CN110569584B - Directed graph-based cloud manufacturing service optimization mathematical model building method - Google Patents

Directed graph-based cloud manufacturing service optimization mathematical model building method Download PDF

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CN110569584B
CN110569584B CN201910798578.9A CN201910798578A CN110569584B CN 110569584 B CN110569584 B CN 110569584B CN 201910798578 A CN201910798578 A CN 201910798578A CN 110569584 B CN110569584 B CN 110569584B
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resource cost
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CN110569584A (en
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刘坤华
陈龙
袁湛楠
张彧
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Sun Yat Sen University
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Abstract

The invention provides a directed graph-based cloud manufacturing service optimization mathematical model establishing method, which takes a service combination scheme with k minimum and maximum indexes as an optimization target, respectively establishes an objective function and a mathematical model for the cloud manufacturing service combination scheme, expresses the directed graph with nodes having resource cost, and converts the directed graph with the nodes having the resource cost into a standard directed graph with only paths having the resource cost nodes without the resource cost on the basis, thereby converting the service combination optimization problem into the shortest path solving problem of the standard directed graph, facilitating the optimization solution of the service combination scheme, improving the solving efficiency, effectively improving the production efficiency of cloud manufacturing enterprises and reducing the production cost.

Description

Directed graph-based cloud manufacturing service optimization mathematical model building method
Technical Field
The invention relates to the technical field of cloud manufacturing, in particular to a directed graph-based cloud manufacturing service optimization mathematical model building method.
Background
Cloud manufacturing is a cross fusion product of advanced information technology, manufacturing technology, emerging internet of things technology and the like, is embodied by a manufacturing-as-a-service concept, adopts a current information technology leading-edge concept including cloud computing, and supports the manufacturing industry to provide services with high added value, low cost and global manufacturing for products under a wide network resource environment.
Because various service resources forming cloud manufacturing capability, such as design service, production service, product service and the like, generally embody the characteristics of fuzziness, uncertainty, dynamics and the like, common knowledge description methods such as fault trees, decision trees, ontology technologies and the like are complex in form, the requirement on background knowledge of technical personnel in related fields is too high, the acquisition of manufacturing capability is seriously influenced, and the production cost is high in the cloud manufacturing service, but the production efficiency is low.
Disclosure of Invention
In order to solve the problem that the manufacturing service scheme is difficult to describe by using a mathematical model in the prior art, the invention provides the digraph-based cloud manufacturing service optimization mathematical model establishing method.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: the cloud manufacturing service optimization mathematical model building method based on the directed graph comprises the following steps:
s1, establishing mathematical models of first k minimum and maximum index service combination schemes of a design service combination scheme, a production service combination scheme, a product service combination scheme and a product combination scheme respectively;
s2, according to the first k minimum and maximum index service combination scheme mathematical models, representing the service combination process of design service, production service, product service and product by a directed graph with resource cost through nodes;
and S3, converting the directed graph with the resource cost of the node into a standard directed graph with the resource cost of the node only having the resource cost, and updating the first k minimum and maximum index service combination scheme mathematical model according to the standard directed graph.
Preferably, the directed graph with the node having the resource cost is as follows:
starting from R, through a path W 00,0j Selecting a node P 0j Completing the selection of the first subtask server, and then passing through the path W 01,1j Selecting a node P 1j Completing the selection of the second subtask server, and proceeding in sequence until passing through the path W (n-1)j,n1 Sending the service result to the demander P n1 And completing a service combination scheme.
Preferably, the index includes service time, service cost, manufacturing capability, and comprehensive capability.
Preferably, the objective function of the first k minimum or maximum index service combination schemes of 4 service types of design service, production service, product service and product can be uniformly expressed as follows:
Figure BDA0002181658760000021
wherein, beta ij P ij For the resource cost of the selected subtasks, α ij W ij,(n+1)j For the path resource cost, γ, between adjacent subtasks (n-1)j W (n-1)j,n1 The path resource cost from the last selected subtask to the demand side; if 4 service types of design service, production service, product service and product are established by taking service time and service cost as indexes, K =1, otherwise K =1/n.
