Program of Route Optimization for Surface Mount Jianguo Jiang, Chunyan Liu, Kun Zhang

Zhongxu Wang, Zhiwen Tan,Xiaoze Chen Computer School

Xidian University Xi'an, Shaanxi, 710071, China

E-mail:{ jjg3306, lcy3306 }@126.com

Abstract—Based on the Ant Colony Algorithm, a new algorithm is proposed for solving the route optimization of surface mount. According to the actual condition, a new state transition strategy for choosing the next electronic component is provided to reduce the numbers of changing of suction mouths. Considering the features of informational hormones updating integrally, a new strategy is presented to update the informational hormones, which is suit for the actual condition of surface mount. Without so many constraints as old algorithm and the deviation from the working facts because of simplifying the problems, it has many advantages. Theoretical analysis and experiments show that this new algorithm is better than the traditional ones in optimizing the route of surface mount.

Keywords-surface mount; ant algorithm; simulation modeling

I. INTRODUCTION Surface mount is the determinant[1] of

automation, assembly precision and production efficiency in the assembling of SMT products. However, most of the surface mounts take serial manner to mount the components one by one, whose speed is lower than that of other ways. Therefore, sequencing it reasonably and improving its efficiency are the key technologies for solving the speed bottleneck of assemble and make it more productive.

In the early 1990s, M.Dorigo[2], Iralian scholar proposed a new simulation evolutionary algorithm---Ant System(AS) [3] , which succeed in solving the Traveling Salesman Problem (TSP) and obtained superior result to any other algorithms[4]. This algorithm has less dependence on initial solution than the Tabu Search Algorithm. Compared with genetic algorithm (GA), AS makes the communication and delivery of information among the individuals continuously, and its positive feedback mechanism enables us obtain better solution easily.

Most route optimization algorithms of surface mount simplify the mounting process as TSP model, but they ignore the time spent on picking up components and changing suction mouth. Considering the influence of the size of component on numbers of changing suction mouth, the state transition strategy of basic ant

colony algorithm is improved. For example, the non-cross-section updating strategy is proposed to avoid that the algorithm sinks into a local optimal solution too soon, and the guidance of possible border cities speeds up the convergence of the algorithm. With those advantages, the efficiency of the algorithm is greatly improved.

II. ANALYSIS OF SURFACE MOUNT’S

WORKING PROCESS

The core of the mounting process is the circulation of pick-mount, which includes reclaiming, correcting and pasting. The mount head sucks a set of components at the reclaiming point, pastes them in the corresponding position, then returns to the reclaiming point and sucks another set of components for the next cycle. In practical work, the head of mount will move to the mouth-station and then change the mouth automatically or suspend the operation to enable the operator change it manually[5] if it fails to suck the components in a certain size, when sucking components different in size. It may occur that the mount head changes suck mouth frequently if the order of sucking components is unreasonable. Even though the whole mount path is the shortest, the mount process is low in efficiency and high in time cost. Therefore, it will inevitably benefit us to speed up the STM assemble line, if we arrange the order of mounting components reasonably, reduce the numbers of changing suck mouth and cycle times of the surface mount and optimize the mount route of the surface mount.

III. PATH OPTIMIZATION MODELING A. The Objective Function of Algorithm

In order to make the research easier, the structure of the surface mount is simplified appropriately. Supposed that the head of mount sucks all components in the same position, takes four components each time and makes sure the capacity of the reclaiming point is sufficient, so it will succeed in sucking component each time, as shown in Fig 1.

978-1-4244-5874-5/10/$26.00 ©2010 IEEE

Figure 1 Path Optimization Modeling Therefore, the route optimization problem of

the surface mount can be summarized as follows: finding a order of components mounting {u1 , u2, … uw} to make sure the following objective function minimum.

1 4 4 1 4 1 0

4 0 0

( 1)/4 /4 11

1 1 0/4 1

1

( ) ( , ) ( , ) ( , )

( , ) ( , )

i i k k k

k w

w ww

i k kw

k

DU d u u d u u d u u

d u u d u u

⎢ ⎥ ⎡ ⎤⎣ ⎦ ⎢ ⎥

+ + +

⎡ ⎤⎢ ⎥

− −−

= = =−

=(1)

= − +

+ +

∑ ∑ ∑

∑

In the formula, ui (i = 1, 2,…w) represents the coordinate of the ith assembly component, d(ui, ui+1) represents the distance between two adjacent assembly position. d(u4k+1,u0) represents the distance from reclaiming point to the first mounting position in one pick-mount cycle, d(u4k+1,u0) represents the distance from the last mount position to the reclaiming point in one pick-mount cycle.

