CN113157338B - Benefit maximization method for safety task unloading in edge cloud environment - Google Patents

Benefit maximization method for safety task unloading in edge cloud environment Download PDF

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CN113157338B
CN113157338B CN202110437136.9A CN202110437136A CN113157338B CN 113157338 B CN113157338 B CN 113157338B CN 202110437136 A CN202110437136 A CN 202110437136A CN 113157338 B CN113157338 B CN 113157338B
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task
service
security
execution
cloud
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CN113157338A (en
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胡海洋
司先晨
李忠金
陈振辉
李前辉
潘健
魏泽丰
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Hangzhou Dianzi University
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00Arrangements for program control, e.g. control units
    • G06F9/06Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/44Arrangements for executing specific programs
    • G06F9/445Program loading or initiating
    • G06F9/44594Unloading
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60Protecting data
    • G06F21/64Protecting data integrity, e.g. using checksums, certificates or signatures
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06NCOMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00Computing arrangements based on biological models
    • G06N3/004Artificial life, i.e. computing arrangements simulating life
    • G06N3/006Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06NCOMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00Computing arrangements based on biological models
    • G06N3/12Computing arrangements based on biological models using genetic models
    • G06N3/126Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00Reducing energy consumption in communication networks
    • Y02D30/70Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a benefit maximization method for safe task unloading in an edge cloud environment. The full service comprises confidentiality service and integrity service, the confidentiality service and the integrity service are operated, a calculation formula of a safety grade is obtained according to the operation time of the confidentiality service and the integrity service, and the grade of using the safety service is determined according to joint probability risks under the two services, so that the safety of data can be ensured by using the safety service. And comprehensively considering the safety requirement of the task and the deadline of the task, and formulating a maximum benefit (PM) problem. The method adopts a genetic algorithm, considers the execution positions and the execution sequence of tasks, and designs cross and mutation operations to realize the maximization of the total benefit in the edge cloud computing environment.

Description

Benefit maximization method for safety task unloading in edge cloud environment
Technical Field
The invention relates to a benefit maximization method for task unloading, in particular to a benefit maximization method for safe task unloading in an edge cloud environment.
Background
The development of the internet and wireless communication technology has made people communicate with each other very conveniently. In recent years, emerging 5G mobile networks offer higher network bandwidth, and mobile devices and applications are rapidly growing and gaining wide popularity. Various mobile services and applications are continually emerging driven by wireless communication technologies and high-performance mobile devices. In particular, as artificial intelligence technology has been developed, more and more artificial intelligence applications have been developed and applied. However, such artificial intelligence applications are typically computationally intensive applications, and running all applications on one mobile device can result in unacceptable execution time and energy consumption.
Mobile edge computing sinks computation, storage, and network resources to the network edge. Thus, the mobile device can offload computationally intensive artificial intelligence applications to the near-end edge node, reducing its battery consumption and task completion time. In a real scene, an edge node only deploys a small-scale physical server, but simultaneously serves a large number of mobile devices. Fortunately, the advent of edge cloud computing architectures also allowed edge nodes to offload compute-intensive tasks to remote clouds over backhaul networks. In this case, the edge node and the remote cloud will collectively handle challenging artificial intelligence applications faced by resource-limited mobile devices.
However, offloading of tasks from the edge nodes to the remote cloud can result in longer data transfer times, causing significant delays. In addition, running a mobile application on a nearby edge node or remote cloud may face security issues. Because both data and applications are sources of security threats, they may be attacked by malicious cloud users or external attackers. Although a great deal of research has been conducted on data and network security in cloud computing and mobile edge computing, deploying the necessary security protection mechanisms in an edge cloud environment is also a significant challenge.
For the task offloading problem in the mobile edge calculation, energy consumption optimization and delay optimization have been widely studied. However, the above work has focused on energy and latency issues, and has not taken into account data security issues. The use of security services to protect private data has been widely adopted in cloud computing and mobile edge computing. The related work of data security considers cost, time and energy consumption optimization from the perspective of cloud users and mobile users, however in the edge cloud environment, the edge nodes are mainly concerned about benefits.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a benefit maximization method for unloading a safety task in an edge cloud environment from the perspective of an edge node.