Preferably, the specific operation of converting the directed graph with the nodes having the resource cost into the standard directed graph with the paths having the nodes without the resource cost is as follows:
for the first n-1 stage subtasks, the resource cost of the node is accumulated into the path from the node of the previous stage to the node, and the resource cost of the node is released, that is, the resource cost on the path is the sum of the resource cost of the original path and the resource cost of the node at the end point of the path, and the specific formula is as follows:
W′ ij,(i+1)j ＝W ij,(i+1)j +P ij
S.T.
i＝{1,2,...n-1}
j＝{1,2,...m}
wherein, W' ij,(i+1)j For the resource cost of the path from the node of the previous stage to this node, W ij,(i+1)j For the resource cost of the original path, P ij A resource cost of a node that is a path destination;
for the nth subtask, as the subtask realizes the logistics transportation from the last subtask server to the demand side, the resource cost of the node is 0, and the resource cost on the path is the resource cost of the original path, the specific formula is as follows:
W′ (n-1)j,n1 ＝W (n-1)j,n1 +P n1
＝W (n-1)j,n1
in the formula, W (n-1)j,n1 Resource cost to the demander for the last subtask, P n1 Is the resource cost of the demander.
Preferably, the mathematical model of the first k minimum and maximum index service combination schemes is in the final form:
Figure BDA0002181658760000031
W′ ij,(n+1)j for resource cost on path, α ij Is a coefficient, γ (n-1)j W (n-1)j,n1 And (4) the path resource cost from the finally selected subtask to the demand side, wherein i is the ith subtask and j is the jth server side.
Compared with the prior art, the beneficial effects are that: the invention takes the service combination scheme of the former k minimum and maximum indexes (service time, service cost, manufacturing capability and comprehensive capability) as the optimal target, respectively establishes an objective function and a mathematical model for the cloud manufacturing service combination scheme, expresses the directed graph with the nodes having the resource cost, and converts the directed graph with the nodes having the resource cost into the standard directed graph with the nodes having the resource cost and no resource cost only by paths on the basis, thereby converting the service combination optimal problem into the shortest path solving problem of the standard directed graph, facilitating the optimal solution of the service combination scheme, improving the solving efficiency, effectively improving the production efficiency of cloud manufacturing enterprises and reducing the production cost.
Drawings
Fig. 1 is a flowchart of a method for establishing a cloud manufacturing service optimization mathematical model based on a directed graph according to an embodiment of the present invention;
fig. 2 is a directed diagram of a preferred embodiment of a cloud manufacturing service combination provided in an embodiment of the present invention;
fig. 3 is a standard directed graph of a cloud manufacturing service combination optimization scheme provided in an embodiment of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent; for the purpose of better illustrating the present embodiments, certain elements of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and should not be construed as limiting the present patent.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "long", "short", etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the drawings, it is only for convenience of description and simplicity of description, but does not indicate or imply that the device or element referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationships in the drawings are only used for illustrative purposes and are not to be construed as limitations of the present patent, and specific meanings of the terms may be understood by those skilled in the art according to specific situations.
The technical scheme of the invention is further described in detail by the following specific embodiments in combination with the attached drawings:
examples
Fig. 1 shows an embodiment of a neural network model optimization method based on the ThLU function, which includes the following steps:
s1: respectively establishing first k minimum and maximum index service combination scheme mathematical models of a design service combination scheme, a production service combination scheme, a product service combination scheme and a product combination scheme;
s2: according to the first k minimum and maximum index service combination scheme mathematical models, the service combination process of design service, production service, product service and product is represented by a directed graph with resource cost through nodes;
s3: and converting the directed graph with the resource cost at the node into a standard directed graph with the resource cost only at the path and without the resource cost at the node, and updating the mathematical models of the first k minimum and maximum index service combination schemes according to the standard directed graph.
