CN102866912A - Single-instruction-set heterogeneous multi-core system static task scheduling method - Google Patents
Single-instruction-set heterogeneous multi-core system static task scheduling method Download PDFInfo
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- CN102866912A CN102866912A CN2012103912768A CN201210391276A CN102866912A CN 102866912 A CN102866912 A CN 102866912A CN 2012103912768 A CN2012103912768 A CN 2012103912768A CN 201210391276 A CN201210391276 A CN 201210391276A CN 102866912 A CN102866912 A CN 102866912A
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Abstract
Provided is a single-instruction-set heterogeneous multi-core system static task scheduling method. The method includes five steps: step 1, population initialization; step 2, fitness value calculation; step 3, selection operator operation; step 4, cross operator operation; and step 5 variation operator operation. A local sequence represents an executing sequence of two tasks without depending relations, population initialization efficiency and effective individual are greatly improved, the executing sequence of the tasks is determined through a pre-order-relation matrix, and defects of a traditional height value method are overcome. The method can widen a hunting range of optimal individuals. When the population scale is large enough, a part of optimal solutions missed by the height value method can be found so as to obtain a more optimal scheduling sequence. For the same task set, finishing time of the whole task set is short, power consumption is low, and a purpose of energy conservation and consumption reduction is achieved.
Description
Technical field
The present invention relates to a kind of single instrction collection heterogeneous multi-core system Static task scheduling method based on multi-objective Optimization Genetic Algorithm (multi-objective optimization genetic algorithm), belong to the Computer Systems Organization technical field.
Background technology
The rise of cloud computing makes the energy consumption rapid growth of data center, yet energy consumption is not utilized effectively.Single instrction collection heterogeneous multi-nucleus processor is a kind of new architecture that in recent years proposes, and compares with the isomorphism polycaryon processor, and this processor has better power dissipation ratio of performance, but has brought huge challenge to task scheduling simultaneously.
Scheduling problem has the characteristics such as complicacy, multiple constraint, is the np complete problem in the combinatorial optimization problem, and it is unpractical adopting the method for exhaustion to search for optimal scheduling.Heuritic approach has time complexity preferably and obtains under given conditions the ability of near-optimum solution, but heuritic approach is local optimal searching, can't guarantee the quality of separating, the researchist begins to attempt other searching algorithms, such as genetic algorithm, simulated annealing, particle cluster algorithm etc., wherein genetic algorithm is most widely used, can be in large at random efficient sampling and search of state space, and very rapid convergence arrives optimum solution or near-optimum solution, can solve np complete problem, all obtained application in a lot of fields such as task schedulings.
Genetic algorithm be simulation biological in physical environment the heredity and evolution process and a kind of adaptive global optimization probability search method of forming, E.S.H Hou is applied to multi-processor task scheduling with genetic algorithm first.The advantage of heterogeneous multi-nucleus processor is power dissipation ratio of performance, and generally, performance and power consumption are conflicts, and high-performance just means high power consumption.Estimate the quality of heterogeneous multi-nucleus processor dispatching algorithm and will see simultaneously performance and two aspects of power consumption, this is typical multiple-objection optimization (Multi-Objective Optimization) problem, and the present invention uses multi-objective Optimization Genetic Algorithm to seek Static task scheduling scheme optimum under the heterogeneous multi-core environment.
Innovative point of the present invention has two aspects, the one, for the existing height value method wretched insufficiency that execution sequence and dependence exist that sets the tasks, propose with first order relation matrix set the tasks execution sequencing and provided operational pattern, the 2nd, the overall situation ordering that the gene position of expression task sequencing in the chromosome coding structure is defined from general algorithm changes the partial order between two tasks that do not have dependence into, and the effective individual proportion when making initialization of population becomes 100%.
Summary of the invention
1, goal of the invention:
The invention provides a kind of single instrction collection heterogeneous multi-core system Static task scheduling method.This method uses partial ordering's sign without the execution sequence of two tasks of dependence, initialization of population efficient and effective individuality are improved greatly, with the execution sequence that first order relation matrix sets the tasks, overcome the wretched insufficiency that traditional height value method exists.This method can enlarge the optimum individual hunting zone, when population scale is enough large, and the part optimum solution that can find the height value method to miss, thus obtain more excellent scheduling sequence.For same task-set, use this method can make the deadline of whole task-set shorter, power consumption is lower, realizes energy-saving and cost-reducing purpose.
2, technical scheme:
2.1 problem description
If heterogeneous multi-core system forms C={C by a plurality of processor cores that are distributed on the different processor
1, C
2..., C
n, operating load has been decomposed into a series of thread-level task T={T
1, T
2..., T
m, n and m are respectively processor core number and task number.This Task Assignment Model can be used seven element group representations: (C, T, Θ, Ψ, Ω, E, Λ).
