CN110928678B - Block chain system resource allocation method based on mobile edge calculation - Google Patents

Block chain system resource allocation method based on mobile edge calculation Download PDF

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CN110928678B
CN110928678B CN201910972698.6A CN201910972698A CN110928678B CN 110928678 B CN110928678 B CN 110928678B CN 201910972698 A CN201910972698 A CN 201910972698A CN 110928678 B CN110928678 B CN 110928678B
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block chain
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CN110928678A (en
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李立欣
吴隆喆
梁微
李旭
王大伟
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Northwestern Polytechnical University
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Abstract

The invention discloses a block chain system resource allocation method based on mobile edge calculation, which comprises the following steps: step 1, constructing a block chain system model based on MEC; step two, establishing an energy utility function in the block chain system based on the MEC
Figure DDA0002232611840000011
Step three, maximizing energy efficiency function in block chain system
Figure DDA0002232611840000012
The problem of the energy consumption is high in the block chain system based on MEC now is solved.

Description

Block chain system resource allocation method based on mobile edge calculation
[ technical field ] A method for producing a semiconductor device
The invention belongs to the technical field of wireless communication, and particularly relates to a block chain system resource allocation method based on mobile edge calculation.
[ background of the invention ]
The blockchain system is a promising distributed data management framework and has been applied to many distributed system scenarios. However, the "mining" process in a blockchain system typically consumes a large amount of computing resources, and it is obvious that the limited computing power and battery life of a common mobile device are difficult to meet. To address the above-mentioned problems, it is an efficient method to transfer the computationally intensive tasks of miners in a blockchain system to a Mobile Edge Computing (MEC) server. Compared with the method of unloading the computing task to the cloud computing center, the method has the advantages that the computing task is transmitted to the MEC server, a core network and a data center are not needed, local service localization service can be achieved, energy consumption is reduced, the low-delay requirement of the service is met, and the like.
To solve the problem of insufficient computation and communication resources in the mobile blockchain system and to facilitate the application of blockchain techniques in future wireless mobile communication networks, a great deal of work related to the research on resource allocation problems in the mobile blockchain system has been completed. These tasks effectively solve or alleviate the problem of insufficient computing and communication resources in the above-mentioned blockchain system to some extent under different computing task offloading or caching modes. However, for binary computation task offload mode in a moving blockchain system, the computation task is usually not partitioned. It is therefore clear that multi-user MECs with binary offload mode are more complex communication scenarios, which typically involve non-convex combinatorial optimization problems, which are not solved by the current existing related work, and which do not effectively solve the energy consumption problem in MEC-based blockchain systems.
[ summary of the invention ]
The invention aims to provide a method for allocating resources of a block chain system based on mobile edge calculation, which aims to solve the problem of high energy consumption in the conventional block chain system based on MEC.
The invention adopts the following technical scheme: a method for allocating system resources of a block chain based on mobile edge calculation comprises the following steps:
step 1, constructing a block chain system model based on MEC:
the blockchain system includes N users acting as miners, N being 1, 2, …, N;
miners solve the computationally intensive PoW problem to obtain hash values linking previous blocks to current blocks,
the computational task for the nth miner is represented as:
Figure BDA0002232611820000021
wherein D isnSize of input data for a task, CnAre the computing resources required to complete a computing task,
Figure BDA0002232611820000022
representing a task maximum delay threshold;
the block chain system also comprises an MEC server, and the MEC server is connected with the N user data;
step two, establishing an energy utility function in the block chain system based on the MEC
Figure BDA0002232611820000023
Modeling the calculation task unloading distribution problem of each miner in the block chain system through a binary calculation unloading method, and based on an energy utility function in the MEC block chain system
Figure BDA0002232611820000024
Calculation of miner's Total energy efficiency eta from MECMECAnd locally calculating the energy efficiency eta of the minersLocalTwo parts are formed;
step three, maximizing energy efficiency function in block chain system
Figure BDA0002232611820000025
The problem of binary computation offload in a blockchain system is formulated to maximize the energy efficiency function in the blockchain system under consideration of energy consumption
Figure BDA0002232611820000026
The complex large-scale mixed integer linear programming problem of (1), called MINLP problem; and solving the MINLP problem in a distributed parallel mode by utilizing an algorithm framework based on a Benders decomposition method.
