CN107704319A - Improve the CMP method for scheduling task of fireworks algorithm - Google Patents
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Abstract
The invention discloses the CMP method for scheduling task for improving fireworks algorithm, belong to field of computer architecture.Specific steps include：Set initial parameter；The position vector of N number of fireworks is generated at random；Calculate the explosive spark quantity, blast amplitude and fitness value of fireworks；Carry out blast operations and Gaussian mutation operation；Optimal task schedule sequence is exported after iterating.The present invention introduces repulsion operator in fireworks algorithm；Meanwhile apply nonlinear inertial weight factor on the dimension for repelling operation；The encoding scheme of use retains the characteristics of fireworks position is multi-C vector, only redefines the implication and span of every one-dimensional representation.The present invention ensures that spark caused by fireworks is effective, is advantageous to the optimizing that the algorithm iteration later stage carries out careful property near optimal value, and coding is convenient, efficiently, and the higher solution of precision can be found in shorter time, effectively increases the execution efficiency of task under CMP architecture.
Description
Technical Field
The invention belongs to the field of computer architecture structures, and particularly relates to a CMP task scheduling method for improving a firework algorithm.
Background
Due to the influence of hardware resource sharing among kernels and dependency among tasks, the dependent CMP task scheduling is easy to generate resource contention, the throughput rate of the multi-core processor is reduced, and the parallelism and the high efficiency are not effectively exerted.
The CMP task scheduling problem is a type of NP-complete combinatorial optimization problem. At present, a Genetic Algorithm (GA) is a combinatorial optimization Algorithm which is applied to a task scheduling problem more, but the Genetic Algorithm is easy to be premature, and due to complex cross mutation operation, the time complexity and the execution efficiency of the Algorithm are easily affected by the number of tasks, so that the task scheduling result cannot meet the actual requirement.
The firework Algorithm (FWA) is a novel group intelligent optimization Algorithm proposed by martin in 2010. The firework algorithm shows good performance characteristics in solving a global optimal solution of a complex problem, has low limitation on the solved problem, and is suitable for a combined optimization problem.
As the firework algorithm is limited by the number and the amplitude of explosion when the fireworks explode, and the number of the explosion sparks of the fireworks with the best fitness value is large but the amplitude is too small, the distance between the generated sparks and the fireworks is too close or even overlapped, so that the sparks are invalid, the computing resources are wasted, and the operation efficiency of the algorithm is limited.
Disclosure of Invention
The invention aims to provide a CMP task scheduling method for improving a firework algorithm, which improves the efficiency of task scheduling under a CMP framework and ensures the effectiveness of sparks generated by fireworks.
The purpose of the invention is realized by the following technical scheme:
the CMP task scheduling method for improving the firework algorithm comprises the following steps:
(1) setting the number N of fireworks, the number of basic explosion sparks, the basic explosion radius, the rejection operation defining distance, the initial value of the action dimension of the rejection operation, the maximum iteration number and an initial DAG (direct current) graph;
(2) randomly generating position vectors of N fireworks according to the coding scheme of the invention;
(3) calculating the number of explosion sparks, the explosion amplitude and the fitness value of the fireworks;
(4) carrying out explosion operation and Gaussian variation operation to generate explosion sparks and Gaussian variation sparks, and mapping sparks exceeding the range of the feasible region back to the feasible region;
(5) judging whether the sparks generated by the fireworks with the optimal fitness values need to be subjected to repulsion operation, if so, turning to step ⑥, and if not, turning to step (7);
(6) randomly selecting the dimension of the sparks to perform exclusion operation, and mapping the sparks into a feasible domain if the excluded sparks exceed the feasible domain range;
(7) calculating the fitness values of the explosion sparks and the Gaussian variation sparks;
(8) reserving the fireworks or sparks with the best fitness value to the next generation, and selecting the rest N-1 fireworks according to the roulette rule based on the Euclidean distance;
(9) if the algorithm termination condition is met, the maximum iteration times are reached, if the maximum iteration times are met, an optimal task scheduling sequence is output, and the algorithm is stopped; if not, go to step (3).
