JPH04152451A - High speed execution processing system for branch limiting method - Google Patents

Abstract

PURPOSE:To carry out a branch limiting method at a high speed by attaining a constitution where the communication processing and problem solving processors carry out their own processing operations based on their own object data and by reference to the common control data. CONSTITUTION:In a branch limiting method processor consisting of plural parallel clusters 1 connected to a communication network 2, a communication processor 3 and a problem solving processor 4 carry out their own processing operations by using the object data 11-14 in a shared data space 5 as their own processing subject data. At the same time, the processors 3 and 4 disperse the load and perform other processing operations by reference to the control data 7-10 to which both processors have accesses in common. In such a constitution, the highly efficient data accesses and dispersion of load and cutting of branches can be carried out. Then, a branch limiting method is carried out at a high speed.

Description

[Detailed Description of the Invention] C Overview] This invention relates to a branch-and-bound high-speed execution processing method in a branch-and-bound processing device configured by connecting a plurality of parallel clusters to a communication network.

Each parallel cluster is connected to a communication network with two
It has a communication processing processor, a plurality of problem processing processors, and a shared data space, and within the shared data space, object data as processing target data for each processor and control data commonly referenced by each processor are provided. Each processor is configured to execute its own processing based on its own object data and to execute processes such as load distribution by referring to the control data.

[Industrial application field]

In the present invention, a plurality of parallel clusters communicate with each other.

The present invention relates to a branch and bound method high-speed execution processing method in a branch and bound method processing device configured to be connected to a network.

The branch and bound method is used in the field of business management such as production planning and layout planning, the field of human intelligence such as processing of constraints and reasoning, and the field of LS design for layout etc. However, when structuring data in the form of a tree structure, for example, a large number of branches are generated and undesired branches are pruned, resulting in an enormous amount of processing.

[Conventional technology]

In this type of processing, the following processing B has conventionally been used. That is, ■ Perform a best-first search using a sequential processing evaluation function. Once an integer solution (optimal solution candidate) is found, pruning is performed using the objective function value.

■ Parallel processing (b) Hector meter X machine 1z swarming process Each node of the enumeration tree is processed by a hector computer.

(b) Processing by multiprocessors Allocate processors (PEs) in order from the top of the enumeration tree, and have each PE perform a horizontal search.

[Problem to be solved by the invention]

■ In the case of the above sequential processing.

Recently, the scale of systems has been gradually increasing, and when the number of integer variables exceeds, for example, 100, there are increasing cases where current sequential high-performance computers cannot handle the number of integer variables.

■ In the case of the above parallel processing (a) In the case of processing using a hector computer Since the tableau matrix given as a problem for each node is sparse, the performance can only be expected to be about three times that of a scalar computer.

(b) In the case of processing by multiprocessors In a system in which each node of 1 enumeration woodworking is assigned to each PE of the multiprocessor in order from the root node of enumeration water to solve child problems, at the nth stage of enumeration water, 2 ″ processors are required, and it is not possible to find an integer solution quickly.

Moreover, even if all PEs are made to perform best-first search, PE
As the number of nodes increases, there is a risk that more nodes will be searched than the number of nodes searched in sequential processing, which is not necessarily efficient. The purpose is to enable high-speed execution by performing efficient load distribution and efficient pruning.

Means for Solving Problem C] FIG. 1 shows the basic configuration of the present invention. Code 1-i in the figure
is a parallel cluster, and 2 is a communication network.

3-4 is a communication processing processor, 4-ij is a problem-solving processor, and 5-1 is a data space 26 in the parallel cluster.
is a control data holding unit, F to 10 are control data, respectively;
Items 1 to 14 represent object data, respectively.

Each parallel cluster 1-i has 9 communication processing processes.

The two communication networks 2 are connected to each other via the bus 3-i, and mutually execute processing including load distribution processing while communicating with each other.

