange heuristic were used. Results showed
that the assembly cycle times were minimized when both the feeder rack and PCB
table were able to move (Egbelu et al. [4]). Some researchers (see, e.g.,
[5]) have tackled the subproblems independently but
also have some researchers (see, e.g.,  Ho and Ji [6] ) preferred to solve these subproblems in an integrated way. The literature is rich with work that has tackled this subject,
especially investigating how to improve the efficiency of SMM [7, 8]. The
technological characteristics of the SMM can also influence the nature of some
of the subproblems to be solved and the formulation of the associated models
[9]. As a result,
many researchers solved the problem as a unique problem since the problem
relies heavily on the machine characteristics (Ho and Ji, 2003). This causes
difficulties in applying or comparing the various approaches from the
literature.In the recent years, a heuristic approach was developed
to solve the subproblems. Genetic algorithms (GAs) have been applied successfully to a wide
variety of optimization arrangement/sequencing
problems [10]. The GA and its many
versions have been popular in academia and the industry mainly because of their
intuitiveness, ease of implementation, and the ability to effectively solve
highly nonlinear, mixed integer optimization problems that are typical of
complex engineering systems. The drawback of the GA is its expensive
computational cost. Particle swarm optimization (PSO), introduced
by [11] is a relatively recent heuristic search method
whose mechanics are inspired by the swarming or collaborative behavior of
biological populations. PSO is similar to the GA in the sense that these two
heuristics are population-based search methods. In other words, PSO and the GA
move from a set of points (population) to another set of points in a single iteration
with likely improvement using a combination of deterministic and probabilistic
rules. Critical ingredients for the success of PSO are simplicity, ease of
operation, and great flexibility.When the SMM has more than one nozzle per head (or
even a single nozzle per head), choosing an effective nozzle group (or a
nozzle) is important since a nozzle change operation is time consuming.
Optimizing the pick and place operations without considering the nozzles changing operations
may not be efficient since it may cause many unnecessary nozzle changes that
will significantly reduce the machine throughput. However, to date, only a few
researchers [3] have tackled the nozzle optimization
problem. Due to its global and local exploration
abilities, simplicity in coding and consistency in performance, PSO has been
widely applied in many fields beyond its original applications to the solution
of continuous optimization problems. In our research, we mainly use discrete
data to process SMM problems. Therefore, developing a mechanism to realize discrete
optimization problem is attractive. Hence,
in this paper, we develop a discrete particle swarm optimization (DPSO) algorithm for nozzles selection and sequencing
components pick and place operations in a SMM equipped with multiple placement
heads. The objective of the algorithm is to minimize the nozzle selection for
sequencing component pick and place operations so as to increase the machines
throughput.The organization of this paper is as follows. Section2 is a description of
the SMM problem and its assumptions. In Section 3, we propose a DPSO algorithm
for multihead
SMM which is used to minimizing the
nozzle changes and minimizing the pick and place operations. The fourth
section discusses the experiment results we have gained for the heuristics
described in this paper applied to 10 test print circuit boards of SMM. The last section covers the conclusions we have
drawn from this research and gives a brief overview of planned future research.


## 2. SMM Description and Assumptions

SMMs are classified
into five categories based on their specification and operational methods.
These are: dual delivery, multistation, turret style, multihead, and a
sequential SMM. In general, each SMM has a feeder rack (sometimes called a
feeder carrier), a PCB table (or worktable), head(s), nozzle(s) (or gripper(s)),
and a tool magazine. The multihead
surface mounting machine is becoming increasingly popular. Its strong point is that
the mounting speed is high though the price is low. Components are supplied to
the machine by reels. Each reel contains only one type of components. Two
feeder racks are located on both sides of the conveyor, and each feeder rack
has a number of slots for reels. The actual pick-and-place unit is the arm,
which has multiple heads. The arm always moves from one location to another
along a straight line at a constant speed. Therefore, the distance between two
coordinate positions(x1,y1) and (x2y2) can be defined as |x1−x2|2+|y1−y2|2 which is called the Euclidean metric. The
heads pickup components from feeders and place them on the board. Since the
distance between adjacent heads is equal to a multiple of the distance between
two adjacent slots, the arm can pick multiple components simultaneously by one
pickup operation. This operation is called simultaneous pickup. Each
head has a nozzle that grips and holds a component until it is placed on the
board. Nozzles of different diameters are used depending on the size of the
component to be retrieved. The nozzle is automatically changed at the automatic
nozzle changer (ANC) (see Figure 1) when
it cannot grip the required component. The assumptions of the problem are as follows.
(1)
The number of heads is not limited. That is the
arm may have any number of heads.(2)
The different types of components cannot be
contained in one reel.(3)
The number of reels required to complete the
job is, at most, equal to the capacity of the feeder racks.
The above assumptions are practical and true in real settings.Figure 1
Schematic diagram of a multihead surface mounting machine.