In particular, it is possible to use, for example,
the coding mode is as follows: the encoding preserves the feature that the position of each firework is a multi-dimensional vector, and only redefines the meaning represented by each dimension. By XiA position vector representing fireworks i, namely: xi＝[x1,x2,…,xj,…,xm]Wherein x isjRand (1, n), n representing the number of processor cores, rand (1, n) representing randomly taking integer values between 1 and n; m denotes the number of tasks, xjIndicates that the jth task is assigned to xjExecuting on the processor core. The coding mode ensures that one task can be only distributed to one processor core to execute, and each processor core can process a plurality of tasks.
The exclusion operation method comprises the following steps: the rejection operation is carried out when the distance between the firework with the best fitness value and the spark generated by the firework is smaller than an acceptable range:whereinThe k-th dimension value of the position vector representing the spark generated by the firework i,the k-dimension value of the spark position vector after the exclusion action is obtained, the Delta s is an exclusion operator, and the exclusion operator value applied to the CMP task scheduling is as follows in consideration of the characteristics of the CMP task scheduling: Δ s ═ rand (0, n-1), where n denotes the number of processor cores, and rand (0, n-1) is a function of randomly chosen integers between 0 and n-1.
The iterative method of the exclusion operation action dimension z is as follows: z (t) w z (t-1), where z (t) represents the value of the action dimension of the t-th iteration exclusion operation, z (t-1) represents the value of the action dimension of the t-1-th iteration exclusion operation, and w is a non-linear inertia weight value that decreases as the number of iterations t increases, such that: w (t) ═ 1/2tWhere w (t) is the value of w for the tth iteration.
The invention has the beneficial effects that:
the characteristics of high convergence speed and high solving precision of the basic firework algorithm are fully utilized, and the exclusion operator is introduced into the basic firework algorithm to perform exclusion operation on the fireworks with the best fitness value, so that the waste of computing resources caused by the fact that the distance between the generated sparks and the fireworks is too close or overlapped and no practical significance is caused is avoided; and a nonlinear inertia weight factor is added on the dimension of the exclusion operator action, so that the global exploration capability of the algorithm at the initial stage of iteration is enhanced, and the detailed optimization capability of the algorithm at the later stage of iteration is enhanced.
Drawings
FIG. 1 is a DAG diagram of the example one;
FIG. 2 is a schematic diagram of a scheduling process of the first embodiment;
FIG. 3 is a schematic diagram of an optimized scheduling process of the example;
FIG. 4 is a flow chart of the present invention;
Detailed Description
The following further describes embodiments of the present invention with reference to the accompanying drawings:
the invention improves the firework algorithm and applies the improved firework algorithm to the task scheduling problem under the CMP architecture. The method comprises the steps of firstly, rejecting fireworks with optimal fitness values of each generation in a firework algorithm to ensure that sparks generated by the fireworks are effective and avoid computing resource waste caused by spark failure; meanwhile, a nonlinear inertia weight factor is applied to the dimension of the exclusion operation, so that the algorithm has stronger global exploration capability at the initial stage of iteration and can perform detailed optimization at the later stage of iteration.
The present invention will be described in detail with reference to fig. 1 to 4.
1. CMP task scheduling definitions
The CMP task scheduling problem is to schedule tasks on different cores according to an algorithm and to minimize the time it takes to execute a complete task.
The CMP task scheduling problem may be represented by the triplet Π ═ (P, G, PT). Where P is the set of processor cores. G is a Directed Acyclic Graph (DAG) in Graph theory, and represents tasks and dependencies between tasks. PT is a matrix representing the computational overhead of different tasks on different processor cores, PTipIs task TiOverhead is calculated on the processor core p.
A DAG graph representing tasks and dependencies between tasks may be represented by a triplet G ═ (V, S, W), where the meaning of each variable is:
(1) v represents the set of vertices of the DAG graph, consisting of all tasks that the processor needs to complete. Ith task TiCorresponding to vertex V in DAG graphi；
(2) S represents the edge set of the DAG graph and consists of communication relations among tasks, if the task T isiAnd TjHas a communication relationship therebetween, and TiIs TjIf there is an edge S in the corresponding DAG graphijIn the direction of the arrow on the side ViPoint of direction Vj；
(3) W is a set of weight values on edges of the DAG graph, W ═ Wi1,Wi2,…,Wij,…,WinWhere m denotes the number of tasks with scheduling, WijRepresenting a task TiAnd its predecessor task TjThe overhead of communication between. When the task i and the task j are distributed to the same core to execute, the communication overhead is 0.