Each parallel cluster 1-1 has two communication processing processors 3-1.
It has one problem-solving processor 4-ij and a data space 5-i. Additionally, within the data space 51, there are objects and
Data 11 to 14 and (11) each processor 3.4 updates itself appropriately and 5
In addition, there are control data sets 10 that are commonly referenced by other processors.

Each of the processors 3 and 4 refers to the control data and is linked together to perform, for example, load distribution processing.

[For production]

The node data is structured in a tree structure, and an index is created for this node data based on Search 1, and these are combined as object data.

(A) Efficient data access management (1) In order to avoid concentration of access to object data, depending on the processing content of the processor (hereinafter abbreviated as PE).

View object data as local/global. In other words, in the development of 5 enumerated water, own PE
It is regarded as local data for the purpose of use, and as global data in load distribution processing.

(2) In order to increase the access speed based on the search for tree-structured node data (child problems), an index such as 8-Tree should be provided.

(B) Efficient load distribution processing (1) Avoid performing load distribution processing in a unified manner in the same data space, and allow each PE to perform load distribution processing autonomously.

(2) In order to avoid repeated and wasteful accesses to object data when a PE in an idle state searches for valid node data, control data is used to control the macro state of object data and the access method. Let me remember it. To obtain the desired object data, trace the control data connected in a ring structure and compare the contents of each control data (number of note data, maximum and minimum values of index keys, search strategy, etc.) This ensures that appropriate object data is obtained.

(C) Efficient pruning processing (1) When pruning information is obtained at a certain PE,
This information is written into the control data amount corresponding to each PE. As a result, each PE for problem solving uses the order of the tree structure and deletes object data based on the pruning information. The PE for communication processing transmits this pruning information to other parallel clusters in order to reflect this information.

(2) Since the timing of pruning is performed immediately after node selection, pruning is performed at this time using the pruning information in the own control data area.

(D) Efficiently updating control data (1) Pruning information is updated by a certain PE every time good pruning information is obtained by that PE.

(2) When deciding which object data to allocate as a load to a PE in an idle state, it is not necessary to perform very strict management, and it is sufficient to keep it appropriately, so to speak, the control data is This allows the load balancing process to reduce exclusive control waiting for the update.

〔Example〕

Hereinafter, the explanation will be given assuming that the method solves the branch and bound method used in mixed integer programming.

FIG. 2 shows the configuration of an embodiment of the problem-solving processor.

Reference numerals 4 and 5 in the figure correspond to those in FIG. 1, and 15 is a node selection section, which is generated in plural numbers. 16 is a pruning processing unit that performs undesired pruning based on the objective function value of the integer solution; It is a part of the technical and wet farming division that divides the questions based on the answers solved using the simplex method.

Further, I8 is a control data management section, and control data 7.8
．． 9.10 Management such as accessing 19
20 is a node management unit that manages the nodes that are currently being processed in the tree structure; 20 is an index management unit that manages indexes in the object data 11 12 13 14; and 21 is a load distribution processing unit. It performs processing related to load distribution.

The problem is divided based on the answer solved by the simplex method described above, but if it becomes infeasible as a result of processing using the simplex method, the problem is discarded and another problem is selected using the search strategy and split into two. Continuing to make losses. As a search strategy, one problem-solving processor (PE#0) 4-〇〇 has the function of performing depth-first search that improves the objective function value, and other problem-solving processors 4- ON performs horizontal search. Therefore, the tree-structured node data is ordered by the objective function value, and in order to improve the efficiency of horizontal search, indexes regarding depth are created for the node data.

Starting from problem solving PE #0 in one of the parallel clusters, all PEs in that cluster and in other clusters are activated.

After that, the problem solving PE40 in the representative parallel cluster
extracts a problem from the data space 5-0 and searches for two enumerations in the vertical direction while repeating two branch failures. The resulting child problem is stored as object data 12. and.