The general idea of the inventive method is:
the safety service comprises confidentiality service and integrity service, the confidentiality service and the integrity service are operated, a calculation formula of a safety grade is obtained according to the operation time of the confidentiality service and the integrity service, and the grade of using the safety service is determined according to joint probability risks under the two services, so that the safety of data can be ensured by using the safety service. And comprehensively considering the safety requirement of the task and the deadline of the task, and formulating a maximum benefit (PM) problem. The method adopts a genetic algorithm, considers the execution positions and the execution sequence of tasks, and designs cross and mutation operations to realize the maximization of the total benefit in the edge cloud computing environment.
The method comprises the following specific steps
And (1) constructing a security model to ensure that the used security service can ensure the security of data.
And (2) formulating a PM problem of safe task unloading, and providing a calculation formula of edge node benefit at a time interval tau in consideration of task safety, task deadline limit and far-end cloud cost.
And (3) initializing a population, and respectively generating m schemes of the execution positions and the execution sequence of the mission plan, namely m individuals in the population.
And (4) performing crossing and mutation operations on the m individuals in the population to generate different schemes for solving the PM problem. And continuously iterating to generate a final task unloading scheme.
It is a further object of the present invention to provide a computer-readable storage medium having stored thereon a computer program which, when executed in a computer, causes the computer to perform the above-mentioned method.
It is a further object of the present invention to provide a computing device comprising a memory having stored therein executable code and a processor that, when executing the executable code, implements the method described above.
The invention has the beneficial effects that:
the invention introduces a security model to ensure the security of data, then combines security protection with task unloading, and provides a security task unloading method of edge nodes based on a genetic algorithm to realize the maximization of total profit in an edge cloud computing environment.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic cross-operation of the actuation position;
FIG. 3 is a schematic diagram of the interleaving operation of the execution sequence;
FIG. 4 is a schematic diagram illustrating a variation operation of the execution positions;
FIG. 5 is a schematic diagram illustrating a variation of the execution sequence;
Detailed Description
The present invention is further analyzed with reference to the following specific examples.
The benefit maximization method for task safety unloading in the edge cloud environment provided by the invention is specifically implemented as the following steps in a figure 1:
step S1 builds a security model, and the security services include confidentiality services and integrity services.
Step S1-1 runs all confidentiality services and integrity services to get their execution time, and assumes that the longer the execution time of the running service is, the higher the security level, and accordingly, the security level of the confidentiality service is calculated as:
Figure BDA0003033610770000031
wherein
Figure BDA0003033610770000032
The execution time for the kth confidentiality service;
Figure BDA0003033610770000033
a security level for a kth confidentiality service; q1 is an artificially defined confidentiality service execution time reference, which may be 0.85.
The security level of the integrity service is calculated as:
Figure BDA0003033610770000034
wherein
Figure BDA0003033610770000035
Representing an execution time of a kth integrity service;
Figure BDA0003033610770000036
represents a security level of a kth integrity service; q2 is a human defined integrity service execution time reference, which may be 0.13.
The execution time of step S1-2 is proportional to the data size, and can result in:
Figure BDA0003033610770000037
wherein
Figure BDA0003033610770000038
Represents the execution time of the security service S under the single CPU for the data of 1 MB; d is the data size;
Figure BDA0003033610770000039
representing the execution time of the s-service; n represents the number of CPUs; cd denotes confidentiality service; ig represents an integrity service;
step S1-3 assumes that the external attack times obey Poisson distribution, then the security level is added as
Figure BDA00030336107700000310
The risk probability of the task of the security service of (1) is an exponential distribution as follows:
Figure BDA00030336107700000311
wherein sd s Representing the security requirements of the task; pi s To representRisk factor of security service s;
Figure BDA00030336107700000312
represents the security level of the kth security service s;
the joint risk probability under both security services is therefore:
Figure BDA00030336107700000313
step S1-4, in order to ensure the safety of the task submitted by the mobile equipment, the safety level of the safety service S meeting the task requirement is greater than or equal to sd s
Figure BDA0003033610770000041
sd s Maximum value of security requirements for cloud and edge nodes for security service s
sd s =max{sd s (edge), sds (cloud) }, s ∈ { cd, ig } formula (7)
Wherein sd s (edge) represents security requirements on the edge node; sd s (cloud) represents security requirements on the cloud
Figure BDA0003033610770000042
In this case, it is preferable that the air conditioner,
Figure BDA0003033610770000043
Figure BDA0003033610770000044
indicates a usage grade of
Figure BDA0003033610770000045
Can ensure the safety of data
Step S2 formulates benefit maximization problem for security task offloading
Step S2-1 setting x i As task t i Of the execution position, x i 1 denotes task t i Is offloaded to a remote cloud and executed, x i 0 denotes task t i At the edge node (i.e. locally) is performed, i.e.:
Figure BDA0003033610770000046
s (τ) {1,2, …, n (τ) } denotes a set of index numbers of tasks, and n (τ) is the number of tasks.