The CMP task scheduling problem applicable to the invention requires that a standard DAG graph is adopted to represent tasks and the dependency relationship among the tasks, namely the DAG graph is required to have a unique inlet node and a unique outlet node. FIG. 1 is one of the present inventionExample of task scheduling model, T1Being a unique entry node, T9For the only egress node, the computation overhead matrix PT of the 4 tasks on the 3 processor cores in this example is:
dependent task scheduling problem requires task TiCan only start to execute T after all the precursor tasks are executediThen, in a set of task schedules, task TiThe time required for completion of execution is exe [ T ]i]The calculation method comprises the following steps:
exe[Ti]＝Wij+PTip+max{exe[Tj]}
Tj∈pre(Ti)
wherein pre (T)i) Representing a task TiSet of predecessor tasks of, WijRepresenting a task TiAnd task TjCommunication overhead, PTipFor task TiComputation overhead on processor core p, max { exe [ T ]j]Is task TiThe predecessor tasks of (1) are all executed for the elapsed time.
The mathematical definition of the CMP task scheduling problem that is dependent is: TS ═ min { exe [ T [ ]last]}
Wherein exe [ Tlast]The time it takes for the last task to finish execution, and TS is the task scheduling length, i.e., the time it takes for all tasks to finish execution.
2. Fitness value
The task scheduling method provided by the invention reserves the characteristic that the firework algorithm evaluates the quality of fireworks or sparks according to the size of the fitness value. The firework with good quality has small adaptability value; the firework with poor quality has a large adaptability value.
The size of the task scheduling length TS is defined as the size of the fitness value. When the TS is larger and the time for completing the execution of all tasks is longer, the quality of the fireworks is worse; on the contrary, when the TS is smaller and the time for completing the execution of all tasks is shorter, the quality of the fireworks is better.
The fitness value function is:
f(Xi)＝TS(Xi)
wherein
3. Position updating scheme introducing exclusion operator
The basic firework algorithm shows good optimizing capability in various combined optimization problems, but the explosion radius of the firework with the best adaptability value is very small and even 0, so that the generated sparks lose the actual value, the calculation resources of the algorithm are wasted, and the algorithm is easy to fall into the local optimal solution.
In order to avoid the adverse effect generated by the characteristic of the firework algorithm, the invention introduces a repulsion operator to correct the position of the spark, and the repulsion effect is effective when the distance between the firework i and the spark generated by the firework i is not within an acceptable range.
The distance between the fireworks and the sparks generated by the fireworks is measured by Euclidean distance, and the conditions for carrying out the repelling operation are as follows:
wherein XiIndicating the position vector, X, of the fireworks ihThe position vector of the sparks h generated by the fireworks i is represented and deltar represents the minimum acceptable distance of the fireworks i from the sparks h generated thereby.
The exclusion operation method comprises the following steps:
whereinThe value of the kth dimension of the position vector representing the spark h,is the value of the k-dimension of the position vector of the spark h after the repulsion operation, and Δ s is the repulsion operator.
Considering the characteristics of CMP task scheduling, the value of the exclusion operator is as follows: Δ s ═ rand (0, n-1)
Where n represents the number of processor cores and rand (0, n-1) is a function of randomly chosen integers between 0 and n-1.
The exclusion operator does not exclude all dimensions of the firework, only z dimensions are randomly selected for exclusion operation, and z satisfies the following conditions: z (t) ═ w x z (t-1)
Wherein z (t) represents the value of t iteration exclusion operation action dimension z, z (t-1) represents the value of t-1 iteration exclusion operation action dimension z, w is a nonlinear inertia weight value which decreases with the increase of the iteration number t, and the following conditions are met: w (t) ═ 1/2tWhere w (t) is the value of w for the tth iteration.