The status of the object data 12 is periodically reflected in the control data 8 corresponding to itself. If an integer solution is found, the pruning information is reflected in each control data 8, and its own object data 120 is pruned. If all of the two object data 12 are removed from the pruning process, the control data 7.9 connected in a ring structure
．． 10, it is searched by the index whether or not a node (child problem) close to the root of the tree structure remains to be processed. If there is no node (child B) in the cluster 1-0, a node request instruction is written in the control data 7 managed by the communication processing PE 9.

In problem-solving PEs other than PE#0, there is no object data at first, so control data in a ring structure7.8
．． 9. While searching for 10, push out the object data of the PE that is likely to have data close to the root, extract nodes (child problems) that are close to the 2nd root, and use them as your own object data. If the node is not in your own cluster 1-0, then the other cluster 1-1.・・・
. . . In order to issue a node request to 1-n, a note request instruction is written to the control data file handled by the PE for 2211 communication processing. When object data is lost due to pruning, the same processing as described above for PE#0 is performed.

The object data 11 of the PE for communication processing is as follows.

These are transmission data and reception data regarding nodes (child problems). Control data 7 for this data.

If there is a node request instruction, a node request is made to other clusters. When a node is sent from another cluster, it is stored in the object data 11. This data is retrieved by the requesting problem solving PE. When a node request is made to a communication processing PE in a representative parallel cluster from all PEs in the cluster, and a note request is made from communication processing PEs in all other clusters, the processing of all PEs is terminated.

FIG. 3 shows a processing flow of one embodiment of a representative parallel cluster, and corresponds to the above processing. That is, process ①: Start the problem solving program (PE#0).

Processing ■: The processor (PE#0) creates the 2-control wholesale data 8 and starts other processors.

Processing ■: For the relevant bromo (PE#O).

Assign the problem corresponding to the root of the tree structure.

Processing■: In the processor (PE#O), (1) if there is a load acquisition request, connect the quintuplet problem to the control data 8 and share the processing with other processors, (ii) first perform the pre-integer search Performs a contract search for , and performs pruning when the integer value is found.

Process ■: Check whether it has completed normally.

Processing ■: Load distribution processing is performed using the ring structure in the control data holding unit 6.

Process ■: Check whether the number of child problems on hand has run out. If there are any remaining, return to process ■.

Process ■; If there is an error in process ■, output the error.

Processing (2) In a problem-solving processor (PE#N) other than the processor (PE#0), the search trajectory is pruning.

Other than that, it is the same as Bromosu (PE#O).

FIG. 4 shows detailed processing of the load distribution processing in FIG. 3.

Process ■: Turn off the load re-request flag.

Processing ■: (1) Find control data for load acquisition using the control data holding unit 6, and (ii) count the number of processors in the waiting state.

Process ①: Check whether the number of waiting processors is n-1. Verify that all processors are waiting.

If YES, check whether the load request flag is OFF. If NO, jump to process ■.

If YES, wait for the processor in question. Set the flag to ONL, and set the load request flag to ONL. Turn on.

A child problem was connected to the control data, but Find out.

If No, it is checked whether the wait flag of the processor is ON. If YES, return to process ■.

If NO in process Turn on the lag. Then, return to processing ■.

If YES in process■, take the child problem. Processing: Processing: Processing: Processing: Processing: Processing: and turns off the wait flag.

Processing [phase]: If the number of child problems is "1" at this time, it is the end.

Process ■; If NO in Process ■ and the number of child problems is "0", the process ends.

An application example of the present invention will be explained below by giving an example.

FIG. 5 shows a common example.

<Example title> Based on a material with a length of 100 m, five types of products Y, (
Consider the problem of creating i=1.2.3.4.5). It is assumed that each product only needs to be made one at most, and the remainder X after cutting the product from the material is disposed of, and 0 per 1 m is used.
．． Assume that there will be a loss of 5,000 yen. In this situation,
The question is how to get the most profit.

Figure 5(a) shows the length and profit of each product.

Here, the following integer variables are defined for product j (j=1.2, 3, 4.5).

