Snake optimization budget-aware scheduling algorithm based on negative shift mechanism in heterogeneous cloud

Abstract

The application discloses a snake optimization budget-aware scheduling algorithm based on a negative offset mechanism in a heterogeneous cloud. The application simulates the foraging and breeding behaviors of snakes through a mathematical method, designs different update mechanisms of an exploration mode, a development mode, a struggle mode and a mating mode to search in a solution space, and then combines the negative offset mechanism to ensure that the update of the position of an individual is no longer random exploration without purpose, but is directional position offset of the individual in the direction of reducing the cost based on the cost characteristics of the individual exceeding the budget, so that the problems of the existing snake optimization algorithm in the heterogeneous cloud environment, such as being prone to falling into a local optimal solution, aggravating the complexity and uncertainty of a search path and improving the calculation difficulty, are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cloud computing, and more particularly to a snake optimization budget-aware scheduling algorithm based on a negative offset mechanism in a heterogeneous cloud. BACKGROUND

[0002] In recent years, cloud computing technology has made rapid progress. Its computing method is cost-effective and easy to use, not only revolutionizing the way global users share computing resources over the Internet, but also as a key component of the national "new infrastructure" strategy, cloud computing technology has injected strong impetus into the development of 5G, Internet of Things, industrial Internet and other cutting-edge technology fields, and has become an indispensable important support. Cloud centers, with their powerful computing capabilities, have been widely used to solve massive data and complex workflow problems in various fields such as biology, physics and astronomy. Virtualization technology is a key technology in cloud computing, which can achieve dynamic scheduling and expansion of resources. Through virtualization technology, a large number of computing nodes are integrated together to form a huge resource pool, and users use the resources in the resource pool in a "pay-as-you-go" manner through the Internet. In a heterogeneous cloud computing center, computing resources have different computing capabilities and characteristics, and users can rent them at any time in any quantity.

[0003] Based on the above elastic and heterogeneous computing environment, the workflow scheduling algorithm of the cloud center needs to consider how to find the most appropriate mapping relationship between a series of interdependent tasks and a group of heterogeneous virtual resources, so as to minimize or maximize the specified target that users care about, which is crucial for a sustainable and efficient cloud data center. However, workflow scheduling is an NP-hard problem, and it is currently difficult to achieve optimal scheduling of workflows. Therefore, people usually explore the workflow scheduling problem under the constraints of user-defined Quality of Service (QoS).

[0004] Currently, the mainstream solutions to workflow scheduling problems mainly include heuristic and meta-heuristic methods, and with the development of deep reinforcement learning (DRL), DRL-based methods are gradually applied to workflow scheduling problems. The heuristic algorithm can quickly develop a workflow scheduling strategy based on expert experience, but such an algorithm is mainly applied to small-scale workflows, simple rules are adopted, and it is easy to fall into a local optimal solution, and it is difficult to find an optimal solution in a dynamic cloud environment. The DRL-based method is still in its infancy, and when used to solve large-scale complex application scheduling problems, it still faces challenges such as sparse rewards, super parameter sensitivity, and low exploration efficiency. In contrast, the meta-heuristic algorithm uses a combination of random search and local utilization to find an approximate optimal solution, has good optimization performance, and is widely used in large-scale workflows to find an approximately optimal scheduling solution. The snake optimization (SO) algorithm is a new meta-heuristic algorithm that simulates the foraging and breeding behavior of snakes through mathematical methods, designs different update mechanisms to search in the solution space, and solves a series of continuous optimization problems that mimic the special mating behavior of snakes, significantly outperforms existing technologies in the meta-heuristic field, and exhibits a high performance advantage.

[0005] In CN202311463211.4, a cloud resource planning and scheduling method with a global search mechanism and fast convergence is disclosed, which includes the following steps: S1, obtaining the initialization parameter data of a user, the parameter data including task byte size and virtual machine bandwidth; then establishing a target function; S2, obtaining an optimal population by using an improved snake optimization algorithm; S3, selecting an individual with the smallest target function value from the optimal population as an optimal resource scheduling scheme. This patent can further improve the rationality of cloud resource scheduling and maximize resource utilization. However, by introducing randomness and enhancing diversity to avoid the difficulty of the snake optimization algorithm easily falling into a local optimal solution, this approach promotes the global search capability of the algorithm, but also increases the complexity and uncertainty of the search path, thereby increasing the computational difficulty of approaching the global optimal solution. SUMMARY

[0006] The main technical problem to be solved by the present application is the deficiency that the introduction of randomness and enhanced diversity in the prior art to avoid the snake optimization algorithm easily falling into a local optimal solution aggravates the complexity and uncertainty of the search path and increases the computational difficulty. When using the snake optimization algorithm to accurately solve the complex workflow scheduling problem with a budget cost as a constraint condition and a scheduling length as an optimization target, the present application considers balancing randomness and directionality, provides a snake optimization budget-aware scheduling algorithm based on a negative offset mechanism in a heterogeneous cloud to realize dual optimization of search efficiency and solution quality.