Further, the system energy utility function is expressed as:
Figure BDA0002232611820000027
wherein eta isLocalAnd ηMECCalculating the energy efficiency of the miners separately for the local and MEC's total energy efficiency, δnAs a decision variable for deciding the nth miner to perform local calculation or MEC calculation,
Figure BDA0002232611820000031
indicating the time at which the computational task of the nth blockchain miners was completed locally,
Figure BDA0002232611820000032
representing the nth miner's local processing power consumption,
Figure BDA0002232611820000033
represents the power consumption, R, of the nth MEC calculated blockchain minersnIs the throughput of the nth miner;
defining two emission powers p for minersnConcave function of
Figure BDA0002232611820000034
And
Figure BDA0002232611820000035
the system energy utility function is rewritten as:
Figure BDA0002232611820000036
linearization
Figure BDA0002232611820000037
Is composed of
Figure BDA0002232611820000038
And maintaining a concave function
Figure BDA0002232611820000039
The approximated system energy utility function is expressed as:
Figure BDA00022326118200000310
further, the fixed problem P1 that maximizes the system energy utility function is expressed as:
Figure BDA00022326118200000311
wherein the content of the first and second substances,
Figure BDA00022326118200000312
is the nth MEC to calculate the maximum transmit power, I, of the minersnIndicating the interference value of the nth MEC computed user,
Figure BDA00022326118200000313
is a preset interference threshold, P1 is the MINLP problem;
defining sub-problem P2 as a binary variable in fixed problem P1 to obtain the optimal continuous variable value, sub-problem P2 is expressed as:
Figure BDA00022326118200000314
Figure BDA0002232611820000041
wherein the content of the first and second substances,
Figure BDA0002232611820000042
is a constraint on the value of a binary variable,
Figure BDA0002232611820000043
is a bivariable in a constraint formula (9), and the constraint formula (9) is a fixed binary variable value constraint;
when solving the main problem P3 mixed integer programming problem, fixing continuous variables and updating a loop index to l + 1;
the main question P3 is expressed as:
Figure BDA0002232611820000044
wherein the constraint formula (12) is a clipping constraint in the Benders decomposition method, αdownIs the lower limit of the introduced scalar variable α; in each iteration, a new Benders cut will be generated and added to the main problem P3, the previous Benders cut also remaining in the constraint, and after P3 is solved, the optimal values of δ and α in the iteration are stored to solve the sub problem P2 again;
the subproblem P2 is equivalently written as a parametric subtraction using the dichotomy:
Figure BDA0002232611820000045
restating the subproblem P2 as:
Figure BDA0002232611820000046
in each iteration, the non-negative variable rj updates its value until the optimal value r is obtained*；
Introducing an auxiliary variable q as a global replica according to the ADMM principle, then adding a new equality constraint to the problem of equation (14);
therefore, restating the problem of equation (14) as problem P4:
Figure BDA0002232611820000051
wherein h isn,iIs the channel gain between the nth MEC calculated miner and the ith MEC calculated miner, the augmented lagrange function of equation (15) is expressed as:
Figure BDA0002232611820000052
wherein, munIs bivariate, rho is an augmented Lagrange parameter, and rho is more than 0; the ADMM solver of problem P4 consists of iterations including a P-minimize update, a q-minimize update and a bivariate μ update, and the MEC server updates the global auxiliary variable q as a central controllernBlock chain miners update local variable pn；
The main problem P3 is converted into the equivalent pure integer programming problem form:
Figure BDA0002232611820000053
obviously, the main problem P3 is a knapsack problem, which is expressed as:
Figure BDA0002232611820000054
Figure BDA0002232611820000061
wherein ξTIs a vector with non-negative elements, W is a non-negative scalar; to enumerate all possible deltasnEnumerating solutions by solving the knapsack problem P5 by using a branch and bound method; the branch-and-bound algorithm, when executed in detail, branches the problem into sub-problems and bounds these sub-problems to obtain an optimal solution.
The invention has the beneficial effects that: the method for allocating the resources of the block chain system based on the mobile edge calculation maximizes an energy efficiency function in the system under the condition of considering energy consumption and delay, and realizes energy consumption saving and calculation time saving.
