CN113365355A - Multidimensional resource management method and system under air-space-ground integrated network - Google Patents
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Abstract
A multidimensional resource management method and system under an air-space-ground integrated network comprises the following steps: constructing a capacity resource time-varying graph; giving task flow and initial definition of arc capacity on the basis of a capacity resource time-varying graph; modeling a task scheduling problem of multidimensional resource management in an air-space-ground integrated network into a multi-constraint maximum flow problem based on a capacity resource time-varying graph; according to the weak coupling relation of problem constraint, a joint resource algorithm based on original decomposition and branch and bound is provided, the original problem is decomposed into parallel independent sub-problems, and the original high-complexity resource allocation problem is efficiently solved through a divide and conquer thought. The invention provides a network utility maximization algorithm based on original decomposition and branch-bound aiming at the SAGIUM air-space-ground integrated network utility maximization problem, and the algorithm has comprehensive advantages in the aspects of time complexity, convergence and network profit maximization.
Description
Technical Field
The invention belongs to the technical field of network resource management, and particularly relates to a multidimensional resource management method and system under an air-space-ground integrated network.
Background
The multidimensional resource management algorithm in the air-space-ground integrated network is still in the initial stage. The air-space-ground integrated network is used as a multi-dimensional heterogeneous network in the future direction, and relates to various heterogeneous networks such as a ground internet, a space-based network and the like. The prior art only considers a small amount of resource management strategies under a space-based network and does not consider the time-varying property, the heterogeneity and the multi-dimensionality of resources of an air-space-ground integrated network. Aiming at the problem of multidimensional resource allocation under the air-space-ground integrated network, namely network utility maximization, a method is urgently needed to solve the problem.
Disclosure of Invention
The invention aims to provide a multidimensional resource management method and system under an air-space-ground integrated network, so as to solve the problems.
In order to achieve the purpose, the invention adopts the following technical scheme:
a multidimensional resource management method under an air-space-ground integrated network comprises the following steps:
constructing a capacity resource time-varying graph according to an emergency scene of the air-space-ground integrated network model;
giving task flow and initial definition of arc capacity on the basis of a capacity resource time-varying graph;
modeling a task scheduling problem of multidimensional resource management in an air-space-ground integrated network into a multi-constraint maximum flow problem based on a capacity resource time-varying graph;
according to the weak coupling relation of problem constraint, a joint resource algorithm based on original decomposition and branch and bound is provided, the original problem is decomposed into parallel independent sub-problems, and the original high-complexity resource allocation problem is efficiently solved through a divide and conquer thought.
Furthermore, a system planning period of the air-space-ground integrated network model is divided into T periods, which are recorded as T ∈ Γ ═ 1, … T }, and meanwhile, a capacity resource time-varying graph is constructed and used
And (4) showing.
Further, arc flow definition is given on the basis of a capacity resource time-varying graph
Arc capacity definition
Viable task flow definition
Feasible task data flow definition
Further, the execution process of the task under the emergency scene in the air-space-ground integrated network is represented by a feasible task flow in the capacity resource time-varying graph, and the task scheduling problem of multidimensional resource management in the air-space-ground integrated network is modeled into a multi-constraint maximum flow problem based on the capacity resource time-varying graph, which specifically comprises the following steps:
capacity constraints
The feasible task data flow can not exceed the arc capacity upper limit, namely can not exceed the maximum capacity resource provided by the node, and the feasible task data flow is modeled as the following inequality
Constraint of conservation of flow
Definition of
Representing the arc flow belonging to a processing arc in a feasible data stream, the flow conservation constraint is modeled as the following equation
Handling constraints
Definition BmThe maximum processing capacity of the relay node is represented in unit (bit), and the processing arc flow of each time slot is less than the maximum processing capacity Bm；
For the initial throughput at the start of a slot, the processing constraints are modeled as the following equation:
transmission constraints
Definitions of the incoming Boolean variable u (i)t，jt)，u(it，jt) 1 indicates that a transmission arc is available, that is, in the t time slot, the node i and the node j transmit data; otherwise, u (i)t，jt) 0 means that a transmission arc is not available, and the transmission link is a bidirectional link; in addition to define
Representing all transmission arcs at the time T, and defining u ═ { u (T) |1 ≦ T } to represent the transmission arcs of the whole system planning period; the transmission constraint is modeled as the following equations and inequalities:
observation constraints
The Boolean variable o (i) is defined in the same way as the transport constraintst，jt)，(it，jt) 1 indicates that an observation arc is available, i.e., that there is an observation opportunity for node i and node j in time slot tTransmitting observation data; otherwise, (i)t，jt) 0 means observation is not available, and similarly, the observation link is also a bidirectional link; in addition to define
Representing all observation arcs at the time T, and defining that o ═ { o (T) |1 ≦ T ≦ T } represents the observation arcs of the whole system planning period; the observation constraint is modeled as the following equation:
problem modeling
Based on the constraints, a network utility maximization framework is adopted to model the maximization network utility problem SAGIUM in the air-space-ground integrated network into the form
Wherein U (f) represents a network utility function, and the utility function represents the 'satisfaction' level of a task after a certain number of tasks;
and the data processing amount of the node i at the last T moment of the time slot of the feasible task flow is shown.