Θ is the execution time matrix of a m * n, its element θ
IjExpression task T
iAt processor core C
jOn execution time, different from the isomorphism multiple nucleus system, the execution time of same task on dissimilar nuclears is different in the heterogeneous multi-core system.Therefore need to represent with a matrix, suppose that the execution time of each task is predicted.When the power consumption of computation processor nuclear, only consider two states, task run is arranged and without task run.When task run is arranged, take dynamic power consumption as main, relevant with clock frequency and voltage; When not having task run, take quiescent dissipation as main.
Ψ is the communication delay matrix of a m * m, its element ψ
IjExpression task T
iWith T
jBetween communication delay.Communication delay between the task is relevant with the transmitted data amount between them, and is also relevant with the relative position of the processor core at their places.
Ω is the task allocation matrix of a m * n, ω
Ij=1 expression task T
iBe assigned to processor core C
jOn, otherwise, ω
Ij=0.
E is the directed edge collection in the Task Dependent graph of a relation.＜T
i, T
j∈ E is illustrated in task T
iBefore not finishing, task T
jCan not carry out, i.e. T
iBe T
jDirect precursor, T
jBe T
iImmediate successor.
Λ is the task elder generation order relation matrix of a m * m, λ wherein
IjExpression task T
iWith T
jBetween restriction relation, be defined as follows:
Dependence between the first order relation matrix representation task of task, this is to guarantee the correct key of scheduling result.The sequencing that prior art generally sets the tasks and carries out with height value.Be defined as follows:
Wherein, H (T
i) expression T
iHeight value, pred (T
i) expression task T
iForerunner's node set.
H (T
i) definition just provided an adequate condition that obtains dispatching efficient solution, yet it is not a necessary condition, can not obtain all efficient solutions of problem according to this definition, Zhang Cong has provided an expanded definition for this reason:
Wherein, G (T
i) expression T
iHeight value, succ (T
i) expression task T
iSuccessor node set.Two height value H (T of each node among the DAG figure have just been obtained according to formula (2) and (3)
i) and G (T
i), represent respectively minimum height values and maximum height value that each task may obtain.Definition HG (T
i)=random (H (T
i), G (T
i)) be task T
iThe true altitude value, it is between H (T
i) and G (T
i) between random integers.If the height value of the k on the processor core task satisfies HG (T
1)≤HG (T
2)≤... ≤ HG (T
k), then meet the scheduling sequence of this restriction relation for effectively dispatching sequence.
The present invention finds, come the dependence between the statement task not strict with height value, such as, if DAG figure is made of a plurality of disconnected subgraphs, namely there are simultaneously a plurality of incoherent programs to move simultaneously, do not have restriction relation between the task of each subgraph, decide dispatching sequence obviously unreasonable according to height value this moment; For another example, even for two tasks of a subgraph, the task that the task that height value is little and height value are large is not necessarily to have restriction relation yet.The numeral of task next door mark is the height value of this task among Fig. 1 and Fig. 2, and the former is H (T
i), the latter is G (T
i).As seen from Figure 1, T
2Height value be 1, T
5Height value be 2, according to height value definition, T
2Must be at T
5Carry out before, but T in fact
2And T
5Between restriction relation not, as long as T
3Output data after (no matter on which nuclear) is finished are delivered to T
5The processor core at place, T
5Just can carry out T
2Can be at T
5Afterwards operation.Expanded definition G (T
i) do not change the inadequate natural endowment of height value, in Fig. 2, T
2True altitude value HG (T
2) can value be 0,1,2.If HG is (T
2)=0, then T
3With T
8Between all tasks must wait T
2Could move after finishing, in fact except T
7Outer all the other tasks and T
2Do not have any restriction relation, if HG is (T
2)=2, then T
2Must be at T
1, T
3, T
5Could move after finishing, obviously also unreasonable.On the other hand, if two processor cores are arranged, task on each processor core satisfies first order relation, and after not meaning that certain task finishes, the next task that is close on this processor core just can be moved immediately, still will see on other processor core and the task of this task Existence dependency relationship end of run all whether, if also have dependence task not finish, their end of runs and data transmission need equally to wait for, until could start the execution of this task after complete.The present invention proposes to use first order relation matrix to replace the comparison that height value is used for the Task Dependent relation.For DAG figure shown in Figure 1, its first order relation matrix is shown in 4.a.