In order to realize service optimization, a service combination scheme with k minimum and maximum indexes (service time, service cost, manufacturing capability and comprehensive capability) is taken as an optimization target, an objective function and a mathematical model are respectively established for the service combination scheme, and the mathematical model is analyzed on the basis of a directed graph.
And respectively establishing an objective function of a design service combination scheme, a production service combination scheme, a product service combination scheme and a product combination scheme. The general parameters in the embodiment of the invention are defined as follows:
Figure BDA0002181658760000051
Figure BDA0002181658760000052
i is the ith sub-task, i = {0,1, 2. (n-1) }; j is the jth server, j = {1,2,. M }.
For designing a service combination scheme, the service combination scheme is designed by sequentially selecting each sub-design service party and selecting logistics service to complete the process of designing the service, the service results of the sub-design service parties are represented in the forms of electronic drawings and the like, and the transmission mode of the service results among the service parties is electronic communication without considering logistics time and cost.
The service time for designing the service combination scheme is the sum of the service time of each selected sub-design service party:
Figure BDA0002181658760000053
wherein, T D The sum of the service time of the service side is designed for each sub,
Figure BDA0002181658760000054
the service time of the jth service party of the ith subtask.
The service cost for designing the service combination scheme is the sum of the service cost of each selected sub-design service party:
Figure BDA0002181658760000055
wherein, C D The sum of the service time of the service side is designed for each sub,
Figure BDA0002181658760000061
the service time of the jth service side of the ith subtask.
Designing the design service capability of the service combination scheme, wherein the design service capability is the average number of the sum of the service capabilities of the selected sub-design service parties:
Figure BDA0002181658760000062
wherein Q D The sum of the service time of the service side is designed for each sub,
Figure BDA0002181658760000063
the service time of the jth service side of the ith subtask.
The integrated capabilities of the individual servant in the design process need to be computed before the integrated capabilities of the service composition scheme is computed and designed. The comprehensive capacity of a single service party is the sum of the reciprocal of the design service time, the reciprocal of the design service cost, the sum of the design service capacity and the number of the evaluated people multiplied by different weights:
Figure BDA0002181658760000064
the comprehensive capability of the design service combination scheme is the average of the sum of the comprehensive capabilities of the selected sub-design service parties:
Figure BDA0002181658760000065
wherein S is D The sum of the service time of the service side is designed for each sub,
Figure BDA0002181658760000066
the service time of the jth service party of the ith subtask.
For the production service combination scheme, the production service combination scheme is a process of orderly selecting each sub-production service party and selecting logistics service to complete production service. Because the sub-production service parties transmit real objects such as workpieces and the like, and the sub-production service parties can have geographical position differences, logistics cost and logistics time exist in the transmission process. If the logistics time and the logistics cost do not exist between two adjacent sub-production service parties, the logistics time and the logistics cost are set to be 0, and the logistics time and the logistics cost between the non-adjacent sub-production service parties are infinite.
The service time of the production service combination scheme is the sum of the service time of each selected sub-production service party and the logistics time of each adjacent selected sub-production service party, and the logistics time from the last selected sub-production service party to the demand party:
Figure BDA0002181658760000071
the service cost of the production service combination scheme is the service cost of each selected sub-production service party, the logistics cost of each adjacent sub-production service party and the logistics cost from the selected production service party to the demand party:
Figure BDA0002181658760000072
the production service capacity of the production service combination scheme is the average of the sum of the service fees of the selected sub-production service parties:
Figure BDA0002181658760000073
the comprehensive capacity of the production service combination scheme is the average of the sum of the comprehensive capacities of the selected sub-production service parties:
Figure BDA0002181658760000074
the comprehensive capacity of the sub-production service party is the sum of products of the weight of the reciprocal of the production service time, the reciprocal of the production service cost, the production service capacity and the number of the practicabs:
Figure BDA0002181658760000081
for the product service combination scheme, the product service comprises each sub-design service, each sub-production service and a logistics service.