Further, a maximum algorithm based on original decomposition and branch-and-bound network utility is proposed for solving the SAGIUM problem; the problem is solved using the original decomposition algorithm: decoupling coupling relationships between successive time slots by introducing auxiliary vectors
Where L represents a state vector of a processing resource, having the following properties
It is introduced into the stream conservation constraint and converted into the following form:
further, the original constraint is converted into a new constraint by introducing an auxiliary vector, and the original problem is converted into a new problem as follows:
decomposing into each time slot to solve independently;
the original decomposition algorithm is introduced to convert P1 into a sub-problem related to time slot t, and an optimization function qt is defined as (l)F(t)) and an auxiliary vector lF(T) wherein 1 < T < T. Definition of
The original problem is converted into the following problem:
given lF(t) processing the resource state vector to solve the problem p4
Further, p3 needs to calculate the sum of L _ f (T) in all planning periods, the problem p4 is solved by giving L, the problem p4 is decomposed into T independent sub-problems, each independent sub-problem is solved in parallel to obtain a feasible task planning vector f (T), a transmission planning vector u (T) and an observation planning vector o (T);
the idea of branch and bound is adopted to solve the observation of each time slot and transmit a selection strategy; will passInput variable u (i)t，jt) Observation of variable o (i)t，jt) Relaxation is carried out so that 0 < u (i)t，jt)＜1，0＜o(it，jt) < 1, variable u (i) after relaxationt，jt) Expressed as the proportion of time between nodes at which there is a transmission opportunity, o (i)t，jt) Representing the proportion of time between nodes at which there is an observation opportunity;
defining the LP problem as the relaxation problem of the P3 problem, then solving the LP problem to obtain the upper bound of the candidate solution, which can also be set as minus infinity; the stack is then initialized and the solved link is restored to a feasible link, the variable u (i)t，jt)＝1，o(it，jt) The link with 1 is set as a variable u (i) which is a non-feasible link according to the constraintt，jt)＝0，o(it，jt) Continuously stacking the nodes in the setting process of the link of 0; and continuously updating the upper and lower bounds and the optimal solution at the same time, if the difference between the upper and lower bounds is less than the minimum parameter epsilon and is more than 0, ending the process, otherwise, popping the node, executing branch decision, namely selecting u (i)t，jt) Branching near 1 and stacking the branch; if so, the link u (i)t，jt) Set to 1, the other branch to 0;
solving the time slot problem P4 to obtain a problem target q (1) corresponding to P3, defining q★Is q (l)F(t)), the goal of the problem p3 is to find the optimal L★Further find the optimal q★(ii) a Therefore, the optimal L is found by adopting a sub-gradient algorithm★(ii) a Update by the following iterative manner
Where k is the iteration number, a ^ (k) is the forward iteration step size factor, g (l ^ (k)) is the sub-gradient of vector l at point l (k), respectively [ ·]And ^ + is the mapping of l on the feasible domain created by the storage constraint.