## 3. Discrete Particle Swarm Optimization Algorithms

PSO
is inherently continuous but recently the discrete particle swarm optimization
algorithm has been proposed to solve discrete problems successfully. Ucar and Tasgetiren
[12] proposed a discrete particle swarm
optimization algorithm to determine a sequence of n jobs to be processed through m machines that minimizes the number of tardy jobs. Other papers proposing discrete
particle swarm optimization algorithms can be found in Shen et al. [13], Tasgetiren et al. [14], Onwubolu [15], and Clerc [16].Since, for each
printed circuit board, the location of each component has been decided, the
critical decisions left for optimization are where the different reel groups
should be placed in feeder slots. Moreover, in the multihead case, the optimal
solution does not only require the local optimization of a single head but also
the global optimization of the head group. In addition, there is only a finite
number of feeder slots, and each feeder slot can only contain one reel of
component(s). These properties match the properties of particle swarm
optimization that is why we propose the DPSO algorithms to solve the SMM's arrangement/sequencing problems.Considering the
characteristics of the multihead case, we decompose the component arrangement/sequencing problem into three
phases: assignment of reels to heads, construction of reel-groups, and the assignment
of component placement. In phase I, heads assignment algorithm, the most
critical decision is to assign jobs to each head with a balanced loading simultaneously.
Therefore, in order to balance the loading of each head, first, we construct a
head-nozzle relative matrix; then, an algorithm is developed to minimize the
variance of component loadings on each head based on the component types and
their associated nozzle types to produce an optimal solution of head
assignment.


### 3.1. Phase I: Heads Assignment Algorithm

In order to balance the loading of each
head, the heads assignment algorithm essentially solves the following linear programming
problems. LetH be the head set where Hi denoted the nozzle types which assigned to
head i. Let N be the nozzle set where Nj is the set which contained the components
associated with the nozzle type j, and
let Mj be the number of components associated to
nozzle type j. Then,Step 1.1.
Construct a head-nozzle relative matrixA(i,j) through randomly assigning each nozzle to each head
and satisfied:(1)H=AN,whereA(i,j)=0or1,∑jA(i,j)=1,foreveryi.A(i,j)=1 means that the nozzle j has been assigned to head i;
in contradiction to this, A(i,j)=0 means that there is nothing assigned to
head i.Step 2.2.
Calculate the fitness of head assignment to minimize the variance of
component loading on each head:(2)MinFitness=∑i(∑jMj×A(i,j)−Average_loading)2.


### 3.2. Phase II: Reel Grouping Optimization

In phase II, since the time for the
operation of pick-and-place for each component is constant, the only difference
is how many nozzle changes are needed in the pick-and-place process. The
assignment of nozzles to each head was optimally determined by phase I; therefore,
the next objective is to minimize the total number of times of nozzle changes
in the pick-and-place process according to the different type of nozzle needed.
In addition, each reel on the feeder rack can only hold one kind of component. The
optimal number of reel groups needed to minimize the number of times of nozzle
changes can be developed as follows.Step 1.1.
Based on phase I, construct a matrix of component assigned for the head
group, that isH=AN≈Hi=∪A(i,j)×Nj.Step 2.2.
From the component matrix, randomly assign components to each head and
generate the reel group,{reel_groupi(j,k)∣1≤i≤No_reel_group}, where reel_groupi(j,k) means that the component assigned to head k on the jth row for the ith reel
group.Step 3.3.
Determine whether it is necessary to change the nozzle from the
consecutive component group assignment, if so, calculate the number of nozzle
changes and create a new reel group, otherwise, continue the assignment
process.Step 4.4.
Evaluate the performance of assignment to minimize the number of nozzle
changes and repeat Steps1 and 3 until a stop criterion is met.


