CN113240324A - Air and space resource collaborative planning method considering communication mechanism - Google Patents

Air and space resource collaborative planning method considering communication mechanism Download PDF

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CN113240324A
CN113240324A CN202110612085.9A CN202110612085A CN113240324A CN 113240324 A CN113240324 A CN 113240324A CN 202110612085 A CN202110612085 A CN 202110612085A CN 113240324 A CN113240324 A CN 113240324A
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task
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communication
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裴新宇
高晓倩
韩长兴
楚博策
刘敬一
郭琦
高峰
耿虎军
陈金勇
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CETC 54 Research Institute
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention provides an air and space resource collaborative planning method considering a communication mechanism, which overcomes the defect that the current air and space collaborative planning algorithm cannot adapt to the planning requirements of multi-class heterogeneous resource collaborative planning, variable communication conditions and large-scale task outbreak in the air and space resource management and control field; a task collaborative planning framework based on a contract network mechanism is determined, and the generation of an optimal task planning scheme under the scene of large-scale task centralized explosion and large-scale heterogeneous resource collaborative planning is realized; compared with the traditional planning method, the method has the advantages that the plan preferred algorithm LFDA is formed, the scheme generation efficiency and the scheme income are balanced, and the method is more suitable for the air-to-ground observation resource control scene under the condition of communication mechanism change.

Description

Air and space resource collaborative planning method considering communication mechanism
Technical Field
The invention relates to an aerospace resource collaborative planning method considering a communication mechanism, in particular to various heterogeneous aerospace resource collaborative planning methods for large-scale task centralized outbreak in the field of management and control.
Background
The air-space integrated system including observation resources such as satellites and unmanned aerial vehicles plays a key role in aspects of national security, emergency rescue and the like. With the progress of satellite and unmanned aerial vehicle technologies and the increasing task demands of users on various aerospace resources, the traditional planning method for scheduling and allocating aerospace resources by means of subjective experience is gradually eliminated. A large number of intelligent optimization algorithms such as a simulated annealing algorithm, a tabu search algorithm, a particle swarm algorithm, an ant colony optimization algorithm and the like are used for aerospace resource planning. The following disadvantages remain:
(1) single-class resource isolation planning has reached a bottleneck. With the development of satellite and unmanned aerial vehicle technologies, the demands of different application fields on sky resources are continuously improved, single-class sky resource isolation planning cannot meet the diversified demands of users, the limitation of various resources restricts the sky integration system to exert the maximum efficiency, and therefore the collaborative planning of heterogeneous sky resources is a necessary trend.
(2) The real communication condition is not considered in the heterogeneous air and space resource collaborative planning. The traditional collaborative planning method has the problems that:
the centralized planning without considering the traffic condition completely does not conform to the current situation of air and space resource management. In the field of control, heterogeneous air and space resources are generally independently commanded by a plurality of command centers, and only part of the air and space resources can be directly communicated under the authorized condition. In the air and space resource collaborative planning process considering the real communication architecture, the task can be finally determined to be executed only through multiple rounds of communication, a large amount of time is consumed, and the task execution efficiency cannot be guaranteed.
And secondly, the space-air collaborative planning method considering the communication condition in a small amount does not meet the communication condition under a real control scene. Currently, an air-to-air collaborative planning method considering a communication mechanism is mostly based on a special scenario, and a communication condition is explicitly specified, for example, a part of air-to-air observation resources can support communication and a part of areas can communicate. However, in a real task scenario, the communication condition is complex and changeable, the communication link between the space-sky observation resources is at any time in danger of breaking, and the unchangeable communication condition is contrary to the changeable task execution scenario.
(3) The practicability of the air-space collaborative planning method based on small-scale data set verification cannot be verified. In the field of control over space-to-ground observation resources, tasks in a certain area often explode intensively in a large scale, and hundreds of space-to-ground observation resources in a plurality of planning centers need to be planned in a short time in a coordinated manner. The traditional aerospace collaborative planning is based on the effectiveness of a small-scale data verification method, the total number of simulated aerospace observation resources in a simulation experiment is small, the size of a simulation scene task is small, the real planning requirement of the aerospace earth observation resource management and control field is difficult to represent, and the practicability of the method under the situation that tasks are intensively outburst on a large scale cannot be verified.