Wherein, the 1st row table task T
1, the 2nd line display task T
2, the rest may be inferred.Task T is shown in the 1st tabulation
1, task T is shown in the 2nd tabulation
2, the rest may be inferred.Whether a task can be moved, and depends on whether the row at this task place in the task elder generation order relation matrix is 0 or 1 all, does not namely have-1, if having, just illustrates that the predecessor task of this Task Dependent does not also finish.After a tasks carrying was complete, then the row with this task place all were set to 0.From initial matrix 4.a, only has T this moment
1Therefore the capable full 0 at place only has T
1Can move T
1Behind the end of run, with T
1The row at place all set to 0, and shown in 4.b, the first order relation matrix of this moment is except T
1Outward, T
2And T
3The row at place is full 0 or 1 also, and T is described
2And T
3Can bring into operation this moment.
2.2 encoding and decoding structure
Each chromosome represents a solution, and chromosome is carried out the basis that correct coding is genetic algorithm.Coded system is wanted easy to understand and realization efficiently, and improves the algorithm search ability.
This paper uses and the essentially identical integer coding scheme of prior art, and each gene position in the chromosome is an integer, and scope is relevant with quantity and the number of tasks of processor core.Suppose that population scale is popSize, body is exactly a chromosome one by one, represents a kind of feasible scheduling scheme, and namely all task is assigned on the processor core and satisfies restriction relation.Each chromosome coding is divided into two parts, u () and v (), u () represents the dispatching sequence, requires to satisfy the first order relation between the task, which processor core is v () expression task be assigned on, and the length of u () and v () is number of tasks.U (i)=k represents task T
iBe in k position among the dispatching sequence, v (i)=j represents task T
iBe assigned to processor C
jOn.Unlike the prior art be that the present invention stipulates that the dispatching sequence among the u () is the relative order that does not have between two tasks of restriction relation, is partial ordering, rather than the overall situation of mentioning in existing method ordering.If the dispatching sequence among the u () is overall situation ordering, what then generate at random during initialization of population effectively knows from experience seldom, and major part be invalid individuality, in order to generate more effective individuality, has to expend the more time.Such as, for the DAG figure of 10 tasks, if the entrance task only has 1, the effective arrangement probability that then produces at random is less than 1/10, if consider the sequencing of other tasks, actual effective arrangement meeting is still less again.
Decoding is the inverse process of coding, refers to draw Gantt chart according to chromosome.Gantt chart can clearly be given distribution locations and the dispatching sequence who goes out on missions exactly.Decode procedure also will be seen matrix computing time, communication delay matrix and task relational matrix etc. except will seeing chromosome coding information.Fig. 3 has provided a decoding example, can obtain locus and the time sequencing of 8 tasks according to u () and v ().
2.3 the basic procedure of method
In sum, see Fig. 7, a kind of single instrction collection of the present invention heterogeneous multi-core system Static task scheduling method, the method concrete steps are as follows:
Step 1: initialization of population
The generation of genetic algorithm initial population has two kinds of methods usually, and the one, without any condition restriction, generation initial population at random; The 2nd, the generation of population must be satisfied certain requirement, in the generation initial population that satisfies under the prerequisite of these conditions more at random.Select corresponding method according to particular problem.
If n is processor quantity, m is total number of tasks.When the u of chromosome S () part was the overall situation ordering of task, the initialization of population step was as follows:
(1) produces a new chromosome S.
(2) the v () part of initialization chromosome S, each gene position wherein is random number, and type is integer, and span is [0, n-1].
(3) the u () part of initialization chromosome S, value is 1,2 ..., the arrangement of m in view of the problem that overall situation ordering exists, is used partial ordering in u () part here, is used for determining two execution sequences between the task of not having a dependence.Therefore, any one random series all is effectively, does not need to judge whether individuality is effective, and therefore the process of initialization of population becomes simple.
(4) when population scale reaches setting value, withdraw from initialization, otherwise, turn to (1) to continue to produce new individual.
Step 2: calculate fitness value
The regulation goal of realizing is to seek a scheduling strategy, m subtask is assigned on n the processor core, and the execution order of each subtask of reasonable arrangement is so that each subtask is under the constraint of satisfying dependence graph, the deadline of whole task is as far as possible short, and power consumption is as far as possible low.Multi-objective Optimization Genetic Algorithm does not need to arrange weight coefficient as the method for weighting, still calculate like that respectively the fitness value of a plurality of targets with the single goal optimized Genetic Algorithm, adopts the Pareto method to judge whether noninferior solution of a solution.The regulation goal of heterogeneous multi-core system is total task deadline and power consumption, therefore need to calculate simultaneously two fitness values.The calculating of fitness value is to finish on the basis of Gantt chart, and the gunter map generalization also wants and execution time matrix Θ, communication delay matrix Ψ, task allocation matrix Ω, the order relation matrix Λ of task elder generation.