FIG. 5(b) shows a mathematical expression. FIG. 6 shows the maximum value obtained for two of the mathematical expressions, objective function 2, after satisfying the constraint conditions.

Part 6 shows created nodes and examples of calculation results. What is shown in FIG. 6 is a solution obtained for objective function 2 shown in FIG. 5 under the constraints shown in FIG. 9. Z, Vl in the diagram
The values of y5 to y5 are listed in correspondence with the node numbers of the enumeration trees in FIGS. 7 and 6, which will be described later. Here, as a provisional part, node number 13 is larger among note numbers 3 and 13, and 20.0 is the optimal solution to be found.

FIG. 7 shows an explanatory diagram illustrating how processes are assigned to parallel clusters and each processor.

[First step]: In FIG. 7, the root node O is the processor 4-00 of the parallel cluster 1-0, which is the representative cluster.
, and solve it using the simplex method) Create child problems ■ and ■. Two child problems (1) and (2) of y3-1 are generated.Since the child problems will be generated in the same procedure below, they will be omitted for the sake of brevity). Processor 4-0 for solving the problem of parallel cluster 1-0 from among these generated child problems ■ and ■
0 takes the child problem with a high evaluation function value and assigns the remaining child problems ■ to others.

In the initial state, since the request from the other parallel cluster 1-j is strong, the remaining child problem (2) is received by the communication monitor of the parallel cluster #1, which has one higher priority. And the child problem■
is assigned to processor 4-10. Note that the hatched problems in FIG. 7 represent examples of problems with higher evaluation function values.

[Second step]: Processor 1-00 of parallel cluster 1-0 executes the child problem and generates child problems ① and ②.

Parallel cluster 1 from among these generated child problems ■ and ■
Processor 1-00 of -0 picks the child problem (■) with a high evaluation value and assigns the remaining child problems (■) to others. Processor 4-
Assuming that the request from 01 (not shown) is strong, the child problem ■
For example, it is assigned to processor 4-1.

[Third step]: Processor 4 of parallel cluster 1-0
~00 executes the child problem ■ to obtain an integer solution, and the processor 401 of the parallel cluster 1-0 executes the child problem ■ to generate child problems ■ and ■. These generated child problems■
, Processor 4-00 of parallel cluster 1-0 from ■
Take the child question ■ that has a high evaluation value. Thereafter, the remaining child problem (2) is assigned to the processor 4-02 (not shown) of the parallel cluster 1-0.

(Fourth step) The processor 4-00 of the parallel cluster 1-0 executes the child problem ■ with a high evaluation value, and the child problems ■, ■
and processor 4 of parallel cluster 1-0
-02 executes the child problem ■ and gives up. Among these generated child problems ■ and ■, processor 1 of parallel cluster 1-0
-00 takes the child problem ■ with a high evaluation value, and the remaining child problems ■
have others share the work. Here, then the remaining child problems ■
For example, it is assumed that the processor 4-03 (not shown) of the parallel cluster 1-0 is assigned.

[Fifth step]: Processor 4-00 of parallel cluster l-0 executes child problem (2) and gives up.

Processor 4-03 of parallel cluster 1-0 executes child problem (2) and obtains infeasibility.