Disclosure of Invention
The invention aims to provide an aerospace resource collaborative planning method, which overcomes the defects that the aerospace resource cannot adapt to the requirements of multi-class heterogeneous resource collaborative planning, variable communication conditions and large-scale task outbreak in the field at present, determines a task collaborative planning framework based on a contract network mechanism, and realizes the generation of an optimal task planning scheme under the scene of large-scale task centralized outbreak and large-scale heterogeneous resource collaborative planning.
The technical scheme adopted by the invention is as follows:
a space and air resource collaborative planning method considering a communication mechanism comprises the following steps:
(1) the method comprises the steps that a task is transmitted to a nearest planning center, meanwhile, the planning center tests the unblocked situation of a communication link between the planning center and other planning centers, updates a communication matrix of the planning center, serves as a tender issue and tender information, takes the sum of the residual efficiency of resources governed by the planning center in a communication neighborhood as a constraint, divides the task based on an IFDA (election bidding algorithm), and transmits the task to the planning center which wins the bid;
(2) after receiving the tasks, the bid-winning planning center updates a communication matrix of the bid-winning planning center, issues bid-winning information as a publisher, divides the tasks based on an IFDA (Label selection and retrieval) algorithm by taking other aerospace resources in a communication neighborhood as constraints according to the remaining observation capacity of the tasks, and transmits the tasks to bid-winning resources;
(3) judging whether the sum of the remaining observation capacity of the winning resources exceeds the sum of the observation capacity required by the allocation task, if so, turning to the step (5), otherwise, executing the step (4);
(4) the communication matrix of the bid-winning resource is updated, the bid-winning resource is used as bid-attracting information issued by a publisher, other sky resources in the communication neighborhood are used as constraints according to the self residual observation capacity, tasks are divided based on an IFDA (election tagging algorithm), the tasks are transmitted to the bid-winning resource, and the step (3) is returned;
(5) and reporting the self task planning condition to the planning center to which the winning bid resource belongs, and summarizing and generating a final task planning scheme by the planning center.
The task is divided based on an IFDA (index selection and data acquisition) algorithm, and the specific implementation process comprises the following steps:
(101) constructing a planning model:
Figure BDA0003096023830000031
Figure BDA0003096023830000041
in the formula, n represents the number of bidding planning centers or space resources, m represents the number of tasks to be planned in the current round, and BijThe net profit value, X, of task consumption and task profit is comprehensively considered for completing task j for aerospace resources or planning center iijRepresenting aerospace resources or a planning center i to finish a task j; cjThe communication state between the current resource or the planning center and the corresponding planning center or space-sky resource for releasing the task of the current round is represented, the value of 1 represents communication possibility, and the value of 0 represents non-communicationCan communicate; constraint 1 indicates that the task is only completed and not completed by a certain resource or planning center; constraint 2 means that focusing on local all tasks performed does not yield a negative benefit; constraint 3 indicates that the task can only be completed by one resource or planning center;
(102) solving a corresponding relaxation problem of the planning model to obtain an optimal solution, wherein if no solution exists, the planning problem cannot be realized, and no feasible planning scheme exists; if the obtained optimal solutions are all integer solutions meeting the constraint conditions, the integer solutions are the optimal solutions of the planning model, otherwise, the step (103) is carried out;
(103) selecting an item x in the optimal solution which does not conform to the constraint conditionrandomIs set to be less than xrandomThe largest integer being x1Is greater than xrandomThe smallest integer being x2Two constraints are constructed: x is the number of<＝x1And x ═>x2X is a planning scheme to be solved, and a planning model is added to form two subproblems;
(104) respectively calculating the income values of the relaxation problems corresponding to the two sub-problems, recording as Z, and when Z is less than Q x Z0When Z is greater than or equal to Q X Z, step (105) is executed0If so, executing step (106); wherein Z is0The initial value is negative infinity, and Q is a set value;
(105) after the current subproblem is solved, if the solution is not in the subproblem, selecting another item which does not accord with the constraint condition from the optimal solution of the planning model, and executing the step (103) until the branch of the item which does not accord with the constraint condition in the optimal solution of the planning model is completed;
(106) if the optimal solution corresponding to the current subproblem is a solution conforming to the constraint of the planning model, judging Z and Z0The magnitude relationship of Z being greater than Z0When is, Z is0Updating the value of the sub-problem to be Z, selecting another item which does not accord with the constraint condition from the optimal solution of the planning model, and executing the step (103) until the branch of the item which does not accord with the constraint condition from the optimal solution of the planning model is finished, wherein the optimal solution corresponding to the current sub-problem is the final solution of the planning model; if the optimal solution corresponding to the current subproblem is a solution which does not conform to the constraint of the planning model, the most optimal solution of the current subproblemAnd (5) executing the optimal solution (103) until the branch of the item which does not accord with the constraint in the optimal solution of the current subproblem is completed, selecting another item which does not accord with the constraint in the optimal solution of the planning model, and executing the step (103) until the branch of the item which does not accord with the constraint in the optimal solution of the planning model is completed.