1) the task deadline
Suppose an efficient scheduling strategy S, the task of the m among the T is assigned on n the processor core, so task T
iAt processor core C
jOn execution time satisfy:
Finish(T
i,C
j)=Begin(T
i,C
j)+θ
ij （5）
In the formula (5), Begin (T
i, C
j) and Finish (T
i, C
j) represent respectively task T
iAt processor C
jBeginning on the nuclear carried out constantly and finishes and carry out constantly, supposes task T
k∈ pred (T
i) be assigned to processor core C
rOn.The end that can obtain all tasks according to formula (5) is carried out constantly.Total task deadline under certain scheduling strategy S is the concluding time of last task, makes Γ (S)=max (Finish (T
i, C
j)), one of target of task scheduling is to seek a scheduling strategy S, so that Γ (S) minimum.
2) system energy consumption model
The power consumption of processor core is mainly from three aspects: dynamic power consumption P
Dyn, quiescent dissipation P
StaticWith short-circuit dissipation P
ShortPower consumption when dynamic power consumption works from each element of processor core inside; Quiescent dissipation is the power consumption from sub-threshold current leakage and grid leakage current generation; Short-circuit dissipation is the power consumption that transistor produced in the moment that logic gate is opened.The power consumption of processor core is mainly by P
DynDetermine, account for 70%.Dynamic power consumption is formulated as P
Dyn=KCV
2F, wherein, K is transistorized upset number of times, and C is transistorized loading electric capacity, and f is clock frequency, and V is supply voltage.Along with the development of technique, dynamic power consumption is reducing, so that the quiescent dissipation proportion increases.Each processor core has the in pairs Discrete Finite set of coupling of a voltage and frequency, can estimate the dynamic power consumption P={P of each processor core after frequency and voltage are known
Dyn_0, P
Dyn_1..., P
Dyn_n, according to the general proportions relation of quiescent dissipation and dynamic power consumption, can estimate roughly the quiescent dissipation P={P of each processor core
Static_0, P
Static_1..., P
Static_n, ignore for the time being short-circuit dissipation.After the scheduling sequence was determined, the normal working hours of each processor core and free time had just determined that be T the normal working hours of supposing each processor core
Work={ T
Work_0, T
Work_1..., T
Work_n, free time is T
Idle={ T
Idle_0, T
Idle_1..., T
Idle_n, then finish the energy that whole tasks consume
Two of the target of task scheduling is to seek a scheduling strategy S, so that energy (S) minimum.
Step 3: select the operator operation
Selecting operation is that excellent individual in the population is selected, and worst individual is eliminated, and the selection operation of genetic algorithm just is based on the selection of ideal adaptation degree value, and the individual selected probability that fitness value is large is large, and the probability that the individuality that fitness value is little is eliminated is large.Common system of selection has random ergodic sampling, local selection, algorithm of tournament selection, roulette selection etc.This algorithm uses band to put back to the alternative algorithm of tournament selection method of (with replacement).Idiographic flow is: randomly draw two individualities in elite population, record the wherein high individuality of fitness, and then they all are put back in the elite population, if select N individuality, then repeat N time.
Step 4: crossover operator operation
Crossover operator is in order to enlarge the search volume of algorithm, to avoid algorithm to converge on prematurely certain locally optimal solution, preventing precocity.Be used for the crossover operator of task scheduling, guaranteeing that task-set does not increase not subtract, will guarantee also that simultaneously scheduling sequence behind the crossing operation still satisfies the first order relation between the task.
The present invention proposes crossover operator and only acts on chromosomal v () part, u () part no longer changes after initialization of population, reason is that the sequencing between the task guarantees by task elder generation order relation matrix that mainly the sequencing of u () part definition is a kind of replenishing.Specific algorithm is as follows:
(1) from population, selects at random individual S;
(2) from individual S, select at random two tasks, T
xAnd T
y
(3) if task T
xAnd T
yThe processor core at place is different, and namely v (x) ≠ v (y) then intersects,
Otherwise, directly change (4) over to;
(4) withdraw from crossing operation.
Step 5: mutation operator operation
In the heterogeneous multi-nucleus processor task is distributed, can not adopt traditional random variation operation, mutation operator must guarantee total task number and kind is constant, the scope of processor core is also constant.The mutation operator here limits and only acts on the v (), is equivalent to task immigration.Specific algorithm is as follows:
(1) from population, selects at random individual S;
(2) from the v () of individual S, select at random 1 gene position i;
(3) produce at random an integer m ∈ [0, N-1], wherein N is the quantity of processor core;
(4) make v ()=m;
(5) withdraw from the variation computing.