The service time of the product service combination scheme is the sum of the service time of each selected sub-design service party, the service time of each sub-production service party, the logistics time between each sub-production service party and the logistics time from the last selected sub-production service party to the demand party:
Figure BDA0002181658760000082
the service cost of the product service combination scheme is the sum of the service cost of each selected sub-design service party, the service cost of each sub-production service party, the logistics cost between each sub-production service party and the logistics cost from the last selected sub-production service party to the demand party:
Figure BDA0002181658760000083
the product service capability of the product service combination scheme is the average of the sum of the design service capability of each selected sub-design service party and the production service capability of each selected sub-production service party:
Figure BDA0002181658760000084
the comprehensive capability of the product service combination scheme is the average of the sum of the comprehensive capability of the selected sub-design service and the comprehensive capability of the selected sub-production service party:
Figure BDA0002181658760000091
for the product combination scheme, the service time of the product combination scheme is the logistics time from the selected service party to the demand party:
Figure BDA0002181658760000092
the service cost is the service cost of the selected service party plus the logistics cost from the service party to the demand party:
Figure BDA0002181658760000093
the manufacturing capability is the manufacturing capability of the selected service party:
Figure BDA0002181658760000094
the comprehensive capability is the comprehensive capability of the selected service party:
Figure BDA0002181658760000095
in order to uniformly represent a preferred model of each service composition scheme, the embodiment of the present invention uses T to represent service time for designing a service composition scheme, service time for producing a service composition scheme, and service time for producing a service composition scheme:
T＝{T D ,T M ,T PS ,T P }
therefore, the mathematical models of the first k minimum service times and the maximum service time are respectively:
Figure BDA0002181658760000096
and uniformly expressing the service cost of the design service combination scheme, the service cost of the production service combination scheme, the service cost of the product service combination scheme and the service cost of the product combination scheme by C:
C＝{C D ,C M ,C PS ,C P }
therefore, the mathematical models of the first k minimum and maximum service costs are:
Figure BDA0002181658760000101
uniformly expressing the manufacturing capability of the design service combination plan, the manufacturing capability of the production service combination plan, the manufacturing capability of the product service combination plan and the manufacturing capability of the product combination plan by Q:
Q＝{Q D ,Q M ,Q PS ,Q P }
therefore, the first k mathematical models of minimum and maximum manufacturability are:
Figure BDA0002181658760000102
and uniformly expressing the comprehensive capability of the design service combination scheme, the comprehensive capability of the production service combination scheme, the comprehensive capability of the product service combination scheme and the comprehensive capability of the product combination scheme by using S:
S＝{S D ,S M ,S PS ,S P }
therefore, the first k mathematical models of the minimum and maximum comprehensive capabilities are:
Figure BDA0002181658760000103
the mathematical model of the k minimum and maximum index service combination schemes before the design service, the production service, the product service and the 4 service types of the product can be known as follows: the objective functions of all the service combination schemes are the accumulation of corresponding indexes of all the subtask service parties or the average value of the accumulation; each service combination scheme is a combination of each subtask server in order, and the combination process is represented by a directed graph, as shown in fig. 2.