Further, the processor 4-10 of the cluster 1-1, which was assigned the child problem ■ in the first step, executes the child problem ■ in the second step and generates the child problems ■ and @. The processor 4-10 of the parallel cluster 1-1 selects the child problem [phase] with a high evaluation value from among these generated child problems ■, [phase], and
Have others share the remaining children's problems ■. It is sent to the communication monitor of parallel cluster 1-3, which has a higher priority. The communication monitor of parallel cluster 1-3 sends child problem ■ to node B. Finally, it is assumed that the child problem (2) is assigned to the processor 4-30. In the third step, parallel cluster 1-1
The processor 4-10 executes the child problem [phase] and generates the child problems ■ and @. From these generated child problems ■ and @, the integer processor 4-10 of the parallel cluster 1-1 picks the child problem ■ with a high evaluation value, and assigns the remaining child problems @ to other processors 4-11. . In the fourth step, processor 4-10 of parallel cluster 1-1 is a child problem ■
Execute and obtain the child problem @, o. Processor 4- of parallel cluster 1-1 from among these generated child problems @, ■
10 is the child problem with the highest evaluation value @ and the remaining child problems [phase]
is assigned to the processor 4-11. In the fifth step, the processor 4-10 of the parallel cluster 1-1 executes the child problem ■, obtains an integer solution (for example, provisional solution z = 20.0), and the processor 4-11 of the parallel cluster 11 executes the child problem [
Stocks].

Get non-executable.

Furthermore, the processor 4-30 of the parallel cluster 1-3, which has been assigned the child problem (2) in the second step, executes the child problem (2) in the third step, and generates the children B2, (3). From these generated child problems ■ and ■, the processor 4-30 of the parallel cluster 1-3 selects the child interval B■ with a high evaluation value, and the remaining child problem ■ is assigned to the adjacent parallel cluster 1-3 with a high priority.
2 processor 4-20. In the fourth step, the processor 4-30 of the parallel cluster 1-3 executes the child problem [share] and generates the child problems ■ and @. The processor 4 - 30 of the parallel cluster 13 selects the child problem @ with a high evaluation value from among these generated child problems @ and @, and assigns the remaining child problem 0 to the processor 431 . In the fifth step, the processor 4-30 of the parallel cluster 1-3 executes the child problem @ and obtains the child problem @, [phase].
-3's processor 4-31 executes the child problem (2) and gives up. These generated child problems 0. The processor 4-30 of the parallel cluster 1-3 takes the child problem @ with a high evaluation value from among the @, and assigns the remaining child problems [phases] to the processor 4-32. In the sixth step, the processor 4-31 of the parallel cluster 1-3 executes the child problem @ and gives up on it, and the processor 4-32 of the parallel cluster 1-3 executes the child problem [phase] and obtains an unexecutable result.

In the third step again! ! ! Processor 4-20 of parallel cluster 1-2 has been assigned [shares].

In the fourth step, the child problem ■ is executed and the child problems ■ and @ are generated. The processor 4-20 of the parallel cluster 1-2 takes the child problem @ with a high evaluation value from among these generated child problems O1@, and uses the remaining children B [phase] in the adjacent parallel cluster 1-2 with a high priority. 6 processors 4-60. In the fifth step, processor 4 of parallel cluster 1-2
-20 executes the child problem ■ and generates the child problem ■, [phase]. The processor 4-20 of generated raster 1-2 takes the child problem [phase] with a high evaluation value from among these generated child problems [phase], @1, and processes the remaining child problems [share]. Assigned to 21. Parallel cluster 1 in the sixth step
2's processor 4-20 executes the child problem [phase].

At the same time, 2 parallel clusters 1-2 processor 4-
21 executes the child problem @ and obtains not executable.

Also, the processor 4-60 of the parallel cluster 1-6 is assigned the child problem (2) in the fourth step.

In the fifth step, execute the child problem [phase] and obtain an infeasible result.

By the above processing, the provisional solution (z-19,5
), the provisional solution (z = 20.0) found with large ■ is the optimal solution among the provisional solutions (z = 20.0) found with @.
) is the answer. In this way, the priorities of the adjacent parallel clusters 1-1 to which child problems are assigned are set so that the upstream parallel clusters and parallel clusters with smaller numbers are given higher priority, and the root node shown in FIG. It is assigned to the processor 4-OO of O and executed (i
) Processor 4 of the parallel cluster 1-1 with the highest priority among free spaces in the adjacent parallel cluster
-10 or (ii) by allocating it to the idle processor 4-01 of its own parallel cluster and executing it in parallel, it becomes possible to find between integers at high speed.