3, advantage and effect:
The present invention uses partial ordering's sign without the execution sequence of two tasks of dependence, initialization of population efficient and effective individuality are improved greatly, with the execution sequence that first order relation matrix sets the tasks, overcome the wretched insufficiency that traditional height value method exists.This method can enlarge the optimum individual hunting zone, when population scale is enough large, and the part optimum solution that can find the height value method to miss, thus obtain more excellent scheduling sequence.Thereby the deadline that makes whole task-set is shorter, power consumption is lower.
Description of drawings
Fig. 1 directed acyclic synoptic diagram 1
Fig. 2 directed acyclic synoptic diagram 2
Fig. 3 chromosome encoding and decoding synoptic diagram
Fig. 4 elder generation's order relation matrix and height value method dispatching sequence be synoptic diagram relatively
0 task of Figure 53,4 nuclear Pareto forward position synoptic diagram
0 task of Figure 63,8 nuclear Pareto forward position synoptic diagram
Fig. 7 FB(flow block) of the present invention
Symbol description is as follows among the figure:
T
1---expression task 1
T
2---expression task 2
T
3---expression task 3
T
4---expression task 4
T
5---expression task 5
T
6---expression task 6
T
7---expression task 7
T
8---expression task 8
Embodiment
The result difference that uses first order relation matrix and use height value method to cause is described below by two examples.
Example 1:
Can see T from DAG figure shown in Figure 1
2Height value be 1, T
5Height value be 2, according to height value definition, T
2Must be at T
5Carry out, in fact, this constraint condition is dispensable before, as can be seen from Figure 1, and T
2And T
5Between restriction relation not, as long as T
3Output data after (no matter on which nuclear) is finished are delivered to T
5The processor core at place, T
5Just can carry out T
2Can be at T
5Afterwards operation.Same reason is among the DAG figure shown in Figure 2, if use height value, then T
2Height value be 0, T
3With T
5Height value be 1, T then
2Must be at T
5Finish, in fact, this constraint condition also is unnecessary, T before
2In the process of implementation, T
3With T
5Wait in vain, in order to make way for the T on another processor core
4Start as early as possible operation, should allow T
3Prior to T
2Operation.The execution time of supposing all tasks is identical, ignore transmission delay, according to colored graph coding shown in Figure 3, can draw based on the Gantt chart of height value method with based on the Gantt chart of first order relation matrix, as shown in Figure 4, can find out, be smaller than scheduling length based on height value based on the scheduling length of first order relation matrix.Reason is, for some DAG figure, the height value method may be missed some legal solutions, the Xie Gengyou that may obtain than height value method that has in these legal solutions, certainly, also might be poorer than the solution that height value method obtains.DAG figure task quantity illustrated in figures 1 and 2 is few, and the execution time of supposing all tasks is identical and ignore transmission delay, so that can be easy to draw Gantt chart, when task quantity more and task execution time is different, when transmission delay can not be ignored, just need to be by having calculated.
Example 2:
The effect of multi-objective Optimization Genetic Algorithm is carried out emulation testing when more to number of tasks, has realized this algorithm algorithm with the C language.Generate at random DAG figure and the task association attributes of 30 tasks.The configuration of processor core is made as two kinds, 4 nuclears (3 slowcores of 1 fast nuclear) and 8 nuclears (6 slowcores of 2 fast nuclear), and wherein, the dominant frequency of fast nuclear is the twice of slowcore.When the program operation is arranged, the power consumption of processor core mainly is dynamic power consumption, relevant with dominant frequency and voltage, the power consumption of approximate estimation slowcore is 2 energy consumption units, the power consumption of fast nuclear is 5 energy consumption units (are approximately slowcore 2.5 times), and when suppose not have the program operation, the power consumption of examining soon is 1 energy consumption unit, the power consumption of slowcore is 0.5 energy consumption unit, the quiescent dissipation when being mainly used in calculating fast nuclear or slowcore idle waiting.Population quantity is defined as 400, and wherein elite's individual amount is 80(20%*400), all the other are that non-elite is individual, quantity is 320(80%*400), iterations is 1000, the variation probability is 0.25, because crossover and mutation all is the position of change task, can not carry out crossing operation.
See Fig. 7, the present invention proposes the Static task scheduling method based on the excellent optimized Genetic Algorithm of multiple goal towards single instrction collection heterogeneous multi-core system, and the method concrete steps are as follows:
Step 1: initialization of population
The generation of genetic algorithm initial population has two kinds of methods usually, and the one, without any condition restriction, generation initial population at random; The 2nd, the generation of population must be satisfied certain requirement, in the generation initial population that satisfies under the prerequisite of these conditions more at random.Select corresponding method according to particular problem.