B. The Initial Guidance of Algorithm and

Improvement of State Transition Strategy

It can be seen from Fig 1 that the components which are the nearest to the reclaiming point are likely to be the boundary ones. Therefore, it is helpful to speed up the convergence of the algorithm that provided one ant searches the route from possible boundary components in each iteration process. The difference between solving the shortest path which traversals all the components only once and the basic ant colony algorithm is the guidance of possible boundary cities. In each cycle, make sure that one ant starts from a possible boundary city and the remaining ants choose the first city randomly to visit, then, we select the next city according to (2) step by step. Compared with the basic ant colony algorithm, this algorithm increases the heuristic function

µij(t) = cs / cl, where cs = min (ci, cj), cl = max(ci, cj) and ci (i = 1,2,…w) is the size of the component µi, the bigger µij(t) is the more closer the size of the two components are, and the less the possibility in changing the mouth is. γ is the inspiration factor of changing mouth, which shows that how important the information of changing sucking mouth is in selecting path in the movement of the ants.

[ ( )] [ ( )] [ ( )],

[ ( )] [ ( )] [ ( )]( )

0,k

k

t t ti j i j i j if j k t t tp t is is isij s allowed

else

allowedβ γατ η μ

β γατ η μ

⎧⎪ ∈ ⎪⎪ ∑= (2)⎨

⊂ ⎪⎪

⎪⎩

C. The Improved Pheromone Updating

Rules

The pheromones could affect the ants within a certain range, the more ants pass through certain paths, the greater the concentration of the pheromones and the greater the probability of later ants choosing those paths, thus the pheromones intensity on those paths are enhanced[6].

It is much better to update path information using the global information while solving the TSP problem by basic ant colony algorithm However, in each cycle, the paths which the m ants passed should be recorded so that we can select the optimal path by comparing and update the pheromone with high spatial complexity; The asynchronous updating[7] is more faithful to the real ant colony system with less information record, The moment the ants walk one step, it will cause feedback and the pheromone on the path that they have just passed will be updated, that is to say with low spatial complexity. However, it may lead to sinking a local optimal solution easily.

According to the cycle characteristics of the surface mount in sucking mount, we make comprehensive consideration in the advantages and disadvantages of synchronized and asynchronous updating, and the result is that weaken all the information of the paths when a sucking mount cycle is finished, meanwhile, enhance the information of the paths among proximity components which the ant passed just now.

The updating rules of pheromone updating are

( 1) (1 ) ( ) ( )ijij ijt t tτ ρ τ τ (3)+ = − + Δ

1( ) ( )

mk

ij ijk

t tτ τ=

(4 )Δ = Δ ∑In which ρ is the evaporation coefficient of pheromone, ∆τk

ij (t) is the information quantity remained on the path (i, j) by the kth ant in this cycle.

, ( , )

0,( )k

kij

Qif the ant had passed i j

L

otherwisetτ (5)

⎧⎪Δ = ⎨⎪⎩

In the formula above, Q indicates the intensity of pheromone, which affects the convergence speed to a certain extent, Lk represents the length of paths which the kth ant passed in one sucking mount cycle, including the paths going reclaiming point back and forth.

IV. THE ALGORITHM STEPS

(1) Parameter initialization. Extract the information of components according to EDA design file. Initialize the components’ position dij and the size cij then obtain the possible border city ub and the reclaiming point u0, Initialize the taboo table as 0, the number of cities as N, and ants as M. Set the maximum numbers of cycles as maxNc , provided time 0t = , cycles 0cN = .

(2) Provided that one ant is placed in city ub, the remaining ants are randomly placed in other cities j, the numbers of the cities passed is s = 1, and provided that the value

[ ][ ]tabu k j of each ant is 1, 1Nc Nc= + . (3) The number of the cities passed s = s+1 . (4) Ant individual chooses the city j by the

probability that is calculated by (2), [ ][ ]tabu k j = 1 .