Further, a multidimensional resource management system under the air-space-ground integrated network comprises:
the capacity resource time-varying graph constructing module is used for constructing a capacity resource time-varying graph according to an emergency scene of the air-space-ground integrated network model;
the task flow and arc capacity initial definition module is used for giving task flow and arc capacity initial definitions on the basis of a capacity resource time-varying graph;
the task scheduling problem modeling module is used for modeling a task scheduling problem of multi-dimensional resource management in the air-space-ground integrated network into a multi-constraint maximum flow problem based on a capacity resource time-varying graph;
the resource allocation solving module is used for providing a joint resource algorithm based on original decomposition and branch and bound according to the weak coupling relation of problem constraint, decomposing the original problem into parallel independent subproblems, and efficiently solving the original high-complexity resource allocation problem through a divide and conquer idea.
Compared with the prior art, the invention has the following technical effects:
the invention provides a network utility maximization algorithm based on original decomposition and branch-and-bound aiming at the SAGIUM air-space-ground integrated network utility maximization problem, the algorithm converts a problem with a complex scale into sub-problems which can be solved independently in parallel, each sub-problem is solved through the branch-and-bound algorithm, so that less time is consumed, and due to the consideration of a time slot division strategy, the accuracy of the algorithm is improved, and the network utility is improved. Compared with other algorithms, the method has comprehensive advantages in time complexity, convergence and network profit maximization.
Drawings
FIG. 1 is a diagram of an aerospace-geostationary integrated network model in an emergency scenario
FIG. 2 is a time-varying diagram of space-air-ground integrated network capacity resources in an emergency scenario
FIG. 3 algorithm execution time comparison graph
FIG. 4 Algorithm network utility contrast map
Figure 5 comparison of the number of iterations of the algorithm
Detailed Description
The invention is further illustrated by the following set of drawings:
referring to fig. 1 to 5, in the scenario of fig. 1, the system planning period is divided into T periods, which are denoted as T ∈ Γ { (1, … T }. Simultaneous construction of a time-varying graph of capacity resources
And (4) showing.
Arc flow definition is given on the basis of a capacity resource time-varying graph
Arc capacity definition
Viable task flow definition
Feasible task data flow definition
The execution process of the tasks under the emergency scene in the air-space-ground integrated network is represented by the feasible task flow in the capacity resource time-varying graph. Therefore, the task scheduling problem of multidimensional resource management in the air-space-ground integrated network can be modeled into a multi-constraint maximum flow problem based on a capacity resource time-varying graph.
Capacity constraints
The feasible task data flow cannot exceed the arc capacity upper limit, i.e. cannot exceed the maximum capacity resource that the node can provide, and therefore can be modeled as the following inequality
Constraint of conservation of flow
In the air-space-ground integrated networkEach relay node has available computational resources and memory resources, and in order to indicate that the inflow of any node in a feasible task flow is equal to the outflow of the node, a definition is made
Indicating the arc flows belonging to the processing arcs in the feasible data flow. Thus, the flow conservation constraint can be modeled as the following equation
Handling constraints
Defining B considering the computational resource and memory size limit of each nodemThe maximum processing capacity of the relay node is represented in units of (bit). The processing arc flow of each time slot is less than the maximum capacity B of the processingm。
Since the start of a slot is the initial throughput. Thus, the processing constraints can be modeled as the following equation:
transmission constraints
Because each node in the air-space-ground integrated network is provided with unequal numbers of transceiving equipment and sensors, only a part of transmission opportunities in the same time slot can be used for transmitting data, namely whether a transmission arc is available or not. Thus, the definition introduces the Boolean variable u (i)t，jt)，u(it，jt) 1 indicates that a transmission arc is available, that is, that in the t time slot, the node i and the node j can transmit data. Otherwise, u (i)t，jt) 0 means that a transmission arc is not available. Meanwhile, the transmission link is a bidirectional link because the establishment of the transmission link requires the cooperation of transceivers at two ends. In addition to define
And the transmission arcs represent all transmission arcs at the time T, and the transmission arcs representing the whole system planning period are defined as u ═ { u (T) |1 ≦ T ≦ T }. Thus, the transmission constraints can be modeled as the following equations and inequalities:
observation constraints
The Boolean variable o (i) is defined in the same way as the transport constraintst，jt)，(it，jt) 1 indicates that an observation arc is available, that is, an observation opportunity exists between the node i and the node j in the t time slot, and observation data can be transmitted. Otherwise, (i)t，jt) An observation not available is denoted 0, and similarly the observation link is also a bi-directional link. In addition to define