Compared with the prior art, the invention has the following advantages:
compared with the traditional air-to-ground collaborative planning method, the method has the advantages that the communication condition among resources is considered, the generation efficiency and the benefit of the scheme are balanced, and the method is more suitable for application of air-to-ground observation resource management and control scenes.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the embodiments of the invention without limiting the embodiments of the invention. In the drawings:
fig. 1 is a schematic diagram of a space and day resource collaborative planning framework from top to bottom according to an embodiment of the present invention.
Fig. 2 is a multi-turn air and space resource task allocation flow based on a contract network mechanism according to an embodiment of the invention.
FIG. 3 is a comparison graph of run time in simulation experiments for embodiments of the present invention.
FIG. 4 is a comparison graph of task completion rates in simulation experiments according to embodiments of the present invention.
FIG. 5 is a graph comparing the average energy consumption of tasks in a simulation experiment according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
In the following description, while specific embodiments of the present invention are described in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention, it is particularly noted that, in the following description, when detailed description of known functions and designs may make the main content of the present invention obscure, the description will be omitted here.
As shown in fig. 1 and fig. 2, the overall idea of the air and space resource collaborative planning method considering the communication mechanism proposed in this embodiment is as follows:
and after the task T is sensed by the observation system, the plurality of space and sky resource planning centers collaboratively respond. The air and space resource collaborative planning is used as a problem of a traveling salesman, in order to avoid the problem of dimension explosion caused by overhigh total number of tasks to be planned and resources participating in planning, the task collaborative planning flow is divided into different stages from top to bottom from the perspective of task transmission, the problem dimension is reduced by reducing the number of the tasks to be planned and the number of the resources participating in planning, which need to be considered in each stage, and the timeliness of task planning is ensured. It is worth noting that the communication condition of the self-body is updated only when the corresponding planning center or resources need to generate communication, and the time consumption problem caused by frequent large-scale updating of the communication condition is avoided. The invention plans the large-scale tasks through three stages to finally complete the planning of all tasks:
1) at the central collaborative layer, tasks are introduced into the layer after being perceived by the system to begin planning. And after the tasks are transmitted into the corresponding planning centers, the corresponding planning centers update the communication conditions between the planning centers and other planning centers. And then, the communication neighborhood issues task information according to a contract network agreement mechanism, an allocation scheme is determined through multi-planning center negotiation, and the tasks are transmitted to the corresponding planning centers.
2) In the internal negotiation layer, after the tasks are negotiated by the planning center and distributed to the corresponding planning center, the communication matrix between the corresponding planning center and the resources is updated, then according to a contract network protocol mechanism, the corresponding planning center issues task information to the resources in the communicable neighborhood, and the next flowing direction of the tasks is determined through the negotiation between the resources.
3) In the resource cooperation layer, task planning conflict may be caused due to lack of cooperation in planning, communication conditions between the resource layer and other resources are updated by taking resources incapable of completing tasks as a planning center in the resource layer, then task information is issued to adjacent resources according to a contract network agreement mechanism, and the resources for executing tasks are determined by the negotiation of all resources in a communication neighborhood.