(5) If s mod 4 0≡ , update the path information according to (3),(4),(5), otherwise, execute step (6).

(6) If s N< , which indicates that it has not traveled all the N cities, jump to step (3), otherwise execute step (7).

(7) Obtain the current best path of M ants according to (1), if the best path is superior to the prior one, then replace it, otherwise execute step (8).

(8) It will end up and output the result if c cmax

N N≥ which meets the end conditions or the same optimal solution emerges continually. Otherwise, clear tabu and jump to step (2).

V. SIMULATION RESULTS

We solve the four sets of components in two ways ,one is the improved algorithm which is used to solve the of mount model of surface mount (New) and the other is the basic ant algorithm based on the update strategy using Ant-Cycle which is used to solve the TSP model

(Old), each of them runs 10 times. The running results are showed in the table

1, where the running time is the average of ten times. Provided 2.0α = , 3.0β = , 0.02ρ = ,

1.0γ = , 1000 Q = ，the conditions of ending the algorithm is that the same solution emergence 10 times continuously. The path and time cost by mount head on changing suck mouth is not included in the “the shortest path length” and “the running time” which is showed in the following table.

TABLE I RESULTS OF ROUTE OPTIMIZATION BASED

ON DIFFERENT ACO

size algorithm shortest distance average

changing

times time

40 New 9000.382 9024.530 5 0.19

Old 9154.144 9078.352 11 0.20

63 New 64220.420 64344.150 18 0.64

Old 64477.090 64564.500 29 0.73

152 New 65584.605 65620.656 2 8.22 Old 65779.493 65831.265 6 8.67

276 New 233030.929 234505.4 18 51.34 Old 233930.624 234696.6 35 54.95

With comparison of the shortest paths in the

table, it can be seen: due to the fact that the improved algorithm considers the mount head path to and from the reclaiming point, the mount model of the surface mount can obtain a better solution in the surface mount’ path optimization than TSP model does. With the introduction of the heuristic function /ij s lc cμ = , the number of the suck mouth changing is much fewer in the improved algorithm. The guidance of border city and the adopting of information update strategy improve the convergence speed and the efficiency of the algorithm. The advantages of the improved algorithm would be more obvious if the distance and time which are cost in changing suck mouth are included in the “the shortest distance” and “running time”.

The inspiration factor γ, β shows how important it is to give priority to the components of the similar size to reduce the changing times of suck mouth and the adjacent components to shorten the mount path. When γ, β are given different values, the effect pictures of path optimization with 276 components are compared in the Fig.2.

Figure.2 optimized emulation result

a,the figure when γ = 2,β = 1 b,the figurewhen γ = 1,β = 3

The figure uses squares in different sizes to denote the components in different sizes. In order to show the effect clearly, the figure omits the round-trip path between each group of (four) components and the reclaiming point. In the algorithm simulation, the reclaiming point is set in the upper left corner of the substrate. In Fig 2, the changing numbers of suck mouth and the path length in Fig.a is 3 and 234212.416 mm, while in Fig.b is 23 and 233030.929mm.

VI. CONCLUSION

In this paper, the improved ant colony algorithm is applied to the path optimization of surface mount, according to the suck cycle of surface mount, a mathematical model which is suitable to the path optimization of surface mount is proposed. Meanwhile, considering the mount head’ round-trip path between reclaiming point and components, this mathematical model makes the overall motion paths of mount head the shortest. In the path selection of surface mount, the introduction of inspiration factor γ and size proportional function

ijμ enables the surface

mount choose components similar in size to reduce the changing numbers of the suck mouth.

The sub-updating strategy which combines synchronous with asynchronous is not only consistent with the mount model, but also improves the operational efficiency of the algorithm. The guidance of border city accelerates the convergence speed of the algorithm. However, this paper only emphasize the surface mount with four mount head, and it is applied only to serial mount of surface mount, all of these are to be improved which will be studied in the next phase.

The innovations of this paper are as follows: it provides the mount model of surface mount, introduces the new inspiration factor and state transition strategy of improved function, meanwhile, the operational efficiency of the algorithm is improved by the use of updating strategy of new pheromone and the border guidance.

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