If n is processor quantity, m is total number of tasks.When the u of chromosome S () part was the overall situation ordering of task, the initialization of population step was as follows:
(1) produces a new chromosome S.
(2) the v () part of initialization chromosome S, each gene position wherein is random number, and type is integer, and span is [0, n-1].
(3) the u () part of initialization chromosome S, value is 1,2 ..., the arrangement of m in view of the problem that overall situation ordering exists, is used partial ordering in u () part here, is used for determining two execution sequences between the task of not having a dependence.Therefore, any one random series all is effectively, does not need to judge whether individuality is effective, and therefore the process of initialization of population becomes simple.
(4) when population scale reaches setting value, withdraw from initialization, otherwise, turn to (1) to continue to produce new individual.
Step 2: calculate fitness value
The regulation goal of realizing is to seek a scheduling strategy, m subtask is assigned on n the processor core, and the execution order of each subtask of reasonable arrangement is so that each subtask is under the constraint of satisfying dependence graph, the deadline of whole task is as far as possible short, and power consumption is as far as possible low.Multi-objective Optimization Genetic Algorithm does not need to arrange weight coefficient as the method for weighting, still calculate like that respectively the fitness value of a plurality of targets with the single goal optimized Genetic Algorithm, adopts the Pareto method to judge whether noninferior solution of a solution.The regulation goal of heterogeneous multi-core system is total task deadline and power consumption, therefore need to calculate simultaneously two fitness values.The calculating of fitness value is to finish on the basis of Gantt chart, and the gunter map generalization also wants and execution time matrix Θ, communication delay matrix Ψ, task allocation matrix Ω, the order relation matrix Λ of task elder generation.
1) the task deadline
Suppose an efficient scheduling strategy S, the task of the m among the T is assigned on n the processor core, so task T
iAt processor core C
jOn execution time satisfy:
Finish(T
i,C
j)=Begin(T
i,C
j)+θ
ij （5）
In the formula (5), Begin (T
i, C
j) and Finish (T
i, C
j) represent respectively task T
iAt processor C
jBeginning on the nuclear carried out constantly and finishes and carry out constantly, supposes task T
k∈ pred (T
i) be assigned to processor core C
rOn.The end that can obtain all tasks according to formula (5) is carried out constantly.Total task deadline under certain scheduling strategy S is the concluding time of last task, makes Γ (S)=max (Finish (T
i, C
j)), one of target of task scheduling is to seek a scheduling strategy S, so that Γ (S) minimum.
2) system energy consumption model
The power consumption of processor core is mainly from three aspects: dynamic power consumption P
Dyn, quiescent dissipation P
StaticWith short-circuit dissipation P
ShortPower consumption when dynamic power consumption works from each element of processor core inside; Quiescent dissipation is the power consumption from sub-threshold current leakage and grid leakage current generation; Short-circuit dissipation is the power consumption that transistor produced in the moment that logic gate is opened.The power consumption of processor core is mainly by P
DynDetermine, account for 70%.Dynamic power consumption is formulated as P
Dyn=KCV
2F, wherein, K is transistorized upset number of times, and C is transistorized loading electric capacity, and f is clock frequency, and V is supply voltage.Along with the development of technique, dynamic power consumption is reducing, so that the quiescent dissipation proportion increases.Each processor core has the in pairs Discrete Finite set of coupling of a voltage and frequency, can estimate the dynamic power consumption P={P of each processor core after frequency and voltage are known
Dyn_0, P
Dyn_1..., P
Dyn_n, according to the general proportions relation of quiescent dissipation and dynamic power consumption, can estimate roughly the quiescent dissipation P={P of each processor core
Static_0, P
Static_1..., P
Static_n, ignore for the time being short-circuit dissipation.After the scheduling sequence was determined, the normal working hours of each processor core and free time had just determined that be T the normal working hours of supposing each processor core
Work={ T
Work_0, T
Work_1..., T
Work_n, free time is T
Idle={ T
Idle_0, T
Idle_1..., T
Idle_n, then finish the energy that whole tasks consume
Two of the target of task scheduling is to seek a scheduling strategy S, so that energy (S) minimum.