The contract network mechanism is a classic strategy for solving the multi-resource game problem and comprises four stages of bid sending, bid bidding, bid examining and announcement. The method comprises the steps of taking the space resource/planning center where a task is currently located as a bid inviting initiator, taking other space resources/planning centers which need to be considered in the communication field in the game process of the current round, taking the task as a bid of an auction, taking the residual efficiency of the other space resources/planning centers as bids of the auction, and selecting an optimal bid scheme according to a bid selection algorithm IFDA. The collaborative planning process can be regarded as a process that tasks are continuously spread in a communicable neighborhood in a collaborative system until an optimal/superior task execution resource is found. Under a contract network mechanism, the heterogeneous aerospace resource collaborative planning can be regarded as an optimizing solution which is continuously and iteratively completed by a multi-turn bidding process. In the multi-turn bidding process, the same planning center/resource is continuously converted between two roles of the tenderer and the bidder, and the optimal planning scheme is searched by taking the planning center/resource as a communication node to continuously communicate with other resources in a communication neighborhood. In a top-down framework, task transfer can only occur between planning centers that are currently available for communication, and tasks are only transferred within the communicable neighborhood. As tasks are passed, the planning center and resources transition between bidders and publishers.
After the tasks are transmitted into the observation system, the air-space collaborative planning process combining the contract network mechanism is as follows:
(1) the task T is transmitted into the nearest planning center M, and meanwhile, the planning center M tests whether the communication links with other planning centers M are smooth or not, and updates the communication matrix C of the planning center MC. And then, the planning center M serves as a bid issuer to issue task information, other planning centers M in the communication neighborhood divide tasks based on an IFDA (election bidding algorithm) by taking the residual efficiency sum B of resources governed by the planning centers M as a constraint, and the tasks flow into the bid planning center.
(2) After the task is transmitted to the planning center M of winning bid, the communication matrix C of the self is updatedDAnd as a sponsor, issuing bidding information, and entering other aerospace resources R in the communication neighborhood according to the self residual observation capability BAnd (4) line quotation, wherein tasks are divided based on an optional bidding algorithm (IFDA), and the tasks flow into winning bid resources R.
(3) Since the multi-planning center M simultaneously carries out the bidding of the previous stage, the total of the observation capacities required for allocating the tasks to the corresponding resource R may exceed the total of the remaining observation capacities of the resource R. If the total of the observation capacities required by the tasks allocated to the corresponding resource R exceeds the total of the residual observation capacities of the resource R, the step (4) is carried out, and if not, the step (5) is carried out;
(4) corresponding resource R updates communication matrix C between itself and other resourcesR. And (3) issuing bid inviting information by taking the corresponding resource R as a bid issuer, quoting other aerospace resources R in the communication neighborhood according to the residual observation capacity B of the corresponding resource R, dividing tasks based on an option bid algorithm IFDA (index and destination) and enabling the tasks to flow into the bid winning resource R. And (4) returning to the step (3).
(5) And when the residual observation capacity of the winning resources R can complete all tasks of the winning resources R, reporting the task planning condition of the winning resources R to a planning center M to which the winning resources R belong, and summarizing and generating a final task planning scheme S by the planning center M.
In the process, tasks are divided based on an IFDA (index selection algorithm), and a planning model needs to be constructed.
The planning model is the basis of the solution of the space and space resource collaborative planning scheme and is also an abstract process of planning constraint from a physical world to a data world. In order to better represent the influence of communication mechanism change on the air-day collaborative planning, a communication matrix is introduced in the construction of a planning model to participate in the calculation of the total income of a planning scheme. The model is as follows:
Figure BDA0003096023830000091
Figure BDA0003096023830000092
in the formula, n represents the number of bidding planning centers or space resources, m represents the number of tasks to be planned in the current round, and BijNet benefit of task j completion for aerospace resource or planning center i in comprehensive consideration of task consumption and task benefitValue, XijRepresenting aerospace resources or a planning center i to finish a task j; cjThe communication state between the current resource or the planning center and the corresponding planning center or space-sky resource for releasing the task of the current round is represented, the value is 1 and represents communication, and the value is 0 and represents non-communication; constraint 1 indicates that the task is only completed and not completed by a certain resource or planning center; constraint 2 means that focusing on local all tasks performed does not yield a negative benefit; constraint 3 indicates that the task can only be completed by one resource or planning center;