[0007] The object of the present application is achieved by the following technical solutions:

[0008] A snake optimization budget-aware scheduling algorithm based on negative offset mechanism in a heterogeneous cloud, comprising the following steps:

[0009] S1. Generating a random initial population Divide the population into two groups, male and female;

[0010] S2. Start iterative calculation, find the optimal male individual X m,best and the optimal female individual X f,best in the male group and the female group respectively;

[0011] S3. Calculate the food quantity Q and the temperature Temp of the iteration, and select the mode to update the position according to the food quantity Q and the temperature Temp and the set food quantity threshold Q ts and the temperature threshold T ts ;

[0012] S4. After completing the position update, obtain the offspring population Adjust the dimension value x i of the individual in the offspring population ;

[0013] S5. Compare the corresponding individuals in and , and select the better individual to form a new population

[0014] S6. Update the population using the negative offset mechanism to obtain a new parent population entering the next iteration

[0015] S7. Complete the iterative calculation and search to obtain the optimal individual X best .

[0016] Further, the food quantity Q is expressed as:

[0017]

[0018] The temperature Temp is expressed as:

[0019]

[0020] Where d is the current iteration number, D is the maximum iteration number, c1 is a constant equal to 0.5, exp(·) represents the exponential function, and Q and Temp represent the food quantity and temperature at the dth iteration respectively.

[0021] Further, the mode selection for updating the position is:

[0022] If Q < Q ts , the male individual X m,r ​The update mechanism can be represented as:

[0023]

[0024] in, X represents the position of the r-th male individual after the update. m,rand Let X represent the position of a random male individual, c2 be a constant equal to 0.05, and X be a random number. max and X min Let these represent the upper and lower bounds of the solution space, respectively. It indicates the exploratory ability of male individuals;

[0025] Female individual X f,r The update mechanism can be represented as:

[0026]

[0027] in, X represents the position of the r-th female individual after the update. f,rand Indicates the location of a random female individual. It indicates the exploratory ability of female individuals;

[0028] If Q>Q ts Temp > T ts Then the male individual X m,r The update mechanism is represented as follows:

[0029]

[0030] Female individual X f,r The update mechanism is represented as follows:

[0031]

[0032] Among them, X best Parental population The optimal individual in the set, where c3 is a constant equal to 2;

[0033] If Q>Q ts Temp < T ts If rand > 0.6, then the male individual X m,r The update mechanism is as follows:

[0034]

[0035] Among them, X f,best It is the best female among the parent females. It indicates the fighting ability of a male individual;

[0036] Female individual X f,r The update mechanism is as follows:

[0037]

[0038] wherein X m,best is the optimal male individual in the parent male individuals, represents the fighting ability of the female individual;

[0039] If Q > Q ts , Temp < T ts , rand < 0.6, the update mechanism of the male individual X m,r is:

[0040]

[0041] wherein, represents the mating ability of the male individual;

[0042] the update mechanism of the female individual X f,r is:

[0043]

[0044] wherein, represents the mating ability of the female individual.

[0045] Further, the expression is:

[0046]

[0047] the expression is:

[0048]

[0049] Further, the calculation expression is:

[0050]

[0051] the expression is:

[0052]

[0053] Further, the expression is:

[0054]

[0055] the expression is:

[0056]

[0057] Further, the adjusting is: if x i < 1, adjusting x i = 1; if x i > |V|, adjusting x i = |V|, so that x i satisfies [1, |V|].

[0058] Further, the negative offset mechanism step comprises:

[0059] S51. calculating the number of random male individuals ξ m,rand and the number of female individuals ξ f,rand according to the random probability γ;

[0060] S52. selecting ξ m,rand male individuals and ξ f,rand female individuals from the male group and the female group of the population respectively;

[0061] S53. traversing all the randomly selected male individuals and female individuals respectively, and performing position offset on them;

[0062] S531. if the currently traversed individual does not satisfy the budget constraint, calculating the negative relaxation cost of the individual as

[0063]

[0064] and calculating the minimum cost deviation MCD(n i ) and the budget cost Cost bgt (n i ) of all tasks in the individual;

[0065] S532. randomly selecting a dimension value x h of the individual, then finding the offset queue Q O (h) of the h-th dimension, and randomly selecting a virtual machine index from Q O (h) to replace x h .