Step S2-2 uses X (τ) ═ X 1 ,…,x i ,…,x n(τ) Denotes the execution position of the task over the time interval τ. Using Y (τ) ═ Y 1 ,…,y i ,…,y n(τ) Denotes the execution order of tasks at time interval τ, where y i ≠y j
Figure BDA0003033610770000047
Any two tasks cannot have the same execution order.
Step S2-3 task t i Benefits of (1)
Figure BDA0003033610770000048
The calculation is as follows:
calculating the benefit of the task on the edge node:
Figure BDA0003033610770000049
Figure BDA00030336107700000410
indicating the actual value of the end time of the ith task,
Figure BDA00030336107700000411
indicating the expected expiration date, η, for the ith task i Indicating completion of task t i The benefits obtained.
This indicates that if a task cannot be completed by the expiration date, the edge node has a benefit of 0.
Task t i And (3) calculating the benefit when the cloud is unloaded:
if a mission plan is executed on the remote cloud side, security services should be added to ensure the security of the data before offloading. Task t i The method comprises four steps of adding security service, transmitting data to a cloud end, unloading the security service and executing a task. Task t i The actual value of the end time of (c) includes five parts:
Figure BDA00030336107700000412
wherein
Figure BDA0003033610770000051
Is task t i The start time of (c) is,
Figure BDA0003033610770000052
is task t i The time to add the security service on the edge node,
Figure BDA0003033610770000053
is task t i The transmission time of the transmission data to the cloud,
Figure BDA0003033610770000054
is task t i The security time consumed to offload the security services,
Figure BDA0003033610770000055
is task t i Execution time on the remote cloud.
For task t i Since the bandwidth is a constant, the bandwidth is constant,
Figure BDA0003033610770000056
and
Figure BDA0003033610770000057
is stationary. To ensure
Figure BDA0003033610770000058
The following conditions should be satisfied:
Figure BDA0003033610770000059
at this time
Figure BDA00030336107700000510
Wherein D i Representing a task t i Data size of W i Representing a task t i The workload of (2);
from the above equation, we can compute task t i Minimum resources required at cloud
Figure BDA00030336107700000511
Figure BDA00030336107700000512
The cost of the cloud is:
Figure BDA00030336107700000513
where p represents the calculated cost per unit time for 1MB of data,
Figure BDA00030336107700000514
representing a task t i Total elapsed time at the cloud. And is
Wherein
Figure BDA00030336107700000515
Task t computed on the cloud i The benefits of the method are as follows:
Figure BDA00030336107700000516
the total benefit of step S2-4 at the time interval τ edge node is calculated as follows:
Figure BDA00030336107700000517
step S3 uses a genetic algorithm to maximize the above-mentioned total benefit ψ at each time interval τ. The benefit Ψ (·) can be viewed as a function relating X (τ) and Y (τ), X (τ) { X } 1 ,…,x i ,…,x n(τ) Y (τ) { Y } Y 1 ,…,y i ,…,y n(τ) And represents the execution sequence of tasks. The search spaces for X (τ) and Y (τ) satisfy the following formula:
Figure BDA00030336107700000518
Figure BDA00030336107700000519
Figure BDA0003033610770000061
S(τ)={1,2,..,n(τ)}
step S3-1 population initialization, randomly generating a number E in [0,1]]If e is less than or equal to 0.5, x i 0, otherwise x i =1。
Step S3-2 repeats step S3-1 until n (τ) execution positions are generated.