after the planning model is determined, a model selection algorithm needs to be determined. In the traditional algorithm solving process, along with the increase of the profit, the time consumption is increased exponentially, and the final one-hundredth of profit increase needs to consume more than ten times of time for optimal solving. In order to solve the problem of huge time consumption caused by a small amount of task benefits in the model solving process, the invention develops an improved algorithm IFDA based on branch and bound, and converts the originally determined algorithm target into a fuzzy benefit interval by introducing an uncertain parameter Q, thereby realizing the balance of planning efficiency and planning benefits. The traditional branch-and-bound algorithm shrinks the solution space by continuous pruning, and finally determines the planning result. The invention converts the finally determined solution into a solution randomly generated in a certain profit error solution space by introducing an uncertain parameter Q. The strategy can ensure a certain algorithm gain, and effectively reduce the algorithm time consumption. The IFDA algorithm flow is as follows:
solving a relaxation problem: solving a corresponding relaxation problem of the planning model to obtain an optimal solution, wherein if no solution exists, the planning problem cannot be realized, and no feasible planning scheme exists; if the obtained optimal solutions are all integer solutions meeting the constraint conditions, the integer solutions are the optimal solutions of the planning model, and otherwise, the operation is switched to step two;
② a branching process: selecting an item x in the optimal solution which does not conform to the constraint conditionrandomIs set to be less than xrandomThe largest integer being x1Is greater than xrandomThe smallest integer being x2Two constraints are constructed: x is the number of<＝x1And x ═>x2X is the planning scheme to be solved and is added into the planning model respectivelyType, two subproblems are formed;
thirdly, respectively calculating the income values of the relaxation problems corresponding to the two subproblems, recording the income values as Z, and when Z is less than Q x Z0When Z is greater than or equal to Q X Z, step (105) is executed0If so, executing step (106); wherein Z is0The initial value is negative infinity, and Q is a set value;
fourthly, after the solving of the current subproblem is finished, if the solution is not in the subproblem, selecting another item which does not accord with the constraint condition from the optimal solution of the planning model, and executing the step II until the branch of the item which does not accord with the constraint condition in the optimal solution of the planning model is finished;
judging Z and Z if the optimal solution corresponding to the current subproblem is the solution conforming to the constraint of the planning model0The magnitude relationship of Z being greater than Z0When is, Z is0Updating the value of the sub-problem to be Z, selecting another item which does not accord with the constraint condition in the optimal solution of the planning model, and executing the step II until the branch of the item which does not accord with the constraint condition in the optimal solution of the planning model is finished; and if the optimal solution corresponding to the current subproblem is a solution which does not accord with the constraint of the planning model, executing the optimal solution of the current subproblem until the branch of the item which does not accord with the constraint in the optimal solution of the current subproblem is completed, selecting another item which does not accord with the constraint condition in the optimal solution of the planning model, and executing the step II until the branch of the item which does not accord with the constraint condition in the optimal solution of the planning model is completed.
In order to verify the effectiveness of the method, the effectiveness of the improved planning algorithm IFDA is verified through an AUS planning algorithm taking random optimization as a core idea, an SSA planning algorithm taking a greedy algorithm as a core, a BCP planning algorithm taking branch and bound as a core algorithm and an MCP planning algorithm taking a Mosek solver as a core. The uncertain parameter Q in the simulation experiment was set to 1.1. In the simulation experiment, two satellite planning centers are set for the task to respectively manage 30 low orbit satellites, and two unmanned aerial vehicle planning centers respectively manage 30 unmanned aerial vehicles. In order to verify the planning effectiveness of the algorithm in a communication condition change scene, communication matrix representation communication changes among planning centers, between planning centers and administered resources and among resources are randomly generated after each task occurs. By combining fig. 3, fig. 4 and fig. 5, it can be seen that the LFDA planning method balances the planning efficiency and the task completion rate, and the sacrifice is less. When the number of tasks exceeds two hundred, the time of MCP and BCP algorithms pursuing the highest global benefits begins to increase sharply, and when the number of tasks exceeds four hundred, the operation time of the two algorithms reaches a small level, which is obviously unacceptable for the sky-to-earth observation resource control scene emphasizing the planning efficiency. When the number of tasks exceeds two hundred, the AUS and SSA planning pursuing planning efficiency are unacceptable in comparison with other three algorithms, namely, the planning completion rate and the average energy consumption for completing the tasks are too poor. The LFDA algorithm provided by the invention improves the operation efficiency by thousands of times on the premise of losing one tenth of the completion rate. In addition, under the real space-to-ground observation resource control scene, the method can further improve the applicability by adjusting the uncertainty coefficient Q and balancing the contradiction between the planning completion rate and the planning efficiency.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (2)