All observation arcs at the time T are represented, and the observation arcs of the whole system planning period are defined as o ═ { o (T) |1 ≦ T ≦ T }. Thus, the observation constraint can be modeled as the following equation:
problem modeling
Based on the above constraints, a network utility maximization framework can be adopted to model a maximization network utility problem (SAGIUM) in the space-ground integrated network into the following form
Where u (f) represents a network utility function, the utility function generally represents the "satisfaction" level of a task after a certain number of tasks, and in fact depends on the set of questions, the utility may be throughput, revenue, etc., by employing a suitable utility function, such as a continuously differentiable concave function for example: f. ofi(x)＝wiln (x) to achieve fair resource allocation for the task. The amount of data transferred by the task is considered here. Considered here are
And the data processing amount of the node i at the last T moment of the time slot of the feasible task flow is shown. It can be seen that the above problem is a Mixed Integer Linear Programming (MILP) problem, the algorithm complexity of which grows exponentially with increasing variables (exponential explosion)
A method based on original decomposition and Branch-and-Bound network Utility Maximization (PDBB) is proposed for the SAGIUM problem to solve. Observing the above constraints, there is no coupling relationship in networks of different time slots except for the processing constraint, but because of the existence of the stream conservation constraint, there is a coupling relationship in networks of different time slots. It was further found that if global optimization is needed, since the coupling relationship of different time slots can cause great complexity of solving the problem, since the objective function is separable, if the constraint does not exist, the problem can be converted into a maximization problem of each time slot, and finally solved through iteration. The problem of weak coupling relationships between such optimization variables often arises in optimization theory. The present invention contemplates using an original decomposition algorithm to solve this problem. By observing the stream conservation constraints, it can be seen that the coupling relationship between two consecutive time slots is primarily related to the arc flow of the processing arcs in the feasible data stream. Therefore, an auxiliary vector is introduced to decouple the coupling relationship between consecutive time slots
Where L represents a state vector of a processing resource, having the following properties
Introducing it into the conservation of flow constraint can be converted to the following form:
and converting the original constraint into a new constraint by introducing an auxiliary vector, and further converting the original problem into a new problem as follows:
this problem is equivalent to the original problem and can be resolved to each slot to solve separately.
An original decomposition algorithm is introduced to convert P1 into a subproblem related to a time slot t, and an optimization function q is definedt＝(lF(t)) and an auxiliary vector lF(T) wherein 1 < T < T. Definition of
The original problem can be converted into the following problem:
given lF(t) processing the resource state vector, the problem p4 can be solved
p3 needs to find the sum of lf (T) in all planning cycles, which can be obtained by solving the problem p4 for L, the change of the problem p4 due to the constraint can be decomposed into T independent sub-problems, and each independent sub-problem can be solved in parallel to obtain the feasible task planning vector f (T), the transmission planning vector u (T) and the observation planning vector o (T).
Meanwhile, the problem is still a mixed integer linear programming problem, and because of the special structure, the idea of branch and bound is adopted to solve the observation and transmission selection strategy of each time slot. Will transmit variable u (i)t，jt) Observation of variable o (i)t，jt) Relaxation is carried out so that 0 < u (i)t，jt)＜1，0＜o(it，jt) < 1, variable u (i) after relaxationt，jt) Can be expressed as the proportion of time between nodes at which there is a transmission opportunity, o (i)t，jt) Representing the proportion of time between nodes at which there is an observation opportunity.
The LP problem is defined as the relaxation problem of the P3 problem, and secondly, the LP problem is solved to obtain an upper bound of candidate solutions, which can also be set to be minus infinity. The stack is then initialized and the solved link is restored to a feasible link, the variable u (i)t，jt)＝1，o(it，jt) The link with 1 is set as a variable u (i) which is a non-feasible link according to the constraintt，jt)＝0，o(it，jt) And (5) continuously stacking the nodes in the setting process of the link of 0. And simultaneously continuously updating the upper and lower bounds and the optimal solution, and ending the process if the difference between the upper and lower bounds is less than the minimum parameter E and is more than 0. Otherwise, the node is popped, and a branch decision is performed, i.e., u (i) is selectedt，jt) Branch near 1, put it on stack. If so, the link u (i)t，jt) Set to 1 and the other branch to 0. ) Priority queue searching, etc. Considering DFS here, it is implemented by a stack.