Step S3-3 is to copy S (tau) as S;
step S3-4 randomly generates a positive integer E in [1, | S-]Let y i For the element S of the th e in S Then remove the ∈ th element. I.e. y i =s ,S=S-{s };
Step S3-5 repeats step S3-4 until n (τ) execution sequences are generated. This results in an individual comprising the position and order of execution of the mission plan.
Step S3-6 repeats steps S3-1 through S3-5 until m individuals are produced, m being the number of individuals of the artificially set population.
The crossover of step S4 is a key genetic operation, and the effect of crossover is to generate offspring, so that individuals in the population can better explore the unknown solution space. Mutation is another important operation of genetic algorithms to improve fitness values and prevent premature convergence of the algorithm.
Step S4-1 selects two individuals from the population, X 1 And X 2 Representing the execution position vectors of the two individuals, respectively. Randomly selecting a cut-off point from which X is 1 And X 2 Is divided into two sub-strings
Figure BDA0003033610770000062
And
Figure BDA0003033610770000063
swapping their second parts yields two new execution position vectors X 12 And X 21 I.e. by
Figure BDA0003033610770000064
See fig. 2.
Step S4-2Y 1 And Y 2 Respectively representing the execution sequence vectors of the two individuals selected in the last step, randomly selecting a dividing point from which the two individuals are divided into two sub-strings
Figure BDA0003033610770000065
And
Figure BDA0003033610770000066
by swapping two substrings, two temporary execution order vectors Y 'are derived' 12 And Y' 21 I.e. by
Figure BDA0003033610770000067
Next, scanning two temporary individuals from front to back, respectively, and deleting the repeated numbers, which avoids conflict of execution orders, now generating two new execution order vectors. See fig. 3.
Step S4-3 loops through steps S4-1 and S4-2 until all individuals in the population have been selected, which results in m new individuals.
Step S4-4 is performed as follows, traversing all individuals from the population: randomly generating a number e between [0,1], if e < p1, skipping step S4-5, step S4-6, directly executing step S4-7, otherwise executing the mutation operation of step S4-5, step S4-6.
Step S4-5X represents the execution position vector of the current individual, and randomly generates a number of positive integers E' in [1, n (tau)]In between, ∈' is a variation point, then x ∈’ =|x ∈’ -1 |. See fig. 4.
Steps S4-6Y represent the current individual' S execution order vector, randomly generating two values in [1, n (τ) ]]Is a positive integer e 1 And e 2 ,∈ 1 ≠∈ 2 Exchange of
Figure BDA0003033610770000071
And
Figure BDA0003033610770000072
generating a new execution sequence Y'; see fig. 5.
And step S4-7, in the population selection stage, storing the individuals with better solution. At this time, we already have m + m individuals, psi (X (τ), Y (τ)) is an adaptive function, psi values of each individual are respectively calculated, sorting is performed from large to small, and the top m individuals are selected and stored.
Step S4-8 repeats steps (4) to (4.8) M times, M representing the maximum number of iterations of the genetic algorithm. And the individuals with the largest rank are the final task unloading schemes.