Step 3: select the operator operation
Selecting operation is that excellent individual in the population is selected, and worst individual is eliminated, and the selection operation of genetic algorithm just is based on the selection of ideal adaptation degree value, and the individual selected probability that fitness value is large is large, and the probability that the individuality that fitness value is little is eliminated is large.Common system of selection has random ergodic sampling, local selection, algorithm of tournament selection, roulette selection etc.This algorithm uses band to put back to the alternative algorithm of tournament selection method of (with replacement).Idiographic flow is: randomly draw two individualities in elite population, record the wherein high individuality of fitness, and then they all are put back in the elite population, if select N individuality, then repeat N time.
Step 4: crossover operator operation
Crossover operator is in order to enlarge the search volume of algorithm, to avoid algorithm to converge on prematurely certain locally optimal solution, preventing precocity.Be used for the crossover operator of task scheduling, guaranteeing that task-set does not increase not subtract, will guarantee also that simultaneously scheduling sequence behind the crossing operation still satisfies the first order relation between the task.
The present invention proposes crossover operator and only acts on chromosomal v () part, u () part no longer changes after initialization of population, reason is that the sequencing between the task guarantees by task elder generation order relation matrix that mainly the sequencing of u () part definition is a kind of replenishing.Specific algorithm is as follows:
(1) from population, selects at random individual S;
(2) from individual S, select at random two tasks, T
xAnd T
y
(3) if task T
xAnd T
yThe processor core at place is different, and namely v (x) ≠ v (y) then intersects,
Otherwise, directly change (4) over to;
(4) withdraw from crossing operation.
Step 5: mutation operator operation
In the heterogeneous multi-nucleus processor task is distributed, can not adopt traditional random variation operation, mutation operator must guarantee total task number and kind is constant, the scope of processor core is also constant.The mutation operator here limits and only acts on the v (), is equivalent to task immigration.Specific algorithm is as follows:
(1) from population, selects at random individual S;
(2) from the v () of individual S, select at random 1 gene position i;
(3) produce at random an integer m ∈ [0, N-1], wherein N is the quantity of processor core;
(4) make v ()=m;
(5) withdraw from the variation computing.
By computing, obtained the Pareto forward position of 8 processor cores of 4 processor core nuclear, extremely shown in Figure 6 such as Fig. 5, each solution that is positioned at the Pareto forward position is optimum solution, can see that the Pareto optimum solution major part that obtains based on first order relation matrix method all is positioned at the lower-left side of the Pareto optimum solution that obtains based on the height value method.If one is separated S
1Be positioned at another and separate S
2The lower-left side, scheduling scheme S is described
1Energy consumption and the deadline all than scheduling scheme S
2Little, as to be dominant according to Pareto conceptual illustration S
1Be better than S
2This explanation can be found more excellent scheduling sequence based on the method for matrix, thereby can shorten the deadline of whole task, reduces simultaneously power consumption.
Claims (1)
1. single instrction collection heterogeneous multi-core system Static task scheduling method, it is characterized in that: the method concrete steps are as follows: step 1: initialization of population
The generation of genetic algorithm initial population has two kinds of methods, and the one, without any condition restriction, generation initial population at random; The 2nd, the generation of population must be satisfied certain requirement, in the generation initial population that satisfies under the prerequisite of these conditions more at random; Select corresponding method according to particular problem;
If n is processor quantity, m is total number of tasks, and when the u of chromosome S () part was the overall situation ordering of task, the initialization of population step was as follows:
(1) produces a new chromosome S;
(2) the v () part of initialization chromosome S, each gene position wherein is random number, and type is integer, and span is [0, n-1];
(3) the u () part of initialization chromosome S, value is 1,2 ..., the arrangement of m in view of the problem that overall situation ordering exists, is used partial ordering in u () part here, is used for determining two execution sequences between the task of not having a dependence; Therefore, any one random series all is effectively, does not need to judge whether individuality is effective, and therefore the process of initialization of population becomes simple;
(4) when population scale reaches setting value, withdraw from initialization, otherwise, turn to (1) to continue to produce new individual;
Step 2: calculate fitness value
The regulation goal of realizing is to seek a scheduling strategy, m subtask is assigned on n the processor core, and the execution order of each subtask of reasonable arrangement is so that each subtask is under the constraint of satisfying dependence graph, the deadline of whole task is as far as possible short, and power consumption is as far as possible low; Multi-objective Optimization Genetic Algorithm does not need to arrange weight coefficient as the method for weighting, still calculate like that respectively the fitness value of a plurality of targets with the single goal optimized Genetic Algorithm, adopts the Pareto method to judge whether noninferior solution of a solution; The regulation goal of heterogeneous multi-core system is total task deadline and power consumption, therefore need to calculate simultaneously two fitness values; The calculating of fitness value is to finish on the basis of Gantt chart, and the gunter map generalization also wants and execution time matrix Θ, communication delay matrix Ψ, task allocation matrix Ω, the order relation matrix Λ of task elder generation;
