JPH05298283A - Route decision method - Google Patents

Abstract

PURPOSE:To find the shortest closed loop connecting N nodes. CONSTITUTION:Assuming that each node should be selected twice from N nodes, N branches (i,j) are selected in succession in order of shorter length dij, preparing m closing loops by means of the connected branch. Then two branches (i,j) which belong to dissimilar closing loops are selected. When a new closed loop is prepared by removing the two branches and connecting the remaining two openings, a new closed loop is made by finding the shortest combination, and an approximated solution is obtained by repeating the operation until the two closings are made one.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for finding an approximate solution of the shortest closed circuit that goes around N nodes.
It can be applied to determine the shortest route when mounting a plurality of electronic components on a circuit board.

[0002]

2. Description of the Related Art For mounting electronic components on a board,
Various efforts have been made to improve efficiency. For example,
Japanese Laid-Open Patent Publication No. 3-167895 discloses a component feeder,
A component mounting apparatus is described in which the component feeders are arranged so that the component feeders are mounted so that the component feeders are mounted closest to the center of distribution of the components supplied by the component feeders. This is an optimization in component supply, but another method must be used to determine the order when mounting electronic components on a board. One possible solution is to apply one of the optimization methods, the “Circle-Sailsman Problem”. This means that in a fully undirected graph with N nodes (every node pair (i, j) has a branch), the branch (i,
When the length of j) is d _ij (d _ij = d _ji ), the shortest closed circuit (tour circuit) that goes around all nodes is found. If the shortest path is found by applying it when arranging the components one by one on the substrate, the moving distance of the component mounting head or the substrate support can be shortened, which leads to a reduction in working time.

By the way, it cannot be said that any solution method may be used even if it is said that the "Circulating Sailsman Problem" is applied. The greedy method is one that is often used.
This is because N-1 branches (i, j) are selected in order from the shortest length d _ij under the two conditions that a closed path is not formed and each node is not selected more than once. It is formed, and finally, two nodes at the end of the open circuit are connected to create one closed circuit. An example thereof is shown in FIG. The numbers next to the branches indicate the rank of shortness. In this method, the branches formed at the end are often extremely long, and the length of the branches is long as a whole. Regular network (Hop field network, Boltzmann
It is also possible to apply a machine, etc.), but if the number of nodes exceeds several tens, it becomes difficult to find a practical solution within a practical time.

[0004]

DISCLOSURE OF THE INVENTION The present invention finds a shortest closed path connecting a plurality of nodes even if the number of nodes is several hundred, and is sufficiently practical within a practical time. It is an object of the present invention to provide a route determination method that can obtain various approximate solutions.

[0005]

In the present invention, each node has 2 points.
Under the condition that each branch (i, j) is selected in order from the shortest length d _ij , m (where m is an unspecified number) closed loops are selected according to the connected branches. And then select two branches (i, j) belonging to different cycles, remove these two branches, and connect the remaining two open paths to create a new closed path, the shortest combination Then, a new cycle is created, and this work is repeated until the number of cycles becomes one, thereby obtaining an approximate solution.

[0006]

By performing the above procedure, it is possible to find the approximate solution of the shortest closed circuit within a practically permissible time.

[0007]

Embodiment An embodiment will be described with reference to the drawings. There are a total of 15 nodes appearing in FIG. 1, and these are denoted by symbols A to O. Let arbitrary two nodes be i and j, and branches (i, j
The length of j) is d _ij (i = 1, 2, 3 ... N j =
1, 2, 3, ... N i ≠ jd _ij = d _ji ). When this method is applied to the mounting of electronic components, _dij is the time from the mounting of the i component to the mounting of the j component. Branch (i, j) is
_N C ₂ = N · (N−1) / 2 exist. Since N is 15, the number of branches (i, j) in this case is 105. Of these branches (i, j), each node is 2
The N branches are selected in order from the shortest one under the condition that they are selected each time. Through this operation, m (m is an unspecified number) closed circuits are naturally formed by the branches that are connected to each other (when m = 1, they become approximate solutions as they are). In the case of this embodiment, from the distribution of nodes,
(M, N) (A, B) (K, L), ... (N, O) 14
When the branch is selected, two closed circuits and one branch (A, B) are generated. However, the fifteenth branch cannot be selected. In such a case, branch (A, B) is re-selected as the 15th branch. As a result, a closed circuit of (A-B-A) is formed.