[ description of the drawings ]
FIG. 1 is a diagram of a model created according to a scene for a method for allocating resources of a block chain system based on mobile edge calculation according to the present invention;
FIG. 2 is a flowchart of an algorithm framework of a method for allocating resources of a blockchain system based on moving edge calculation according to the present invention;
FIG. 3 is a diagram illustrating the effect of maximum transmit power on the system utility function and total power consumption in an embodiment of a method for allocating resources of a blockchain system based on mobile edge computation according to the present invention;
FIG. 4 is a graph of the relationship between the maximum transmission power of the MEC calculated miner rate and the number of different miners in the embodiment of the method for allocating resources of a block chain system based on the mobile edge calculation;
fig. 5 is a graph showing the relationship between the calculation time and the maximum transmission power for different numbers of miners in the method for allocating resources of a blockchain system based on moving edge calculation according to the present invention.
[ detailed description ] embodiments
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a block chain system resource allocation method based on mobile edge calculation, and for a block chain multi-user communication system assisted by an MEC server, the method comprises the steps of carrying out unloading processing on a calculation intensive task in a block chain miner mining process according to a binary unloading mode, and unloading a calculation task to the MEC server or directly carrying out local calculation to relieve the problem of serious shortage of calculation resources in the system. While the problem of binary computation offload in a system is formulated to maximize the energy efficiency function in a blockchain system under consideration of energy consumption
Figure BDA0002232611820000072
And solving the problem of complicated MINLP by using an algorithm framework based on a Benders decomposition method in a distributed parallel mode. The distributed solution can be provided and the optimal problem solution can be obtained, so that the energy consumption of the system is effectively reduced and the calculation time is saved.
The system model studied by the present invention is shown in fig. 1, and the blockchain system is composed of N users acting as miners. To append a new block of data to the current block chain, a block chain miner is required to solve the computationally intensive PoW problem to obtain hash values linking previous blocks to the current block, which is defined as a "mining" process. The MEC server may provide computing services to all blockchain miners within the system to solve the mining task, and furthermore, each miner has less computing power to perform local computing services.
Each miner in the system may decide whether to perform or offload a computing task in the miner's local deviceIs executed in the MEC, the decision being made by a decision variable deltanAnd (5) representing and determining. If the nth miners decide to perform the task locally, δn0; if the nth miner decides to offload the computation task to the MEC server for resolution, δn1. The MEC compute node can only serve a limited number of blockchain miners with a certain capacity, and each miner can only select one policy for the compute task.
The energy efficiency function of the moving blockchain system consists of two parts, namely the total energy efficiency of miners and the energy efficiency of miners calculated locally for the MEC, so that all equipment in the network can participate in realizing the optimal overall energy efficiency. Thus, the system energy utility function can be expressed as:
Figure BDA0002232611820000071
wherein etaLocalAnd ηMECThe energy efficiency of the user is calculated separately for the local and MEC total energy efficiency of the user,
Figure BDA0002232611820000081
is the nth blockchain mineworker local processing power consumption,
Figure BDA0002232611820000082
it is the nth MEC that calculates the power consumption of the miners,
Figure BDA0002232611820000083
is the time, δ, at which the computational task of the nth miner is done locallynAs a decision variable for the nth miner to perform local or MEC calculations, DnIs the size of the input data of the nth miner task, RnIs the throughput of the nth miner.
To facilitate the subsequent solution process, we define two transmit powers p for the miners nnConcave function of
Figure BDA0002232611820000084
And
Figure BDA0002232611820000085
the system energy efficiency function may be rewritten as:
Figure BDA0002232611820000086
to obtain a concave bound approximation of the system energy utility function, we need to linearize
Figure BDA0002232611820000087
And maintaining a concave function
Figure BDA0002232611820000088
The approximated system energy utility function is expressed as:
Figure BDA0002232611820000089
our goal is to maximize the energy efficiency function of the proposed blockchain system based on moving edge computation. This problem is expressed as:
Figure BDA00022326118200000810
wherein
Figure BDA00022326118200000811
Is the nth MEC to calculate the maximum transmit power, I, of the minersnIndicating the interference value of the nth MEC computed user,
Figure BDA00022326118200000812
is a preset interference threshold, and a decision variable deltanIs a binary variable in the problem. It is clear that the problem P1 we formulated is the MINLP problem. We will use an algorithmic framework based on Benders' decomposition to solve the problem P1 in a distributed parallel manner.