The time slot problem P4 is solved by the algorithm, and then a problem target q (1) corresponding to P3 can be obtained, and q is defined★Is q (l)F(t)) an optimal solution. The goal of the problem p3 is to find the optimal L★Further find the optimal q★. Thus can beTo find the optimum L by using a sub-gradient algorithm★. Update by the following iterative manner
Where k is the iteration number, a ^ (k) is the forward iteration step size factor, g (1^ (k)) is the sub-gradient of vector l at point l (k), respectively [ ·]And ^ + is the mapping of l on the feasible domain created by the storage constraint. In this example, computing this mapping problem may be equivalent to solving the following quadratic programming problem p 5:
Claims (8)
1. a multidimensional resource management method under an air-space-ground integrated network is characterized by comprising the following steps:
constructing a capacity resource time-varying graph according to an emergency scene of the air-space-ground integrated network model;
giving task flow and initial definition of arc capacity on the basis of a capacity resource time-varying graph;
modeling a task scheduling problem of multi-dimensional resource management in an air-space-ground integrated network into a multi-constraint maximum flow problem based on a capacity resource time-varying graph according to the initial definition of task flow and arc capacity;
according to the weak coupling relation of problem constraint, a joint resource algorithm based on original decomposition and branch and bound is provided, the original problem is decomposed into parallel independent sub-problems, and the original high-complexity resource allocation problem is efficiently solved through a divide and conquer thought.
2. The method of claim 1, wherein a system planning period of the aerospace-ground integrated network model is divided into T periods, denoted as T ∈ Γ ═ {1, … T }, and a capability resource time-varying graph is constructed, and the capability resource time-varying graph is used as the capability resource time-varying graph
And (4) showing.
3. The method according to claim 1, wherein the arc traffic definition is given on the basis of a capacity resource time-varying graph
Arc capacity definition
Viable task flow definition
Feasible task data flow definition
4. The method according to claim 1, wherein the execution process of the task in the air-space-ground integrated network under the emergency scene is represented by a feasible task flow in a capacity resource time-varying graph, and the task scheduling problem of the multidimensional resource management in the air-space-ground integrated network is modeled as a multi-constraint maximum flow problem based on the capacity resource time-varying graph, specifically:
capacity constraints
The feasible task data flow can not exceed the arc capacity upper limit, namely can not exceed the maximum capacity resource provided by the node, and the feasible task data flow is modeled as the following inequality
Constraint of conservation of flow
Definition of
Representing the arc flow belonging to a processing arc in a feasible data stream, the flow conservation constraint is modeled as the following equation
Handling constraints
Definition BmThe maximum processing capacity of the relay node is represented in unit (bit), and the processing arc flow of each time slot is less than the maximum processing capacity Bm；
For the initial throughput at the start of a slot, the processing constraints are modeled as the following equation:
transmission constraints
Definitions of the incoming Boolean variable u (i)t,jt),u(it,jt) 1 indicates that a transmission arc is available, that is, in the t time slot, the node i and the node j transmit data; otherwise, u (i)t，jt) 0 means that a transmission arc is not available, and the transmission link is a bidirectional link; in addition to define
Representing all transmission arcs at the time T, and defining u ═ { u (T) |1 ≦ T } transmission arcs representing the whole system planning period; the transmission constraint is modeled as the following equations and inequalities:
observation constraints
The Boolean variable o (i) is defined in the same way as the transport constraintst，jt),(it，jt) 1 indicates that an observation arc is available, that is, an observation opportunity exists between the node i and the node j in the time slot t, and observation data are transmitted; otherwise, (i)t，jt) 0 means observation is not available, and similarly, the observation link is also a bidirectional link; in addition to define
All observation arcs representing time T, defining that o ═ { o (T) |1 ≦ T } represents the observation arcs of the whole system planning period; the observation constraint is modeled as the following equation:
problem modeling
Based on the constraints, a network utility maximization framework is adopted to model the maximization network utility problem SAGIUM in the air-space-ground integrated network into the form
Wherein U (f) represents a network utility function, and the utility function represents the 'satisfaction' level of a task after a certain number of tasks;
and the data processing amount of the node i at the last T moment of the time slot of the feasible task flow is shown.