As the next work procedure, two branches belonging to different closed circuits are selected {(i1, j1), (i2, j2)},
Remove this. Then there are two open paths. When this open circuit is connected to create a new closed circuit, the shortest combination is obtained and the branches are replaced. That is, D _p = d _i1ji + d _i2j2 D _n = MIN {(d _i1i2 + d _j1j2 ), (d _i1j2 +
d _j1i2 )} ΔD = D _n −D _{p In the} above, the branch (i1, j
1), the combination of the branches (i2, j2) is obtained, and the branches are exchanged. In this way, the operation of making two closed circuits into one is repeated until only one closed circuit is finally obtained (m-1 times of replacement are performed). The closed circuit thus created is the approximate solution of the shortest closed circuit.

When the above operation is carried out for the embodiment, branch (H, G), branch (J, K) → branch (H, J), branch (G, K) branch (A, B), branch (C, D) ) → branch (A, C), branch (B, D) In this way, the branches are interchanged, and the closed circuit of FIG. 2 is obtained.

The closed loop obtained by the method of the present invention can be further applied with the iterative improvement method. That is, when the L branches are exchanged and the length of the closed circuit becomes shorter than that before the exchange, the branches are replaced as such. By repeating this, the accuracy of the approximate solution can be improved. In terms of calculation time,
L is 2 or 3. The iterative improvement method applied to the approximate solution obtained in FIG. 2 had no effect. this is,
This is because a good approximate solution has already been obtained only by the procedure of the present invention.

For comparison with the method of the present invention, a case in which the iterative improvement method is applied to the greedy method will be described with reference to FIGS. 3 and 4. First, under the condition that each node is selected only twice and does not form a closed path, 14 branches are selected in order from the shortest branch, and one open path is created. Finally, the fifteenth branch (B, O) is selected to make it a closed circuit (FIG. 3). In this method, the path is considerably longer than the results obtained in FIGS. 1 and 2. The iterative improvement method is applied here. The number of branches to be replaced is 2, and the replacement is continued until the improvement effect disappears. The result is shown in FIG. 4 (replacement of the branch is executed four times). There are improvements, but it's still a bit longer than the one in Figure 2.

[0012]

The method of the present invention finds only one closed loop by allocating the node group to some closed loops and repeating the operation of connecting the two closed loops with the shortest path, and the approximated solution is obtained. However, unlike the greedy method, long branches do not occur, and the accuracy of the approximate solution may vary slightly depending on the conditions (distribution of nodes), but the accurate approximation The solution can be stably obtained.

Further, by using iterative improvement method or other improvement algorithm together, it is possible to reach an accurate approximate solution even under various conditions, which is practical.

[Brief description of drawings]

FIG. 1 is a diagram showing a first step of the present invention, a situation in which m closed circuits are created.

FIG. 2 is a diagram illustrating a second step of the present invention, which is a state in which closed circuits are connected to each other to create only one closed circuit.

FIG. 3 is a diagram of a closed circuit obtained by the greedy method.

FIG. 4 is a diagram showing a case in which an iterative improvement method is applied to the closed circuit obtained in FIG.

[Explanation of symbols]

 A to O nodes

Claims (1)

[Claims] 1. In a completely undirected graph having N nodes (every node pair (i, j) has a branch), each node is found in finding the shortest closed circuit that goes through all the nodes. Branch (i, j) under the condition that is selected twice
N are selected in order from the shortest length d _ij , m closed circuits are created by branches having a connection relationship, and then two branches (i, j) belonging to different closed paths are selected. When the two branches are removed and the remaining two open circuits are connected to create a new closed circuit, the shortest combination is found,
A route determination method characterized in that an approximate solution is obtained by creating a new cycle and repeating this work until there is one cycle.