The leftmost node represents a task, represented by R, and since the task has no resource cost, R =0;
M ij the jth server of the ith subtask, for example: m 1j The jth service side of the 1 st subtask; p ij The resource cost (service time, service cost, manufacturing capability, comprehensive capability) of the jth service party for the ith subtask is as follows:
Figure BDA0002181658760000111
since the service composition scheme includes the process from the last subtask server to the demander, P is defined n1 Is the resource cost of the demand side and order P n1 ＝0。
In the figure, the arrows represent the combined process from the server of one phase subtask to the server of the next phase subtask, during which the resource cost is represented by W ij,(i+1)j Means that when there is no resource penalty between the subtasks, W ij,(i+1)j =0, i.e.:
Figure BDA0002181658760000112
wherein the content of the first and second substances,
Figure BDA0002181658760000113
from one serving side to the next for a phase subtaskService time in the composition process of the service side of the phase subtask,
Figure BDA0002181658760000114
for the service charge in the combined process of the service side of one phase subtask to the service side of the next phase subtask,
Figure BDA0002181658760000115
logistics cost from the selected service party to the demand party;
the dashed box represents one or more subtasks, the unfilled circle indicating that the node has a resource cost, and the filled circle with black indicating that the resource cost of the node is 0. The directed graph of the service composition process can be expressed as follows: from R, through a path W 00,0j Selecting a node P 0j Completing the selection of the first subtask server, and then passing through the path W 01,1j Selecting a node P 1j The selection of the second subtask server is completed, and the steps are performed in sequence until the path W is passed (n-1)j,n1 Sending the service result to the demander P n1 And completing a service combination scheme.
The objective function of the first k min/macro index service composition schemes for 4 service types of design service, production service, product service and product can be expressed uniformly as follows:
Figure BDA0002181658760000121
wherein, beta ij P ij For the resource cost of the selected subtasks, α ij W ij,(n+1)j For the path resource cost, γ, between adjacent subtasks (n-1)j W (n-1)j,n1 The path resource cost from the last selected subtask to the demand side;
in the formula, if 4 service types of design service, production service, product service and product are used for establishing an objective function by taking service time and service cost as indexes, K =1, otherwise K =1/n.
Due to the fact that logistics time and logistics cost exist in the cloud manufacturing service combination process, paths in a directed graph of a service combination scheme may have resource cost, and besides the resource cost of a task and a demand side is 0, other nodes all have resource cost. In the standard directed graph, only the path has resource cost, and the node does not have resource cost, so that the directed graph with the combination optimization is converted into the standard directed graph, the cloud manufacturing service combination optimization problem is converted into the standard directed graph problem, and the shortest/long path between two nodes in the standard directed graph is searched.
For the first n-1 stage subtasks, the resource cost of the node is accumulated into the path from the node of the previous stage to the node, and the resource cost of the node is released, namely the resource cost on the path is the sum of the resource cost of the original path and the resource cost of the node at the end point of the path:
W′ ij,(i+1)j ＝W ij,(i+1)j +P ij
S.T.
i＝{1,2,...n-1}
j＝{1,2,...m}
wherein, W' ij,(i+1)j Cost of resources for the path from the node of the previous stage to the node, W ij,(i+1)j Cost of resources for the original path, P ij The resource cost of the node at the end of the path.
For the nth subtask, namely the last subtask, since the subtask realizes the logistics transportation from the last subtask server to the demand side, the resource cost P of the node n1 And is 0, the resource cost on the path is the original path resource cost:
W′ (n-1)j,n1 ＝W (n-1)j,n1 +P n1
＝W (n-1)j,n1
in the formula, W (n-1)j,n1 For the resource cost of the last subtask to the demander, P n1 Is the resource cost of the demander.
The combined preferred directed graph is converted into the standard directed graph by the method, the resource cost of all nodes is 0, and only the path has the resource cost, as shown in fig. 3, so that the mathematical model of the service combination scheme is as follows:
Figure BDA0002181658760000131
W′ ij,(n+1)j for the cost of resources on the path, α ij Is a coefficient, γ (n-1)j W (n-1)j,n1 And the path resource cost from the last selected subtask to the demand side is represented by i as the ith subtask and j as the jth server side.