5. The method according to claim 4, wherein a SAGIUM problem is solved by a maximum utility algorithm based on original decomposition and branch-and-bound networks; the problem is solved using the original decomposition algorithm: decoupling coupling relationships between successive time slots by introducing auxiliary vectors
Where L represents a state vector of a processing resource, having the following properties
It is introduced into the stream conservation constraint and converted into the following form:
6. the method for managing the multidimensional resources under the air-space-ground integrated network according to claim 5, wherein the original constraint is converted into a new constraint by introducing an auxiliary vector, and the original problem is further converted into a new problem as follows:
decomposing into each time slot to solve independently;
an original decomposition algorithm is introduced to convert P1 into a subproblem related to a time slot t, and an optimization function q is definedt＝(lF(t)) and an auxiliary vector lF(t) related to, wherein 1<t<T; definition of
The original problem is converted into the following problem:
given lF(t) processing the resource state vector to solve the problem p4
7. The method for managing multidimensional resources under the air-space-ground integrated network as claimed in claim 6, wherein p3 is required to find l in all planning cyclesFThe sum of (T) is obtained by solving a problem p4 for L, the problem p4 is decomposed into T independent sub-problems, and each independent sub-problem is solved in parallel to obtain a feasible task planning vector F (T), a transmission planning vector u (T) and an observation planning vector o (T);
the idea of branch and bound is adopted to solve the observation of each time slot and transmit a selection strategy; will transmit variable u (i)t,jt) Observation of variable o (i)t,jt) Relaxation is carried out so that 0<u(it,jt)<1,0<o(it,jt)<1, post relaxation variable u (i)t,jt) Expressed as the proportion of time between nodes at which there is a transmission opportunity, o (i)t,jt) Representing the proportion of time between nodes at which there is an observation opportunity;
defining the LP problem as the relaxation problem of the P3 problem, then solving the LP problem to obtain the upper bound of the candidate solution, which can also be set as minus infinity; the stack is then initialized and the solved link is restored to a feasible link, the variable u (i)t,jt)＝1,o(it,jt) The link with 1 is set as a variable u (i) which is a non-feasible link according to the constraintt,jt)＝0,o(it,jt) Continuously stacking the nodes in the setting process of the link of 0; all in oneContinuously updating the upper and lower bounds and the optimal solution, and if the difference between the upper and lower bounds is less than the minimum parameter E>0, the process ends, otherwise, the node pops up and performs a branch decision, i.e., selects u (i)t,jt) Branching near 1 and stacking the branch; if so, the link u (i)t,jt) Set to 1, the other branch to 0;
solving the time slot problem P4 to obtain a problem target q (l) corresponding to P3, defining q★Is q (l)F(t)), the goal of the problem p3 is to find the optimal L★Further find the optimal q★(ii) a Therefore, the optimal L is found by adopting a sub-gradient algorithm★(ii) a Update by the following iterative manner
Where k is the number of iterations, a ^ ((k)) is the forward iteration step size factor,
respectively, the sub-gradients of the vector l at the point l (k) [. cndot]And ^ + is the mapping of l on the feasible domain created by the storage constraint.
8. A multidimensional resource management system under an air-space-ground integrated network is characterized by comprising:
the capacity resource time-varying graph constructing module is used for constructing a capacity resource time-varying graph according to an emergency scene of the air-space-ground integrated network model;
the task flow and arc capacity initial definition module is used for giving task flow and arc capacity initial definitions on the basis of a capacity resource time-varying graph;
the task scheduling problem modeling module is used for modeling a task scheduling problem of multi-dimensional resource management in the air-space-ground integrated network into a multi-constraint maximum flow problem based on a capacity resource time-varying graph;
the resource allocation solving module is used for providing a joint resource algorithm based on original decomposition and branch and bound according to the weak coupling relation of problem constraint, decomposing the original problem into parallel independent subproblems, and efficiently solving the original high-complexity resource allocation problem through a divide and conquer idea.
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| CN114500296A (en) * | 2022-01-25 | 2022-05-13 | 西安电子科技大学 | Communication, storage and computing resource unified characterization method based on function expansion diagram |
| CN115514652A (en) * | 2022-09-19 | 2022-12-23 | 北京航空航天大学 | Service function chain deployment method, device and storage medium |
| CN116074199A (en) * | 2022-12-28 | 2023-05-05 | 西安电子科技大学 | Fine-grained on-demand service method for 6G space-sky-earth scene |
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