1) the task deadline
Suppose an efficient scheduling strategy S, the task of the m among the T is assigned on n the processor core, so task T
iAt processor core C
jOn execution time satisfy:
Finish(T
i,C
j)=Begin(T
i,C
j)+θ
ij （5）
In the formula (5), Begin (T
i, C
j) and Finish (T
i, C
j) represent respectively task T
iAt processor C
jBeginning on the nuclear carried out constantly and finishes and carry out constantly, supposes task T
k∈ pred (T
i) be assigned to processor core C
rOn; The end that obtains all tasks according to formula (5) is carried out constantly; Total task deadline under certain scheduling strategy S is the concluding time of last task, makes Γ (S)=max (Finish (T
i, C
j)), one of target of task scheduling is to seek a scheduling strategy S, so that Γ (S) minimum;
2) system energy consumption model
The power consumption of processor core is mainly from three aspects: dynamic power consumption P
Dyn, quiescent dissipation P
StaticWith short-circuit dissipation P
ShortPower consumption when dynamic power consumption works from each element of processor core inside; Quiescent dissipation is the power consumption from sub-threshold current leakage and grid leakage current generation; Short-circuit dissipation is the power consumption that transistor produced in the moment that logic gate is opened; The power consumption of processor core is mainly by P
DynDetermine that account for 70%, dynamic power consumption is formulated as P
Dyn=KCV
2F, wherein, K is transistorized upset number of times, and C is transistorized loading electric capacity, and f is clock frequency, and V is supply voltage; Along with the development of technique, dynamic power consumption is reducing, so that the quiescent dissipation proportion increases; Each processor core has the in pairs Discrete Finite set of coupling of a voltage and frequency, estimates the dynamic power consumption P={P of each processor core after frequency and voltage are known
Dyn_0, P
Dyn_1..., P
Dyn_n, according to the general proportions relation of quiescent dissipation and dynamic power consumption, estimate roughly the quiescent dissipation P={P of each processor core
Static_0, P
Static_1..., P
Static_n, ignore for the time being short-circuit dissipation; After the scheduling sequence was determined, the normal working hours of each processor core and free time had just determined that be T the normal working hours of supposing each processor core
Work={ T
Work_0, T
Work_1..., T
Work_n, free time is T
Idle={ T
Idle_0, T
Idle_1..., T
Idle_n, then finish the energy that whole tasks consume
Two of the target of task scheduling is to seek a scheduling strategy S, so that energy (S) minimum;
Step 3: select the operator operation
Selecting operation is that excellent individual in the population is selected, and worst individual is eliminated, and the selection operation of genetic algorithm just is based on the selection of ideal adaptation degree value, and the individual selected probability that fitness value is large is large, and the probability that the individuality that fitness value is little is eliminated is large; Common system of selection has random ergodic sampling, local selection, algorithm of tournament selection, roulette to select; Here using band to put back to is the alternative algorithm of tournament selection method of with replacement; Idiographic flow is: randomly draw two individualities in elite population, record the wherein high individuality of fitness, and then they all are put back in the elite population, if select N individuality, then repeat N time;
Step 4: crossover operator operation
Crossover operator is in order to enlarge the search volume of algorithm, to avoid algorithm to converge on prematurely certain locally optimal solution, preventing precocity; Be used for the crossover operator of task scheduling, guaranteeing that task-set does not increase not subtract, will guarantee also that simultaneously scheduling sequence behind the crossing operation still satisfies the first order relation between the task;
Propose crossover operator and only act on chromosomal v () part, u () part no longer changes after initialization of population, reason is that the sequencing between the task guarantees that by task elder generation order relation matrix the sequencing of u () part definition is a kind of replenishing; Specific algorithm is as follows:
(1) from population, selects at random individual S;
(2) from individual S, select at random two tasks, T
xAnd T
y
(3) if task T
xAnd T
yThe processor core at place is different, and namely v (x) ≠ v (y) then intersects,
Otherwise, directly change (4) over to;
(4) withdraw from crossing operation;
Step 5: mutation operator operation
In the heterogeneous multi-nucleus processor task is distributed, can not adopt traditional random variation operation, mutation operator must guarantee total task number and kind is constant, the scope of processor core is also constant; The mutation operator here limits and only acts on the v (), is equivalent to task immigration; Specific algorithm is as follows:
(1) from population, selects at random individual S;
(2) from the v () of individual S, select at random 1 gene position i;
(3) produce at random an integer m ∈ [0, N-1], wherein N is the quantity of processor core;
(4) make v ()=m;
(5) withdraw from the variation computing.
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