The technical scheme of the algorithm framework based on the Benders decomposition method adopted for solving the MINLP problem of the maximized system energy efficiency function is as follows:
the technical scheme diagram of the algorithm framework adopted by the invention is shown in fig. 2, and the Benders decomposition method decomposes the MINLP problem into a main problem and a sub-problem by a plane cutting method. The main problem is a mixed integer programming problem, which uses a branch-and-bound algorithm to solve the complexity of processing; the subproblem is a fractional programming problem, and a dichotomy-ADMM combined algorithm is proposed to provide a distributed solution. The detailed solving process is as follows:
first, we define the sub-problem as a binary variable in the fixed problem P1 to obtain the optimal continuous variable value, so the sub-problem can be expressed as:
Figure BDA0002232611820000091
wherein
Figure BDA0002232611820000092
Is a constraint on the value of a binary variable,
Figure BDA0002232611820000093
is a bivariate in the constraint (9), and the constraint (9) is a fixed binary variable value constraint. After the sub-problem P2, the bivariable value of the fixed integer variable will be obtained, then the upper and lower limits are generated from the value of the previous variable as the stopping criteria for the iteration, and the difference between the upper and lower limits is obtained. In the process of iteration, when the difference between the upper limit and the lower limit is below a certain preset threshold value, the iteration is stopped, and the result of the I-th iteration is the optimal solution. Otherwise, the iteration will continue.
In solving the main problem mixed integer programming problem, we fix the continuous variable and update the loop index to l ═ l + 1. The main question is represented as:
Figure BDA0002232611820000094
Figure BDA0002232611820000101
wherein
Figure BDA0002232611820000102
Is the transmit power of the nth blockchain miner at a cyclic index of i, the constraint equation (12) is the clipping constraint in the Benders decomposition method, αdownIs the lower bound of the introduced scalar variable alpha. In each iteration, a new Benders cut will be generated and added to the main problem P3, with the previous Benders cut also remaining in the constraint. After solving P3, the optimal values of δ and α in the iteration are stored to solve the sub-problem again.
We equivalently write the subproblem P2 as a parametric subtraction form using the dichotomy:
Figure BDA0002232611820000103
restating the subproblem P2 as:
Figure BDA0002232611820000104
in each iteration, the non-negative variable rj updates its value until the optimal value r is obtained.
According to the ADMM principle, we introduce the auxiliary variable q as a global replica, and add a new equality constraint to the problem (14). Therefore, we restate the equivalent of problem (14) as:
Figure BDA0002232611820000105
wherein h isn,iIs the channel gain between the nth MEC calculated miner and the ith MEC calculated miner. The augmented lagrange function of problem (15) can be expressed as:
Figure BDA0002232611820000111
wherein munIs a bivariate, ρ is an augmented Lagrangian parameter, and ρ > 0. The ADMM solver of problem P4 consists of iterations including a P-minimize update, a q-minimize update and a bivariate μ update, and the MEC server updates the global auxiliary variable q as a central controllernBlock chain miners update local variable pn。
The main problem P3 is converted into the equivalent pure integer programming problem form:
Figure BDA0002232611820000112
obviously, P3 is a knapsack problem, which can be expressed as:
Figure BDA0002232611820000113
in which ξTIs a vector with non-negative elements, and W is a non-negative scalar. To enumerate all possible deltasnWe enumerate solutions using branch-and-bound to solve the knapsack problem P5. The branch-and-bound algorithm, when executed in detail, branches the problem into sub-problems and bounds these sub-problems to obtain an optimal solution.
From the above description, the calculation unloading problem of blockchain miners in a blockchain system based on moving edge calculation is formulated as MINLP problem that maximizes the energy efficiency function under consideration of the system energy consumption.
Examples
The diagrams provided in the following examples and the setting of specific parameter values in the models are mainly for explaining the basic idea of the present invention and performing simulation verification on the present invention, and can be appropriately adjusted according to the actual scene and requirements in the specific application environment.
The invention considers the blocks in the block chain system based on the moving edge calculationThe computational offloading problem for chain miners, as shown in fig. 1, we assume that block chain miners are evenly distributed in a single cell with a radius of 200 m. Setting power spectral density of noise to N0The total bandwidth available for the blockchain system is set to 100MHz at 170 dbm/Hz. Interference threshold setting for the nth MEC calculated miners
Figure BDA0002232611820000121
Initial lower bound alpha of Benders decompositiondownSet to-25 and the stop criterion in the algorithm is set to less than 10-7. In [1,5 ]]Randomly selecting equipment parameter M and task data length DnIn [2,12 ]]Is randomly selected. In [2,12 ]]In randomly selecting the maximum processing time Tn. Further, the capacity of the MEC node W is set to 150.