FIG. 8 shows an example of enumeration tree search by parallel processing.

Here, O to [phase] represent child problems (nodes).

yJ (j=1.2.3.4.5) represents the evaluation function,
2 represents the objective function.

[Effects of the Invention] As explained above, according to the present invention, a processor (PE
) At the same time, depending on the processing content, object data is displayed locally for the own processor and globally for use by other processors.

By structuring the node data, it is expected that the temporally stored node data can be accessed at high speed.

Further, by having each processor (PE) autonomously perform load distribution processing using control data of ring structure coupling, single branch operation and highly independent parallel processing become possible.

Since there is no need to require high precision in the contents of the control data, the control data is updated as appropriate, and thereby the number of times the control data is updated can be reduced. When there is no object data in the cluster, all problem-solving processors in the cluster
In order to make a note request for the control data of the communication processing processor, you do not have to wait for the branching operation of the first node obtained, and if the node transferred from another cluster arrives early, you can transfer that node to other clusters. can be processed by free processors. This makes it possible to increase the utilization rate of the processor.

[Brief explanation of drawings]

Figure 1 is a diagram of the principle configuration of the present invention, Figure 2 is the configuration of an embodiment of a problem-solving processor, Figure 3 is a processing flow of an embodiment of a representative parallel cluster, and Figure 4 is the load in Figure 3. Detailed processing of distributed processing, FIG. 5 shows an application example, FIG. 6 shows an example of created nodes and calculation results, FIG. 7 shows an allocation processing mode, and FIG. 8 shows an example of enumeration tree search by parallel processing. In the figure, 1 is a parallel cluster, 2 is a communication network, 3 is a communication processing processor, 4 is a problem-solving processor, and 5
6 represents a data space, 6 represents a control data holding section, M to 10 represent control data, and 11 to 14 represent object data.

Claims (5)

[Claims] (1) A plurality of parallel clusters (1) are each connected to a communication network (2), and in processing a given objective function under given constraints, the enumeration tree is searched. In a branch and bound processing device that performs pruning on undesired branches, each of the parallel clusters (1) is linked to the communication network (2) by at least one communication processing processor (3). and a plurality of problem-solving processors (4), and a data space (5) shared by the communication processing processor (3) and the problem-solving processor (4), and the data space (5). The communication processing processor (3) and the problem solving processor (4) each have object data (11, 12, 13, 14) as their own processing target data, and the communication Control data (7, 8) that is commonly accessed by the processing processor (3) and the problem solving processor (4)
, 9, 10), each of the processors (3 or 4) executes its own processing using the object data (11, 12, 13, 14). In addition, the above control data (7, 8, 9,
10) A branch-and-bound high-speed execution processing method characterized in that it is combined with other processors with reference to 10). (2) The above object data (11, 12, 13,
14) is characterized in that each processor (3 or 4) has data to be directly processed and an index for high-speed access to the data. Branch and bound fast execution processing method. (3) The control data (7, 8, 9, 10) includes at least the node position of the problem processing that each processor is processing, and the object data (11, 12,
13, 14) and the access method for the object data (11, 12, 13, 14), and each processor updates the corresponding control data and performs each control. Data (7, 8
, 9, and 10) to make a load distribution request. 10. The branch-and-bound high-speed execution processing method according to claim 1, wherein the load distribution request is made with reference to . (4) One of the problem solving processors (4) in the parallel cluster (1) has a function of extracting a problem from the data space (5) and vertically searching the enumeration tree while repeating branching operations. , and all problem-solving processors (4) including one of the problem-solving processors (4) described above,
4. The branch-and-bound high-speed execution processing method according to claim 3, further comprising a function of performing the pruning and a function of acquiring data to be processed based on the load distribution request. (5) Claim (1) characterized in that the communication processing processor (3) has a function of distributing load to other parallel clusters (1) via the communication network (2). ) is a high-speed execution processing method using the branch and bound method.