### 3.3. Phase III: DPSO for Assignment of Component Placement

In Phase III, the assignment of component
placement based on particle swarm optimization approach is developed in order
to minimize the total time of pick-and-place calculated by the traveling
distances, one dimension Euclidean distance times the unit assembly time in the
entire process. The discrete particle swarm optimization (DPSO) approach is
used to search the optimal locations for the reel group. Since the number of
feeder slots in each surface mounting machine is finite and discrete, each
particle cannot fly outside the range of feeder rack, that is, the position of
each particle is constrained. In order to satisfy these constrains, theVmax
velocity update equation is used in
this case, and the maximum velocity which each particle can fly is calculated as
the half of the number of feeder slots. Furthermore, Zhang et al. [17]
proposed a new boundary handling method, which is called as “periodic mode.” It
provides an infinite search space for the flying of particles, which is
composed of periodic copies of original search space with same fitness
landscape. Since each feeder slot can only contain one reel, some modification
on the position update equation with boundary constraints handling should be made
to protect against infeasibility.In this phase, assignment of component placement, the fitness
is determined as follows.(3)A=thedistancethatthearmmovesfromautomaticnozzlechanger(ANC)toreeltopickupcomponent=|P(N(thelastchangeforthispick-up)−P(reel_groupi(j,1)))|, where P(N(the last change for
this pick-up) denotes the last position of associated nozzle type needed to
changed in this pickup sequence. (4)B=thedistancethatarmmovesfromreeltobroadandtoplacethecomponents=|Xid(i)−P(reel_groupi(j,1))|for1≤i≤Opt_No_reel_group, where P(reel_groupi(j,1)) denotes the position of component assigned to
head 1 in the reel group i of jth
row on the print board. (5)C=thedistancebetweenthedifferentcomponentspositionsinthisplacementsequence=∑k=1No_of_head−1|P(reel_groupi(j,k))−p(reel_group(j,k+1))|.(6)D=thedistancebetweenthelastpositionofthisplacementandthepositionofcurrentreelgroup=|Xid(i)−P(reel_groupi(j,No_of_Heads))|.(7)E=thedistancebetweenthelastpositionofthisplacementandthepositionofcurrentnozzletobereleasedonANC=|P(N(thecurrentnozzletypeneededtobechanged)−P(reel_groupi(j,No_of_Heads))|.(8)F=thedistancebetweenthelastpositionofthisplacementandthepositionofnextreelgrouponthefeederslotwithoutchangingnozzle=|P(reel_groupi(j,No_of_Heads))−Xid(i+1)|.(9)G=thedistancethatthearmmovesfromnozzletonozzletochangedifferentnozzletypeonATC=|P(N(i))−P(N(j))|, where P(N(i))
denotes the position of nozzle type i.(10)H=thetimeneededfornozzle′schange.The algorithm for component placement is given below.Step 1.1.
An individual particle of reel groups is randomly assigned to a feeder
rack, and an initial solution based on the optimal assignment of reel groups
from Algorithm II is generated according to the fitness function:(11)fitness=∑i∑j∑k(A+B+C+D+E+F+G)+H×No_of_Changes, where 1≤i≤Opt_No_Reel_Group,1≤j≤Row(i), and Row(i)
denotes the number of rows in reel group i, 1≤k≤No_of_Heads.Step 2.2.
Run the iterations of population with the
following update equation.
(i)
Update the velocity
with maximum velocity,Vmax, constrained
within the range of feeder rack. The velocity update equation is influenced
simultaneously by the individual's experience and neighbor's experience as
follows: (12)Vidnew=w×Vidold+c1×rand1()×(Pid−Xid)+c2×rand2()×(Pgd−Xid),
(13a)ifVid>Vmax,Vid=Vmax,(13b)elseifVid<−Vmax,Vid=−Vmax, where w is the inertia weight in the range
[0, 1], the cognitive parameter c1∈[0.5,2], and the social parameter c2∈[1,3].(ii)
Update the particle's position using the new velocity:(14)Xidnew=Xidold+Vidnew.(iii)
If the reel allocation is out of boundary, then a
boundary constraint handling
modification on position updating is made as the follows:(15)Xidnew=Xidold+(−1)×Vidnew. If the reel
allocation is infeasible, then go to (i) again.Step 3.3.
Based on the fitness function, updatePid and Pgd.Step 4.4.
Repeat Steps2 and 3 until the stopping criterion is met.Figure2 shows
the flowchart of the DPSO for optimization of the operation sequence placement in multiheaded SMM.Figure 2
The flowchart of DPSO.