Fig. 3 shows the effect of maximum transmit power on the system utility function and total power consumption. As can be seen from fig. 3, when the maximum transmission power increases within a certain range, the optimal utility function increases and then remains almost constant. Since the utility function is adversely affected if the maximum transmit power is increased beyond a certain range. Meanwhile, the results of fig. 3 indicate that the total power consumption increases rapidly with the increase of the maximum transmission power, because the local power consumption will dominate the total power consumption after the utility function is saturated.
Furthermore, relaxation algorithms are a common approach to solving MINLP problems. The principle is to amplify the binary variable to a continuous variable between 0 and 1 and then solve the continuous problem of relaxation and obtain a continuous solution. And finally, iterating the integer variables to the optimal feasible solution. As can be seen from fig. 3, the proposed algorithm framework exhibits superior performance in terms of energy saving over the relaxation algorithm and the original render decomposition-based algorithm, since the dichotomy has the advantage of saving memory and computational resources in the block chain system.
Fig. 4 shows the relationship between the MEC calculated miner rate and the maximum transmit power for different numbers of miners. As can be seen from fig. 4, the MEC calculated miner rate increases as the total number of users N increases, but when the maximum transmission power increases to a certain value, the growth rate gradually decreases and stops increasing. As the total number N of users increases, an energy efficient utility function with higher throughput and less power consumption will be obtained. However, as the maximum transmit power increases, the capacity constraint and power consumption also increase. Thus, as the maximum transmit power continues to increase, the MEC calculated miner rate will stop increasing.
Fig. 5 shows the relationship between the calculation time and the maximum transmission power for different numbers of miners. The results show that the proposed algorithm is stable, since the computation time of the algorithm is hardly affected by the maximum transmission power variation, the computation time being stable for a certain time interval. Furthermore, as can be seen from the simulation results, as the number of blockchain miners increases, the computation time will increase rapidly.
The invention relates to a block chain system resource allocation method based on mobile edge calculation, which effectively solves the problem of insufficient calculation resources in the block chain miner mining process. The unloading processing is carried out on the calculation intensive tasks in the block chain miner mining process according to a binary unloading mode, and the calculation tasks are unloaded to an MEC server or are directly calculated locally to relieve the problem of serious shortage of calculation resources in the system.
In the invention, a calculation unloading problem in a mobile blockchain system is customized into an MINLP problem, and the energy efficiency function of the system is maximized under the condition of considering the energy consumption of the system
Figure BDA0002232611820000131
Wherein, we propose an algorithm framework based on Benders decomposition method to solve the MINLP problem. The distributed solution can be provided and the optimal problem solution can be obtained, so that the energy consumption of the system is effectively reduced and the calculation time is saved.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (1)

1. A method for allocating resources of a blockchain system based on mobile edge calculation is characterized by comprising the following steps:
step 1, constructing a block chain system model based on MEC:
the blockchain system includes N users acting as miners, N being 1, 2, …, N;
miners solve the computationally intensive PoW problem to obtain hash values linking previous blocks to current blocks,
the computational task for the nth miner is represented as:
Figure FDA0003450333000000011
wherein D isnSize of input data for a task, CnAre the computing resources required to complete a computing task,
Figure FDA0003450333000000012
representing a task maximum delay threshold;
the blockchain system further comprises an MEC server, wherein the MEC server is connected with the N user data;
step two, establishing an approximate energy utility function in a block chain system based on MEC
Figure FDA0003450333000000019
Modeling the calculation task unloading distribution problem of each miner in the block chain system through a binary calculation unloading method, and based on the approximate energy utility function in the MEC block chain system
Figure FDA00034503330000000110
Calculation of miner's Total energy efficiency eta from MECMECAnd locally calculating the energy efficiency eta of the minersLocalTwo parts are formed;
the system energy utility function is expressed as:
Figure FDA0003450333000000013
wherein eta isLocalAnd ηMECCalculating the energy efficiency of the miners separately for the local and MEC's total energy efficiency, δnAs a decision variable for deciding the nth miner to perform local calculation or MEC calculation,