The value of the nonlinear inertia weight value w at the initial stage of iteration is relatively large, so that global search of a firework algorithm in a large space is facilitated; the value at the later stage of iteration is relatively small, which is beneficial to the algorithm to carry out more detailed optimization near the current optimal value.
4. Encoding strategy
In order to make the firework algorithm with the continuous solution space suitable for the discrete CMP task scheduling problem, the method encodes fireworks.
The encoding scheme described allows each firework or spark in the population to represent one possible task scheduling sequence.
The coding scheme numbers the processor cores: 1,2,. ang, n; and numbers the tasks to be processed 1, 2.
The position vector X of the fireworks or sparks iiCan be expressed as:
Xi＝[x1,x2,…,xj,…,xm]
xj＝rand(1,n)
where n represents the number of processor cores, and rand (1, n) represents a random integer value between 1 and n; m denotes the number of tasks, xjIndicates that the jth task is assigned to xjExecuting on the processor core.
The coding scheme adopted by the invention has four characteristics:
(1) the coding mode is simple and clear, and easy to understand and realize;
(2) the requirement of task scheduling problem is met;
(3) all possible task scheduling schemes are included;
(4) and realizing unique mapping of the position vector of the fireworks or sparks and the task scheduling sequence.
The displacement operation of the CMP task scheduling method implemented by the present invention is: x is the number ofj＝xj+rand(0,Ri)
Wherein xjIndicates that the jth thread is assigned to xjRun on processor core, rand (1, R)i) Is represented by 1 to RiBetween randomly taking an integer value, RiIs the detonation radius of the firework i.
The mapping rule of the CMP task scheduling method realized by the invention is as follows: x is the number ofj＝1+xj% (n-1) wherein xjIndicates that the jth thread is assigned to xjExecuting on the processor core, and n represents the number of processor cores.
The exclusive operation method of the CMP task scheduling method realized by the invention comprises the following steps: x is the number ofj＝xj+ Δ s, where xjDenotes the jth lineThe program is allocated to xjExecuting on the processor core, Δ s is the exclusion operator.
Example one:
according to the encoding method of the present invention, one possible scheduling scheme of the first embodiment is: as shown in fig. 2, the computation overhead matrix in conjunction with the first example can calculate the total task execution completion time of the scheduling sequence to be 33.
In the first example, the only optimal scheduling sequence obtained after the loop iteration of the CMP task scheduling method of the present invention may be X ═ 3,1,1,2, and the execution completion time of all threads of the scheduling sequence obtained according to the calculation overhead matrix of the first example is 10, which is 23 units less than the time taken for the scheduling sequence to execute all threads shown in fig. 2.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. The CMP task scheduling method for improving the firework algorithm is characterized by comprising the following steps of:
(1) setting the number N of fireworks, the number of basic explosion sparks, the basic explosion radius, the rejection operation defining distance, the initial value of the action dimension of the rejection operation, the maximum iteration number and an initial DAG (direct current) graph;
(2) randomly generating position vectors of N fireworks according to the coding mode;
(3) calculating the number of explosion sparks, the explosion amplitude and the fitness value of the fireworks;
(4) carrying out explosion operation and Gaussian variation operation to generate explosion sparks and Gaussian variation sparks, and mapping sparks exceeding the range of the feasible region back to the feasible region;
(5) judging whether the sparks generated by the fireworks with the optimal fitness values need to be subjected to repulsion operation, if so, turning to step ⑥, and if not, turning to step (7);
(6) randomly selecting the dimension of the sparks to perform exclusion operation, and mapping the sparks into a feasible domain if the excluded sparks exceed the feasible domain range;
(7) calculating the fitness values of the explosion sparks and the Gaussian variation sparks;
(8) reserving the fireworks or sparks with the best fitness value to the next generation, and selecting the rest N-1 fireworks according to the roulette rule based on the Euclidean distance;
(9) if the algorithm termination condition is met, the maximum iteration times are reached, if the maximum iteration times are met, an optimal task scheduling sequence is output, and the algorithm is stopped; if not, go to step (3).