In the embodiment of the invention, the service combination scheme of the former k minimum/large indexes (service time, service cost, manufacturing capability and comprehensive capability) is taken as the optimal target, the objective function and the mathematical model are respectively established for the cloud manufacturing service combination scheme, the directed graph with the node having the resource cost is expressed, and on the basis, the directed graph with the node having the resource cost is converted into the standard directed graph with the node having the resource cost and only the path having the resource cost and no resource cost, so that the optimal problem of the service combination is converted into the shortest path solving problem of the standard directed graph, the optimal solution of the service combination scheme is facilitated, the solving efficiency is improved, the production efficiency of cloud manufacturing enterprises is effectively improved, and the production cost is reduced.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (3)

1. A directed graph-based cloud manufacturing service optimization mathematical model building method is characterized by comprising the following steps:
s1: respectively establishing first k minimum and maximum index service combination scheme mathematical models of a design service combination scheme, a production service combination scheme, a product service combination scheme and a product combination scheme;
s2: according to the first k minimum and maximum index service combination scheme mathematical models, a directed graph representation of resource cost is formed in the service combination process of design service, production service, product service and products through nodes;
s3: converting the directed graph with the node having the resource cost into a standard directed graph with the path having the resource cost and the node not having the resource cost, and updating the first k minimum and maximum index service combination scheme mathematical models according to the standard directed graph;
the index includes service time, service cost, manufacturing capability and comprehensive capability;
the objective function of the first k minimum or maximum index service combination schemes of the 4 service types of design service, production service, product service and product can be uniformly expressed as follows:
Figure FDA0003908257420000011
wherein, beta ij P ij For the resource cost of each sub-task selected, α ij W ij，(n+1)j For the path resource cost between adjacent subtasks, gamma (n-l)j W (n-l)j，n1 The path resource cost from the last selected subtask to the demander; if 4 service types of design service, production service, product service and product are established by taking service time and service cost as indexes, K =1, otherwise K =1/n; n is the number of subtasks;
the specific operation of converting the directed graph with the node having the resource cost into the standard directed graph with the path having the node having no resource cost is as follows:
for the first n-1 stage subtasks, the resource cost of the node is accumulated in the path from the node of the previous stage to the node, and the resource cost of the node is released, that is, the resource cost on the path is the sum of the resource cost of the original path and the resource cost of the node at the end point of the path, and the specific formula is as follows:
W′ ij，(i+1)j ＝W ij，(i+1)j +P ij
S.T.
i＝{1，2，...n-1}
j＝{1，2，...m}
wherein, W' ij，(i+1)j Cost of resources for the path from the node of the previous stage to the node, W ij，(i+1)j Cost of resources for the original path, P ij The resource cost of the node which is the path terminal point; m is the number of service parties;
for the nth subtask, since the subtask realizes the logistics transportation from the last subtask server to the demand side, the resource cost P of the node n1 The path resource cost is 0, the path resource cost is the original path resource cost, and the specific formula is as follows:
W′ (n-1)j，n1 ＝W (n-1)j，n1 +P n1
＝W (n-1)j，n1
w 'in the formula' (n-1)j，n1 For resource cost on path, W (n-1)j，n1 For the resource cost of the last subtask to the demander, P n1 Is the resource cost of the demander.
2. The directed graph-based cloud manufacturing service preferred mathematical model building method according to claim 1, wherein the directed graph with the node having the resource cost is as follows:
from task R, via path W 00，0j Selecting a node P 0j Completing the selection of the first subtask server, and then passing through the path W 01，1j Selecting a node P 1j The selection of the second subtask server is completed, and the steps are performed in sequence until the path W is passed (n-1)j，n1 Sending the service result to the demander P n1 And completing a service combination scheme.
3. The method for establishing the cloud manufacturing service optimization mathematical model based on the directed graph according to claim 1, wherein the formula of the first k minimum and maximum index service combination scheme mathematical model is as follows:
Figure FDA0003908257420000021
wherein, W' ij，(n+1)j For resource cost on path, α ij Is a coefficient, γ (n-1)j W (n-1)j，n1 And the path resource cost from the last selected subtask to the demand side is represented by i as the ith subtask and j as the jth server side.
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