[0066] Further, the minimum cost deviation MCD(n i ) is expressed as:

[0067] MCD(n i ) = Cost(n i , vm k ) - Cost min (n i ).

[0068] Cost(n i , vm k ) = w i,kX price k Cost min (n i ) is the minimum execution cost.

[0069] Further, the budget cost Cost bgt (n i ) is expressed as:

[0070]

[0071] Further, the offset queue Q O (h) is expressed as:

[0072]

[0073] Compared with the prior art, the beneficial effects are:

[0074] The present application combines the snake optimization algorithm with the negative offset mechanism, ensures that the update of the individual position is no longer random exploration without purpose, but is guided to the directional position offset in the direction of reducing the cost based on the cost characteristics of the individual exceeding the budget. The negative offset mechanism reduces the total cost of the individual from the individual dimension based on the negative relaxation cost of the individual and the minimum cost deviation degree of the task, speeds up the search speed of the feasible solution meeting the budget constraint in the early iteration stage, and makes the iteration process enter the minimum scheduling length stage earlier. At the same time, the negative offset mechanism has randomness, to a certain extent, gets rid of the local optimum in the solution update stage, and enhances the search diversity. The negative offset mechanism is to balance randomness and directionality, prevent falling into local optimum while improving the success rate of searching for feasible solutions meeting the budget constraint, and efficiently approximate the global optimal solution. The method (NO-SO) described in the present application is used for scheduling workflows with budget constraints in heterogeneous cloud computing, which not only performs well in the success rate of searching for feasible solutions, but also has obvious effect in reducing the scheduling length. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 is the flowchart of the NO-SO algorithm in Example 1.

[0076] Figure 2 is the flowchart of the negative offset mechanism in Example 2.

[0077] Figure 3 is the convergence effect of four algorithms in four types of workflows in Example 3. DETAILED DESCRIPTION

[0078] The following further explains and illustrates the embodiments, but the specific embodiments do not have any form of limitation on the present application.

[0079] Example 1

[0080] The resources of a cloud computing center are usually modeled as a set of heterogeneous virtual machine instances, denoted as VM = {vm1, vm2,..., vm |V|}, where |V| is the number of virtual machine instances. The virtual machine instances are all heterogeneous, with different types and resource configurations. The data communication cost between virtual machine instances can be ignored. For convenience of description, it is agreed that the bandwidth of a virtual machine is considered as ideal bandwidth, and no communication contention occurs between virtual machine instances.

[0081] A workflow application in a cloud computing system represents a set of tasks with data dependency in the form of a directed acyclic graph (DAG), where a task is represented by a node and the dependency between tasks is represented by an edge. It can be represented by a four-dimensional vector G = {N, E, C, W}. Where N = {n1, n2,..., n |N|} represents a set of tasks of a workflow, |N| represents the number of tasks in the workflow. E = {e i,j |n i ,n j ∈N} represents a set of communication edges with data dependency in the DAG graph, each edge represents a task dependency constraint, that is, task n i should complete its execution before task n j starts. c i,j ∈C represents the communication time required for the relevant data of task n i to be transmitted to task n j . If task n i and task n j are allocated to the same virtual machine for execution, the communication time c i,j is zero. w i,k ∈W represents the execution time of task n i on virtual machine vm k . pred(n i ) represents the set of direct predecessor tasks of task n i , and succ(n i ) represents the set of direct successor tasks of task n i . In a given workflow graph, a task without a predecessor task is called an entry task n entry , and a task without a successor task is called an exit task n exit .

[0082] According to the existing workflow scheduling model, the following definitions of related concepts are given.

[0083] The start time and completion time of task n i when executed on the allocated virtual machine vm k are denoted as ST(ni ) and FT(n i ), the calculation expressions are respectively:

[0084]

[0085] FT(n i ) = ST(n i ) + w i,k ,

[0086] avail(vm k ) represents the available time of the virtual machine vm k . For the entry task n entry , there is:

[0087] ST(n entry ) = avail(vm k ).