## 3.1. Phase I: Heads Assignment Algorithm

In order to balance the loading of each
head, the heads assignment algorithm essentially solves the following linear programming
problems. LetH be the head set where Hi denoted the nozzle types which assigned to
head i. Let N be the nozzle set where Nj is the set which contained the components
associated with the nozzle type j, and
let Mj be the number of components associated to
nozzle type j. Then,Step 1.1.
Construct a head-nozzle relative matrixA(i,j) through randomly assigning each nozzle to each head
and satisfied:(1)H=AN,whereA(i,j)=0or1,∑jA(i,j)=1,foreveryi.A(i,j)=1 means that the nozzle j has been assigned to head i;
in contradiction to this, A(i,j)=0 means that there is nothing assigned to
head i.Step 2.2.
Calculate the fitness of head assignment to minimize the variance of
component loading on each head:(2)MinFitness=∑i(∑jMj×A(i,j)−Average_loading)2.


## 3.2. Phase II: Reel Grouping Optimization

In phase II, since the time for the
operation of pick-and-place for each component is constant, the only difference
is how many nozzle changes are needed in the pick-and-place process. The
assignment of nozzles to each head was optimally determined by phase I; therefore,
the next objective is to minimize the total number of times of nozzle changes
in the pick-and-place process according to the different type of nozzle needed.
In addition, each reel on the feeder rack can only hold one kind of component. The
optimal number of reel groups needed to minimize the number of times of nozzle
changes can be developed as follows.Step 1.1.
Based on phase I, construct a matrix of component assigned for the head
group, that isH=AN≈Hi=∪A(i,j)×Nj.Step 2.2.
From the component matrix, randomly assign components to each head and
generate the reel group,{reel_groupi(j,k)∣1≤i≤No_reel_group}, where reel_groupi(j,k) means that the component assigned to head k on the jth row for the ith reel
group.Step 3.3.
Determine whether it is necessary to change the nozzle from the
consecutive component group assignment, if so, calculate the number of nozzle
changes and create a new reel group, otherwise, continue the assignment
process.Step 4.4.
Evaluate the performance of assignment to minimize the number of nozzle
changes and repeat Steps1 and 3 until a stop criterion is met.