1. A space and air resource collaborative planning method considering a communication mechanism is characterized by comprising the following steps:
(1) the method comprises the steps that a task is transmitted to a nearest planning center, meanwhile, the planning center tests the unblocked situation of a communication link between the planning center and other planning centers, updates a communication matrix of the planning center, serves as a tender issue and tender information, takes the sum of the residual efficiency of resources governed by the planning center in a communication neighborhood as a constraint, divides the task based on an IFDA (election bidding algorithm), and transmits the task to the planning center which wins the bid;
(2) after receiving the tasks, the bid-winning planning center updates a communication matrix of the bid-winning planning center, issues bid-winning information as a publisher, divides the tasks based on an IFDA (Label selection and retrieval) algorithm by taking other aerospace resources in a communication neighborhood as constraints according to the remaining observation capacity of the tasks, and transmits the tasks to bid-winning resources;
(3) judging whether the sum of the remaining observation capacity of the winning resources exceeds the sum of the observation capacity required by the allocation task, if so, turning to the step (5), otherwise, executing the step (4);
(4) the communication matrix of the bid-winning resource is updated, the bid-winning resource is used as bid-attracting information issued by a publisher, other sky resources in the communication neighborhood are used as constraints according to the self residual observation capacity, tasks are divided based on an IFDA (election tagging algorithm), the tasks are transmitted to the bid-winning resource, and the step (3) is returned;
(5) and reporting the self task planning condition to the planning center to which the winning bid resource belongs, and summarizing and generating a final task planning scheme by the planning center.
2. The aerospace resource collaborative planning method considering communication mechanism according to claim 1, wherein tasks are divided based on an index selection algorithm IFDA, and the specific implementation process is as follows:
(101) constructing a planning model:
Figure FDA0003096023820000021
Figure FDA0003096023820000022
in the formula, n represents the number of bidding planning centers or space resources, m represents the number of tasks to be planned in the current round, and BijThe net profit value, X, of task consumption and task profit is comprehensively considered for completing task j for aerospace resources or planning center iijRepresenting aerospace resources or a planning center i to finish a task j; cjThe communication status between the current resource or planning center and the corresponding planning center or space-sky resource for distributing the task of the current round is shown, the value of 1 represents communication,a value of 0 represents no communication; constraint 1 indicates that the task is only completed and not completed by a certain resource or planning center; constraint 2 means that focusing on local all tasks performed does not yield a negative benefit; constraint 3 indicates that the task can only be completed by one resource or planning center;
(102) solving a corresponding relaxation problem of the planning model to obtain an optimal solution, wherein if no solution exists, the planning problem cannot be realized, and no feasible planning scheme exists; if the obtained optimal solutions are all integer solutions meeting the constraint conditions, the integer solutions are the optimal solutions of the planning model, otherwise, the step (103) is carried out;
(103) selecting an item x in the optimal solution which does not conform to the constraint conditionrandomIs set to be less than xrandomThe largest integer being x1Is greater than xrandomThe smallest integer being x2Two constraints are constructed: x is the number of<＝x1And x ═>x2X is a planning scheme to be solved, and a planning model is added to form two subproblems;
(104) respectively calculating the income values of the relaxation problems corresponding to the two sub-problems, recording as Z, and when Z is less than Q x Z0When Z is greater than or equal to Q X Z, step (105) is executed0If so, executing step (106); wherein Z is0The initial value is negative infinity, and Q is a set value;
(105) after the current subproblem is solved, if the solution is not in the subproblem, selecting another item which does not accord with the constraint condition from the optimal solution of the planning model, and executing the step (103) until the branch of the item which does not accord with the constraint condition in the optimal solution of the planning model is completed;
(106) if the optimal solution corresponding to the current subproblem is a solution conforming to the constraint of the planning model, judging Z and Z0The magnitude relationship of Z being greater than Z0When is, Z is0Updating the value of the sub-problem to be Z, selecting another item which does not accord with the constraint condition from the optimal solution of the planning model, and executing the step (103) until the branch of the item which does not accord with the constraint condition from the optimal solution of the planning model is finished, wherein the optimal solution corresponding to the current sub-problem is the final solution of the planning model; if the optimal solution corresponding to the current subproblem is a solution which does not conform to the constraint of the planning model, the current subproblemThe step (103) is executed until the branch of the item which does not accord with the constraint in the optimal solution of the current subproblem is completed, another item which does not accord with the constraint is selected from the optimal solution of the planning model, and the step (103) is executed until the branch of the item which does not accord with the constraint in the optimal solution of the planning model is completed.
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