Figure FDA0003450333000000014
indicating the time at which the computational task of the nth blockchain miners was completed locally,
Figure FDA0003450333000000015
representing the nth miner's local processing power consumption,
Figure FDA0003450333000000016
represents the power consumption, R, of the nth MEC calculated blockchain minersnIs the throughput of the nth miner;
defining two emission powers p for minersnConcave function of
Figure FDA0003450333000000017
And
Figure FDA0003450333000000018
the system energy utility function is rewritten as:
Figure FDA0003450333000000021
linearization
Figure FDA0003450333000000022
Is composed of
Figure FDA0003450333000000023
And maintaining a concave function
Figure FDA0003450333000000024
The approximated system energy utility function is expressed as:
Figure FDA0003450333000000025
step three, maximizing approximate energy utility function in block chain system
Figure FDA0003450333000000026
The problem of binary computation offload in a blockchain system is formulated to maximize the approximate energy utility function in the blockchain system under consideration of energy consumption
Figure FDA0003450333000000027
The complex large-scale mixed integer linear programming problem of (1), called MINLP problem; solving the MINLP problem in a distributed parallel mode by utilizing an algorithm framework based on a Benders decomposition method;
the fixed problem P1 of the energy utility function that maximizes the system approximation is expressed as:
P1：
Figure FDA0003450333000000028
Figure FDA0003450333000000029
Figure FDA00034503330000000210
Figure FDA00034503330000000211
wherein the content of the first and second substances,
Figure FDA00034503330000000212
is the nth MEC to calculate the maximum transmit power, I, of the minersnIndicating the interference value of the nth MEC computed user,
Figure FDA00034503330000000213
is a preset interference threshold, P1 is the MINLP problem; defining sub-problem P2 as a binary variable in fixed problem P1 to obtain the optimal continuous variable value, sub-problem P2 is expressed as:
P2：
Figure FDA00034503330000000214
Figure FDA00034503330000000215
Figure FDA00034503330000000216
Figure FDA00034503330000000217
wherein the content of the first and second substances,
Figure FDA0003450333000000031
is a constraint on the value of a binary variable,
Figure FDA0003450333000000032
is a bivariable in a constraint formula (9), and the constraint formula (9) is a fixed binary variable value constraint;
when solving the main problem P3 mixed integer programming problem, fixing continuous variables and updating a loop index to l + 1;
the main question P3 is expressed as:
P3：
Figure FDA0003450333000000033
Figure FDA0003450333000000034
Figure FDA0003450333000000035
α≥αdow (12)，
wherein the constraint formula (12) is a clipping constraint in the Benders decomposition method, αdownIs the lower limit of the introduced scalar variable α; in each iteration, a new Benders cut will be generated and added to the main problem P3, the previous Benders cut also remaining in the constraint, and after P3 is solved, the optimal values of δ and α in the iteration are stored to solve the sub problem P2 again;
the subproblem P2 is equivalently written as a parametric subtraction using the dichotomy:
Figure FDA0003450333000000036
restating the subproblem P2 as:
Figure FDA0003450333000000037
Figure FDA0003450333000000038
Figure FDA0003450333000000039
Figure FDA00034503330000000310
in each iteration, the non-negative variable rjIts value is updated until the optimum value r is obtained*；
Introducing an auxiliary variable q as a global replica according to the ADMM principle, then adding a new equality constraint to the problem of equation (14);
therefore, restating the problem of equation (14) as problem P4:
P4：
Figure FDA0003450333000000041
Figure FDA0003450333000000042
Figure FDA0003450333000000043
Figure FDA0003450333000000044
Figure FDA0003450333000000045
wherein h isn,iIs the channel gain between the nth MEC calculated miner and the ith MEC calculated miner, the augmented lagrange function of equation (15) is expressed as:
Figure FDA0003450333000000046
wherein the content of the first and second substances,μnis bivariate, rho is an augmented Lagrange parameter, and rho is more than 0; the ADMM solver of problem P4 consists of iterations including a P-minimize update, a q-minimize update and a bivariate μ update, and the MEC server updates the global auxiliary variable q as a central controllernBlock chain miners update local variable pn；
The main problem P3 is converted into the equivalent pure integer programming problem form:
Figure FDA0003450333000000047
the main question P3 is a knapsack question, which is expressed as:
P5：
Figure FDA0003450333000000048
s.t ξTδ≤W (21)，
Figure FDA0003450333000000049
wherein ξTIs a vector with non-negative elements, W is a non-negative scalar; to enumerate all possible deltasnEnumerating solutions by solving the knapsack problem P5 by using a branch and bound method; the branch-and-bound algorithm, when executed in detail, branches the problem into sub-problems and bounds these sub-problems to obtain an optimal solution.
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