Claims (5)

1. The benefit maximization method for safety task unloading in the edge cloud environment is characterized by comprising the following steps:
step S1, constructing a security model, wherein the security services of the security model comprise confidentiality service and integrity service; the method comprises the following specific steps:
step S1-1 runs all confidentiality services and integrity services to obtain their execution time, and assumes that the longer the execution time of the running service is, the higher the security level, and accordingly, the security level of the confidentiality service is calculated as:
Figure FDA0003708099810000011
wherein
Figure FDA0003708099810000012
An execution time for the kth confidentiality service;
Figure FDA0003708099810000013
a security level for a kth confidentiality service; q1 performs a time reference for the artificially defined confidentiality service;
the security level of the integrity service is calculated as:
Figure FDA0003708099810000014
wherein
Figure FDA0003708099810000015
Representing the execution time of the kth integrity service;
Figure FDA0003708099810000016
indicating a security level for a kth integrity service; q2 is a human execution time reference for a defined integrity service;
the execution time of step S1-2 is proportional to the data size, and can result in:
Figure FDA0003708099810000017
wherein
Figure FDA0003708099810000018
Represents the execution time of the security service S under the single CPU for the data of 1 MB; d is the data size;
Figure FDA0003708099810000019
representing the execution time of the s-service; n represents the number of CPUs; cd denotes confidentiality service; ig represents an integrity service;
step S1-3 assumes that the external attack times obey Poisson distribution, then adds the security level as
Figure FDA00037080998100000110
The risk probability of the task of the security service of (1) is an exponential distribution as follows:
Figure FDA00037080998100000111
wherein sd s Representing the security requirements of the task; pi s A risk coefficient representing a security service s;
Figure FDA00037080998100000112
represents the security level of the kth security service s;
the joint risk probability under both security services is therefore:
Figure FDA00037080998100000113
step S1-4, in order to ensure the security of the task submitted by the mobile device, the security level of the security service S needs to satisfy the following condition:
Figure FDA00037080998100000114
wherein sd s The maximum value of the security requirements of the cloud and edge nodes on the security service s;
sd s =max{sd s (edge),sd s (cloud) }, s ∈ { cd, ig } formula (7)
Wherein sd s (edge) represents security requirements on the edge node; sd s (cloud) represents security requirements on the cloud;
step S2 formulates benefit maximization problem for security task offloading
Step S2-1 sets x i As task t i Of the execution position, x i 1 denotes task t i Is offloaded to a remote cloud and executed, x i 0 denotes task t i At the edge node, execution is performed, namely:
Figure FDA0003708099810000021
where S (τ) {1,2, …, n (τ) } denotes a set of index numbers of all tasks of the current period τ;
step S2-2 uses X (τ) ═ X 1 ,…,x i ,…,x n(τ) Indicates the execution positions of tasks with different index numbers; using Y (τ) ═ Y 1 ,…,y i ,…,y n(τ) Denotes the execution order of the different index numbered tasks, where y i ≠y j ,
Figure FDA0003708099810000022
Step S2-3, judging whether the task is located at the edge node or is unloaded to the cloud, and then calculating the task t with index number i i Benefits of (1)
Figure FDA0003708099810000023
The method comprises the following specific steps:
if task t i On the edge node, thenAffair t i Calculating the benefit of (1):
Figure FDA0003708099810000024
wherein
Figure FDA0003708099810000025
Representing a task t i Is the actual value of the end time of (1), wherein
Figure FDA0003708099810000026
Figure FDA0003708099810000027
Representing a task t i At the time of execution of the edge node,
Figure FDA0003708099810000028
representing a task t i Expected expiration date value, η i Indicating completion of task t i The benefits obtained;
if task t i When the task is unloaded to the cloud end, the task t i Calculating the benefit of (1):
if a task plan is executed on the remote cloud end, before unloading, a security service should be added to ensure the security of data; task t i The method comprises four steps of adding security service, transmitting data to a cloud end, unloading the security service and executing a task; task t i The actual value of the end time of (c) includes five parts:
Figure FDA0003708099810000029
wherein
Figure FDA00037080998100000210
Is task t i The start time of (c) is,
Figure FDA00037080998100000211
is task t i The time to add the security service on the edge node,
Figure FDA00037080998100000212
is task t i The transmission time of the transmission data to the cloud,
Figure FDA00037080998100000213
is task t i The security time consumed to offload the security services,
Figure FDA00037080998100000214
is task t i Execution time on the cloud;
Figure FDA00037080998100000215
Figure FDA0003708099810000031
wherein D i Representing a task t i Data size of W i Representing a task t i The workload of (2);
computing task t according to the above formula i Minimum resources required at cloud
Figure FDA0003708099810000032
Figure FDA0003708099810000033
The cost of the cloud is:
Figure FDA0003708099810000034
where p represents the calculated cost per unit time for 1MB of data,
Figure FDA0003708099810000035
representing a task t i Total elapsed time at the cloud; and is
Figure FDA0003708099810000036
Task t computed on the cloud i The benefits of the method are as follows:
Figure FDA0003708099810000037
wherein eta i Indicating completion of task t i The benefits obtained;
the total benefit of the edge node of step S2-4 is calculated as follows:
Figure FDA0003708099810000038
step S3 is to use genetic algorithm, initialize population, and respectively generate m schemes of the execution position and the execution sequence of the mission plan, namely m individuals in the population;
and S4, performing cross variation operation on the m individuals in the population, and continuously iterating to obtain a final task unloading scheme.