## 3.3. Phase III: DPSO for Assignment of Component Placement

In Phase III, the assignment of component
placement based on particle swarm optimization approach is developed in order
to minimize the total time of pick-and-place calculated by the traveling
distances, one dimension Euclidean distance times the unit assembly time in the
entire process. The discrete particle swarm optimization (DPSO) approach is
used to search the optimal locations for the reel group. Since the number of
feeder slots in each surface mounting machine is finite and discrete, each
particle cannot fly outside the range of feeder rack, that is, the position of
each particle is constrained. In order to satisfy these constrains, theVmax
velocity update equation is used in
this case, and the maximum velocity which each particle can fly is calculated as
the half of the number of feeder slots. Furthermore, Zhang et al. [17]
proposed a new boundary handling method, which is called as “periodic mode.” It
provides an infinite search space for the flying of particles, which is
composed of periodic copies of original search space with same fitness
landscape. Since each feeder slot can only contain one reel, some modification
on the position update equation with boundary constraints handling should be made
to protect against infeasibility.In this phase, assignment of component placement, the fitness
is determined as follows.(3)A=thedistancethatthearmmovesfromautomaticnozzlechanger(ANC)toreeltopickupcomponent=|P(N(thelastchangeforthispick-up)−P(reel_groupi(j,1)))|, where P(N(the last change for
this pick-up) denotes the last position of associated nozzle type needed to
changed in this pickup sequence. (4)B=thedistancethatarmmovesfromreeltobroadandtoplacethecomponents=|Xid(i)−P(reel_groupi(j,1))|for1≤i≤Opt_No_reel_group, where P(reel_groupi(j,1)) denotes the position of component assigned to
head 1 in the reel group i of jth
row on the print board. (5)C=thedistancebetweenthedifferentcomponentspositionsinthisplacementsequence=∑k=1No_of_head−1|P(reel_groupi(j,k))−p(reel_group(j,k+1))|.(6)D=thedistancebetweenthelastpositionofthisplacementandthepositionofcurrentreelgroup=|Xid(i)−P(reel_groupi(j,No_of_Heads))|.(7)E=thedistancebetweenthelastpositionofthisplacementandthepositionofcurrentnozzletobereleasedonANC=|P(N(thecurrentnozzletypeneededtobechanged)−P(reel_groupi(j,No_of_Heads))|.(8)F=thedistancebetweenthelastpositionofthisplacementandthepositionofnextreelgrouponthefeederslotwithoutchangingnozzle=|P(reel_groupi(j,No_of_Heads))−Xid(i+1)|.(9)G=thedistancethatthearmmovesfromnozzletonozzletochangedifferentnozzletypeonATC=|P(N(i))−P(N(j))|, where P(N(i))
denotes the position of nozzle type i.(10)H=thetimeneededfornozzle′schange.The algorithm for component placement is given below.Step 1.1.
An individual particle of reel groups is randomly assigned to a feeder
rack, and an initial solution based on the optimal assignment of reel groups
from Algorithm II is generated according to the fitness function:(11)fitness=∑i∑j∑k(A+B+C+D+E+F+G)+H×No_of_Changes, where 1≤i≤Opt_No_Reel_Group,1≤j≤Row(i), and Row(i)
denotes the number of rows in reel group i, 1≤k≤No_of_Heads.Step 2.2.
Run the iterations of population with the
following update equation.
(i)
Update the velocity
with maximum velocity,Vmax, constrained
within the range of feeder rack. The velocity update equation is influenced
simultaneously by the individual's experience and neighbor's experience as
follows: (12)Vidnew=w×Vidold+c1×rand1()×(Pid−Xid)+c2×rand2()×(Pgd−Xid),
(13a)ifVid>Vmax,Vid=Vmax,(13b)elseifVid<−Vmax,Vid=−Vmax, where w is the inertia weight in the range
[0, 1], the cognitive parameter c1∈[0.5,2], and the social parameter c2∈[1,3].(ii)
Update the particle's position using the new velocity:(14)Xidnew=Xidold+Vidnew.(iii)
If the reel allocation is out of boundary, then a
boundary constraint handling
modification on position updating is made as the follows:(15)Xidnew=Xidold+(−1)×Vidnew. If the reel
allocation is infeasible, then go to (i) again.Step 3.3.
Based on the fitness function, updatePid and Pgd.Step 4.4.
Repeat Steps2 and 3 until the stopping criterion is met.Figure2 shows
the flowchart of the DPSO for optimization of the operation sequence placement in multiheaded SMM.Figure 2
The flowchart of DPSO.