2. The CMP task scheduling method for improving fireworks algorithm according to claim 1, characterized in that: the encoding mode of the step (2) is as follows:
the coding keeps the characteristic that the position of each firework is a multi-dimensional vector, and only the meaning represented by each dimension is redefined;
by XiA position vector representing fireworks i, namely: xi＝[x1,x2,…,xj,…,xm]、xjRand (1, n), where n denotes the number of processor cores, and rand (1, n) denotes randomly taking an integer value between 1 and n; m denotes the number of tasks, xjIndicates that the jth task is assigned to xjExecuting on the processor core.
3. The CMP task scheduling method for improving fireworks algorithm according to claim 1, characterized in that: the exclusion operation method in step (6) is as follows:
the rejection operation is carried out when the distance between the firework with the best fitness value and the spark generated by the firework is smaller than an acceptable range:
<mrow> <msubsup> <mi>X</mi> <mi>h</mi> <mrow> <mo>&prime;</mo> <mi>k</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>X</mi> <mi>h</mi> <mi>k</mi> </msubsup> <mo>+</mo> <mi>&Delta;</mi> <mi>s</mi> <mo>,</mo> </mrow>
wherein,the k-th dimension value of the position vector representing the spark generated by the firework i,is the k-dimension value of the spark position vector after repulsion, and deltas is a repulsion operator;
considering the characteristics of CMP task scheduling, the value of the exclusion operator applied to the CMP task scheduling is as follows:
Δs＝rand(0,n-1)，
where n represents the number of processor cores and rand (0, n-1) is a function of randomly chosen integers between 0 and n-1.
4. The CMP task scheduling method for improving the firework algorithm as claimed in claims 1 and 3, wherein: the iterative method of the exclusion operation action dimension z in the step (6) comprises the following steps:
z(t)＝w*z(t-1)，
wherein z (t) represents the value of action dimension of the t-th iteration exclusion operation, z (t-1) represents the value of action dimension of the t-1-th iteration exclusion operation, and w is a nonlinear inertia weight value which decreases with the increase of the iteration times t, and satisfies the following conditions: w (t) ═ 1/2tWhere w (t) is the value of w for the tth iteration.
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| CN109858617A (en) * | 2019-02-20 | 2019-06-07 | 哈尔滨工程大学 | A kind of fireworks calculation method optimizing initialization mode |
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| CN110533152A (en) * | 2019-08-12 | 2019-12-03 | 哈尔滨工程大学 | A kind of method for scheduling task based on improvement fireworks algorithm under CMP architecture |
| US20210373946A1 (en) * | 2019-09-23 | 2021-12-02 | Soochow University | Method for scheduling of service processes in hybrid cloud |
| CN111124633A (en) * | 2019-12-06 | 2020-05-08 | 上海交通大学 | Earth-moon relay satellite task scheduling method considering storage limit of detector |
| CN111124633B (en) * | 2019-12-06 | 2023-05-30 | 上海交通大学 | Ground-month relay satellite task scheduling method considering detector storage limit |
| CN112257297A (en) * | 2020-11-27 | 2021-01-22 | 西南交通大学 | Welding shop comprehensive scheduling method based on improved firework algorithm |
| CN112257297B (en) * | 2020-11-27 | 2021-06-25 | 西南交通大学 | Welding shop comprehensive scheduling method based on improved firework algorithm |
| CN113505975A (en) * | 2021-06-18 | 2021-10-15 | 宁波沙塔信息技术有限公司 | Order insertion and scheduling method based on genetic algorithm and firework algorithm |
| CN113505974A (en) * | 2021-06-18 | 2021-10-15 | 宁波沙塔信息技术有限公司 | Multi-target scheduling method based on firework algorithm and genetic algorithm |
| CN113505975B (en) * | 2021-06-18 | 2024-04-09 | 宁波沙塔信息技术有限公司 | Plug sheet scheduling method based on genetic algorithm and firework algorithm |
| CN113505974B (en) * | 2021-06-18 | 2024-04-09 | 宁波沙塔信息技术有限公司 | Multi-target scheduling method based on firework algorithm and genetic algorithm |
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