2. The benefit maximization method for security task offloading in edge cloud environment according to claim 1, wherein step S3 is as follows:
the benefit Ψ (·) is viewed as a function related to X (τ) and Y (τ), X (τ) { X } 1 ,…,x i ,…,x n(τ) Denotes the execution position of the task, and Y (τ) ═ Y 1 ,…,y i ,…,y n(τ) Represents the execution order of tasks; the search spaces for X (τ) and Y (τ) satisfy the following formula:
Figure FDA0003708099810000039
step S3-1 population initialization, randomly generating a number e 1 In [0,1]]If e is 1 ≤0.5,x i 0, otherwise x i 1; the epsilon 1 is used as an execution position;
step S3-2 repeats step S3-1 until n (τ) execution positions are generated;
step S3-3, copying S (tau) as S;
step S3-4 randomly generates a positive integer e 2 In [1, | S]Let y i For the e-th in S 2 An element
Figure FDA0003708099810000041
Then remove the ∈ th 2 An element; namely, it is
Figure FDA0003708099810000042
The e is 2 Is the execution order;
step S3-5 repeating step S3-4 until n (τ) execution sequences are generated, i.e., an individual is generated including the execution position and the execution sequence of the mission plan, respectively;
step S3-6 repeats steps S3-1 through S3-5 until m individuals are produced, m being the number of individuals of the artificially set population.
3. The benefit maximization method for security task offloading in edge cloud environment according to claim 2, wherein step S4 is as follows:
step S4-1 selects two individuals from the population, X 1 And X 2 Representing the execution position vectors of the two individuals respectively; randomly selecting a cut-off point from X 1 And X 2 Is divided into two sub-strings
Figure FDA0003708099810000043
And
Figure FDA0003708099810000044
swapping the second part yields two new execution position vectors X 12 And X 21 I.e. by
Figure FDA0003708099810000045
Step S4-2Y 1 And Y 2 Respectively representing the execution order vectors of the two individuals; randomly selecting a cut-off point from Y 1 And Y 2 Is divided into two sub-strings
Figure FDA0003708099810000046
And
Figure FDA0003708099810000047
by swapping two substrings, two temporary execution order vectors Y 'are derived' 12 And Y' 21 I.e. by
Figure FDA0003708099810000048
Scanning two temporary execution order vectors Y 'from front to back, respectively' 12 And Y' 21 Two new execution order vectors are generated after deleting the repeated numbers;
step S4-3 loops through step S4-1 and step S4-2 until all individuals in the population have been selected, which results in m new individuals;
step S4-4 is performed as follows, traversing all individuals from the population: randomly generating a random number in [0,1]]The number between ∈ 3 If e is 3 < p1, p1 indicates the mutation rate, and the steps S4-5 and S4-6 are skipped, and the step S4-7 is directly performed, otherwise, the mutation operations of the steps S4-5 and S4-6 are performed;
step S4-5X represents the execution position vector of the current individual, and a positive integer epsilon is randomly generated 4 In [1, n (tau)]Is e.g. E 4 Is a point of variation, then
Figure FDA0003708099810000049
Steps S4-6Y represent the current individual' S execution order vector, randomly generating two values in [1, n (τ) ]]Is a positive integer e 5 And e 6 ,∈ 5 ≠∈ 6 Exchange of
Figure FDA0003708099810000051
And
Figure FDA0003708099810000052
generating a new execution sequence Y';
step S4-7, in the population selection phase, storing the individuals with better solution; at the moment, m + m individuals exist, psi (X (tau), Y (tau)) is an adaptive function, psi values of each individual are respectively calculated, sorting is carried out from large to small, and the first m individuals are selected and stored;
step S4-8 repeats steps (S4-1) to (S4-8) M times, M representing the maximum number of iterations of the genetic algorithm; and selecting the individual with the maximum psi value sequence, namely the final task unloading scheme.
4. A computer-readable storage medium, on which a computer program is stored which, when executed in a computer, causes the computer to carry out the method of any one of claims 1 to 3.
5. A computing device comprising a memory having stored therein executable code and a processor that, when executing the executable code, implements the method of any of claims 1-3.
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