## 4. Experiment Results

According to the
DPSO approach proposed in Section3, even though we only considered one machine
to one printed circuit board, there are many possibilities of combination of
processing procedures. Depending on what nozzle is assigned to what head or
what component is assigned to what reel of each head different solutions will
emerge. In this section, we consider a practical SMM that has 3 heads for
a 300×250mm2 board. In order to emphasize the effectiveness
of DPSO, we made a comparison of the standard PSO approach with our DPSO
approach according to the quality of solution found. This is measured by the
optimal solution found, the average traveling time (unit assembly time), the
improvement percentage, and paired t-test
for significance. The computer simulation is performed in the operating
environment of Window XP Professional with Pentium III CPU, 846 MHz, 1 GB RAM.
The software was coded in MATLAB 7.0.Since the exhaustive examination of the quality of
solutions requires a large number of problems, the algorithm is tested on a set
of randomly generated problems. The component locations on the print
board are randomly determined. In these simulations, both DPSO and the standard
PSO use the same parameters. Namely, the population size is 10, and the
relative parameters of velocity update equation, the cognition parameterc1, and the social parameter c2 are set equal to 2 to result in the most
effective search of the problem domain [11].
Furthermore, a linear decreasing inertia weight w is used in this simulation.To illustrate the
performance of this meta-heuristic approach, the number of placements and component
types ranged between 21 and 210 components to be placed and of up to 34
different component types. Tables1 and 2 show the results of 10 different PCB boards with 20 runs
with a different random seed for each problem case.Table 1
The comparison of experiment results between DPSO and the standard PSO.
Average timeOpt_solution_timeImprovementPairedt testComponentsDPSOPSODPSOPSODPSOPSOα=0.052137237531133516.3%10.63%0.289342134513511166117213.3%13.25%0.418763168622431477199012.38%11.29%0.0000*84391647323411420312.90%11.17%0.0000*105592560335282538910.86%10.67%0.3853126598672775357660710.50%9.21%0.0000*147703885626287793710.67%7.30%0.0000*16880879684744388457.96%8.67%0.0000*1899091110138667104174.67%5.41%0.0000*2101179312379100051161715.16%6.15%0.0122**means that the paired t-test is significant, that is, p<α/2.Table 2
The CPU time comparison between DPSO and the standard PSO.
Components21426384105126147168189210ApproachesDPSO16.532517794117137163190204PSO16.65335282106120152173196216Saving (%)0.913.031.926.1011.322.509.875.783.065.56*Saving = (CPU time of PSO-CPU time of DPSO)/ CPU time of PSO *100%.In order to compare the performances of opt_solution_time, we define the improvement
percentage of average time versus opt_solution_time as(16)Improvement=(AverageTime−Opt_Solution_Time)AverageTime×100%. The results
are shown on the fourth column of Table 1. In addition, under the confidence
level of α=0.05,
a paired t-test mentioned on the fifth
column of Table 1 is calculated as follows: t=(X¯−Y¯)(n(n−1))/∑i=1n(x^i−y^i)2 with n−1 degree of freedom and x^i=(xi−X¯),y^i=(yi−Y¯), where X¯ is the sample mean of the observed set {xi=i∣1≤i≤20},
the number of iteration in observation, and Y¯ is the sample mean of the observed set {yi},
the traveling time at iteration i.From Table1, it is easy to see that the DPSO
outperforms the standard PSO in every case; particularly, as the number of
components increased, the difference in performance is more significant.
Moreover, with the reversed modification of boundary handling in (15), the CPU
time needed to search the optimal solution through DPSO is a little shorter than the time taken by the standard PSO,
as shown in Table 2.It shows that DPSO outperforms the standard PSO on the ability to find
the optimal solutions, and the performance improvement is shown in Table2.
From the significance t-paired test,
we also can see that the performance of DPSO is better than the performance of standard
PSO in PCB component assignment/sequencing problems.


## 5. Conclusion

In this paper, we
proposed a DPSO approach to solve the problem of minimizing the PCB assembly
time and simultaneously optimizing assignment/sequencing problems for multiheaded SMM. We decomposed the DPSO approach into three
phases: heads assignment algorithm, reel grouping optimization, and the assignment
of component placement. These results lead to minimize the total assembly time of assignment/sequencing time of the placement of
component on PCB board. From the experiment results, the DPSO outperforms the standard PSO
in the quality of the solution found and in the time
taken to search for the optimal solution.In this paper,
we only discuss the application of DPSO in a SMM. But, it is easy to modify the
DPSO approach for different applications including the consideration of
component placement for multiple printed circuit boards operation
simultaneously and with time limitation on operations. In addition, the
different parameter selection for the DPSO and different velocity updating
equation selection applied in DPSO can be compared and considered.



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*Source: 315950-2008-04-29.xml*