[0088] The scheduling length Makespan of the workflow G refers to the time required from the beginning of the workflow scheduling to the completion of the execution of the workflow, and the calculation expression is:

[0089]

[0090] The embodiment provides a snake optimization budget-aware scheduling algorithm based on a negative offset mechanism in a heterogeneous cloud, as shown in Figure 1 , the steps comprise:

[0091] S1. Construct a cost model;

[0092] The execution cost required by the task n i running on the virtual machine vm k is:

[0093] Cost(n i ,vm k ) = w i,k ×price k .

[0094] The total cost Cost(G) of the workflow G is the sum of the execution costs of all tasks, and can be expressed as:

[0095]

[0096] The task n i executes on different virtual machines, and there is a minimum execution cost Cost min (n i ) and a maximum execution cost Cost max (n i ). Then the minimum cost and the maximum cost of the workflow G can be expressed as Cost min(G) and Cost max (G), the calculation expressions are as follows:

[0097]

[0098] Assume the budgeted cost of workflow G is Cost budget (G) The budgeted cost must be greater than or equal to the minimum cost of the workflow. min (G), and less than or equal to the maximum cost of the workflow. max (G). Otherwise, budgets exceeding the specified limits are invalid. Therefore, the model must satisfy:

[0099] Cost min (G)≤Cost budget (G)≤Cost max (G)

[0100] S2. Generate a uniformly distributed random initial population in the solution space. The initial population has a population size of ξ. Divided into male and female groups, with ξ being the number of male individuals. m The number of female individuals is ξ f The calculation expressions are as follows:

[0101]

[0102] ξ f =ξ-ξ m .

[0103] S3. Begin iterative calculations to find the optimal male individual X in both the male and female groups. m,best And the optimal female individual X f,best Calculate the number of food items Q and the temperature Temp during the iteration:

[0104]

[0105] Where d is the current iteration number, D is the maximum iteration number, c1 is a constant equal to 0.5, exp(·) represents the exponential function, and Q and Temp represent the quantity of food and temperature at the d-th iteration, respectively. That is, as the iteration progresses, the quantity of food gradually increases and the temperature gradually decreases.

[0106] S4. Based on the food quantity threshold Q ts and temperature threshold T ts Determine the abundance of food (Q) and the temperature (Temp) at the current food quantity threshold. ts =0.25, temperature threshold T ts =0.6.

[0107] If Q<Q ts When individual snakes enter exploration mode, their locations will be updated as follows:

[0108] Due to insufficient food in the environment, individual snakes randomly choose a location to search for more food. Male individual X m,r The update mechanism can be represented as:

[0109]

[0110] in, X represents the position of the r-th male individual after the update. m,rand Let X represent the position of a random male individual, c2 be a constant equal to 0.05, and X be a random number. max and X min These represent the upper and lower bounds of the solution space, respectively. The exploratory ability of male individuals is represented by the following expression:

[0111]

[0112] Makespan(·) represents the scheduling length generated by the workflow scheduling scheme represented by the corresponding snake individual.

[0113] Female individual X f,r The update mechanism can be represented as:

[0114]

[0115] in, X represents the position of the r-th female individual after the update. f,rand This indicates the location of a random female individual. The exploratory ability of a female individual is represented by the following expression:

[0116]

[0117] If Q>Q ts Temp > T ts The location of individual snakes entering development mode is updated as follows:

[0118] Although food was plentiful, the ambient temperature remained high, and the snakes only moved to the optimal locations. Male X m,r and female individual X f,r The update mechanisms can be represented as follows:

[0119]

[0120] Among them, X best Parental population c3 is a constant equal to 2.

[0121] If Q > Q ts , Temp < T ts , and rand > 0.6, the snake individual enters the fighting mode to update the position, specifically:

[0122] In the case of sufficient food resources and low environmental temperature, the snake individual exhibits a specific behavioral tendency, i.e., there is a 40% probability of entering the fighting mode and a 60% probability of entering the mating mode. In the fighting mode, male individuals will engage in fierce competition to compete for the mating right with the optimal female individual. At the same time, female individuals will also make careful choices to pair with the most ideal male individual. The update mechanism of the male individual X m,r is as follows:

[0123]

[0124] where X f,best is the optimal female individual in the parent female individuals. represents the fighting ability of the male individual, and the calculation expression is:

[0125]

[0126] The update mechanism of the female individual X f,r is as follows:

[0127]

[0128] where X m,best is the optimal male individual in the parent male individuals. represents the fighting ability of the female individual, and the calculation expression is:

[0129]

[0130] If Q > Q ts , Temp < T ts , and rand < 0.6, the snake individual enters the mating mode to update the position, specifically:

[0131] The mating between each pair of snake individuals is closely related to the number of food. In the mating mode, the female individual may lay eggs and hatch new snake individuals. The update mechanism of the male individual X m,r is as follows:

[0132]

[0133] where, represents the mating ability of the male individual, and the calculation expression is:

[0134]

[0135] Female individual X f,r The update mechanism is:

[0136]

[0137] wherein, represents the mating ability of the female individual, and the calculation expression is:

[0138]

[0139] If the egg hatches, replace the worst male individual X m,worst and the female individual X f,worst , and the expressions are respectively:

[0140] X m,worst = X min + θ × (X max - X min ),

[0141] X f,worst = X min + θ × (X max - X min ).

[0142] S5. After all snake individuals in the population complete position update according to the selected update mode, a child population is obtained. Adjust the dimension value x i of the individual in the child population i to meet [1, |V|], if x i < 1, adjust x i = 1; if x i > |V|, adjust x i = |V|.

[0143] S6. Compare the corresponding individuals in and , and select the better individual to form a new population

[0144] S7. Update the population by using the negative offset mechanism to obtain a new parent population entering the next iteration

[0145] S8. The iteration is ended, and the optimal individual X best is obtained.

[0146] Example 2

[0147] This embodiment provides the algorithm of negative shift mechanism, such as Figure 2 , the steps include:

[0148] S1. Calculate the number of random male individuals ξ according to random probability γ m,rand and the number of female individuals ξ f,rand ;

[0149] S2. Select ξ m,rand male individuals and ξ f,rand female individuals from the male group and the female group of population respectively;

[0150] S3. Traverse all the randomly selected male individuals and female individuals respectively, and shift the positions of them;

[0151] Judge whether the male individual meets the budget constraint, if the individual cost is greater than the budget cost, calculate the negative relaxation cost of the individual as:

[0152]

[0153] Otherwise, judge the next male individual.

[0154] S4. Traverse the minimum cost deviation MCD(n i ) of each task in the scheduling scheme represented by the male individual:

[0155] MCD(n i ) = Cost(n i , vm k ) - Cost min (n i ).

[0156] Budget cost Cost bgt (n i ):

[0157]

[0158] S5. Randomly select a dimension value x h of the individual, and then find the shift queue Q O (h) of the hth dimension;

[0159]

[0160] Where, for the case that there is no vm k such that Cost(n h , vm k ) ≤ Cost bgt (n h ), the individual the offset queue of the h-th dimension is:

[0161]

[0162] S6. From Q O (h) randomly select a virtual machine index to replace x h .

[0163] S5. After traversing all the randomly selected male individuals, traverse all the randomly selected female individuals, and offset the positions according to steps S3-S6.

[0164] Example 3

[0165] In this embodiment, four types of real-world typical scientific workflow applications widely used in the field of high-performance computing are used as the test task set: the first type is the Epigenomics workflow application (EP) in the field of biological genetics; the second type is the LIGO workflow application in the field of gravitational physics; the third type is the Gaussian elimination parallel application (GE); and the fourth type is the Montage workflow application in the field of astronomy.

[0166] The resource pool of the experimental simulation heterogeneous cloud computing system is composed of 128 heterogeneous virtual machine instances, the types and prices of the virtual machine instances are set with reference to Amazon Elastic Compute Cloud (EC2), and the algorithm program is implemented using Python language. In this embodiment, OSAM, MG-PRO and SO are used as comparative algorithms, and the effectiveness of the NO-SO proposed in the present application in solving the workflow scheduling length minimization problem under budget constraints is comprehensively verified and demonstrated through performance comparison with the three algorithms. Since the four algorithms are all population-based meta-heuristic algorithms, consistent population size and maximum iteration number are set in the experiment. In addition, the specific parameters of OSAM, MG-PRO and SO are borrowed from the original works, and the parameter settings of the NO-SO algorithm proposed in this paper are shown in Table 1:

[0167] Parameter Value Description ξ 50 Population size D 1000 Maximum number of iterations γ 10％ Random probability of negative offset phase [c1, c2, c3] 0.5,0.05,2 Step size parameter

[0168] Compared with OSAM, MG-PRO and SO, the success rate of NO-SO in searching for feasible solutions under budget constraints is increased by 49.44%, 34.44% and 18.89% on average, respectively. In the scheduling length comparison experiment under different budget constraints, different task sizes and different numbers of virtual machines, NO-SO is reduced by 42.88%, 33.90% and 34.42% on average compared with OSAM, MG-PRO and SO in terms of scheduling length. The entire optimization process evolves from "reducing cost to meet budget constraints" to "reducing time to minimize workflow scheduling length", and the convergence effect is shown in Figure 3 As shown in Fig. 6, NO-SO achieves higher scheduling performance and obtains smaller scheduling length.

[0169] Obviously, the above-mentioned embodiments of the present application are only examples for clearly illustrating the present application, but are not intended to limit the implementation modes of the present application. Based on the above description, other different forms of changes or variations can also be made by those skilled in the art. Here, it is not necessary and also impossible to enumerate all the implementation modes. Any modification, equivalent replacement and improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A snake-optimized budget-aware scheduling method based on negative offset mechanism for heterogeneous cloud computing workflow scheduling, characterized by the following steps: include: S1. Construct a cost model based on the workflow scheduling model; Define task In virtual machine The execution cost required to run it is: Workflow Total cost The sum of the execution costs of all tasks can be expressed as: The cost model is expressed as: Among them, workflow The minimum and maximum costs can be expressed as and Workflow The budget cost is , This indicates the number of tasks in the workflow. Indicates task In virtual machine Execution time; S2. Generate a random initial population in the solution space. The population was divided into male and female groups; S3. Begin iterative calculations to find the optimal male individual in both the male and female groups. and the optimal female individual ; S4. Calculate the number of foods in each iteration. and temperature According to the amount of food and temperature With the set food quantity threshold and temperature threshold Select the mode update location; S5. Obtain the offspring population after completing the position update. For offspring population Dimensional values ​​of individuals in Make adjustments; S5. Comparison and For each corresponding individual, the better individuals are selected to form a new population. ; S6. Update the population using a negative offset mechanism. This results in a new parental population entering the next iteration. ; The negative offset mechanism includes the following steps: S61. Based on random probability Calculate the number of random male individuals and the number of female individuals ; S62. From the populations respectively The number selected from the male and female groups was [number]. The number of male individuals is Female individuals; S63. Iterate through all randomly selected male and female individuals and offset their positions accordingly; S631. If the currently traversed individual does not meet the budget constraint, calculate the negative relaxation cost of the individual as follows: And calculate the minimum cost deviation for all tasks within that individual. and budget costs ; S632. Randomly select one dimension value for an individual. Then search for the first Dimensional offset queue ,from Randomly select a virtual machine index to replace ; S7. Complete the iterative calculation and search for the optimal individual. .

2. The snake-optimized budget-aware scheduling method based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 1, characterized in that, The update location mode is selected as follows: like Then the male individual The update mechanism can be represented as: in, Indicates the first The updated position of each male individual. Indicates the location of a random male individual. It is a constant. and Let these represent the upper and lower bounds of the solution space, respectively. It indicates the exploratory ability of male individuals; Female individuals The update mechanism can be represented as: in, Indicates the first The updated position of each female individual. Indicates the location of a random female individual. It indicates the exploratory ability of female individuals; like Then the male individual The update mechanism is represented as follows: Female individuals The update mechanism is represented as follows: in, Parental population The optimal individual in the process, It is a constant equal to 2; like Then the male individual The update mechanism is as follows: in, It is the best female among the parent females. It indicates the fighting ability of a male individual; Female individuals The update mechanism is as follows: in, It is the best male among the parent males. It indicates the fighting ability of female individuals; like Then the male individual The update mechanism is as follows: in, Indicates the mating ability of a male individual; Female individuals The update mechanism is as follows: in, It indicates the mating ability of a female individual.

3. The snake-optimized budget-aware scheduling method based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 2, characterized in that, The expression is: The expression is: 。 4. The snake-optimized budget-aware scheduling method based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 2, characterized in that, The calculation expression is: The expression is: 。 5. The snake-optimized budget-aware scheduling method based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 2, characterized in that, The expression is: The expression is: 。 6. The snake-optimized budget-aware scheduling method based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 1, characterized in that, The adjustment described in S4 is: if Then adjust ;if Then adjust ,make satisfy .

7. The snake-optimized budget-aware scheduling algorithm based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 1, characterized in that, Minimum cost deviation Represented as: To minimize execution cost.

8. The snake-optimized budget-aware scheduling method based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 1, characterized in that, Budget costs Represented as: 。 9. The snake-optimized budget-aware scheduling method based on negative offset mechanism applied to heterogeneous cloud computing workflow scheduling according to claim 1, characterized in that, Offset queue Represented as: 。

Images