CN107704319A - Improve the CMP method for scheduling task of fireworks algorithm - Google Patents

Abstract

The invention discloses a CMP task scheduling method for an improved fireworks algorithm, belonging to the field of computer architecture. The specific steps include: setting initial parameters; randomly generating position vectors of N fireworks; calculating the number of explosion sparks, explosion amplitude and fitness value of fireworks; performing explosion operation and Gaussian mutation operation; outputting the optimal task scheduling sequence after repeated iterations. The present invention introduces the repulsion operator in the fireworks algorithm; at the same time, applies the nonlinear inertia weight factor on the dimension of the repulsion operation; the coding scheme adopted retains the characteristics that the position of the fireworks is a multi-dimensional vector, and only redefines the meaning and expression of each dimension Ranges. The invention ensures that the sparks generated by fireworks are effective, which is conducive to the meticulous optimization near the optimal value in the later stage of the algorithm iteration, the coding is convenient and efficient, and the solution with higher precision can be found in a shorter time, effectively improving the efficiency of the CMP framework. task execution efficiency.

Description

CMP Task Scheduling Method Based on Improved Firework Algorithm

technical field

The invention belongs to the field of computer architecture, and in particular relates to a CMP task scheduling method for improving the fireworks algorithm.

Background technique

Affected by the sharing of hardware resources between cores and the dependencies between tasks, CMP task scheduling with dependencies is prone to resource contention, which reduces the throughput of multi-core processors and prevents effective parallelism and efficiency.

CMP task scheduling problem is a kind of NP-complete combinatorial optimization problem. At present, Genetic Algorithm (GA) is a combinatorial optimization algorithm widely used in task scheduling problems, but GA is prone to "premature", and due to its complex cross-mutation operation, the time complexity and execution efficiency of the algorithm are easy. Affected by the number of tasks, the task scheduling results cannot meet the actual needs.

Fireworks Algorithm (FWA) is a new swarm intelligence optimization algorithm proposed by Tan Ying in 2010. The fireworks algorithm shows good performance characteristics in solving the global optimal solution of complex problems, and has a low limit on the problem to be solved, so it is suitable for combinatorial optimization problems.

Because the firework algorithm is limited by the number of explosions and the explosion range when generating explosion sparks, and the number of 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 overlaps, resulting in the failure of the sparks. Computational resources are wasted, and the operating efficiency of the algorithm is limited.

Contents of the invention

The object of the present invention is to provide a CMP task scheduling method for improving the fireworks algorithm which improves the efficiency of task scheduling under the CMP framework and ensures the effectiveness of the sparks produced by the fireworks.

The purpose of the present invention is achieved through the following technical solutions:

The CMP task scheduling method for improving the fireworks algorithm includes the following steps:

(1) Set the number N of fireworks, the number of basic explosion sparks, the basic explosion radius, the distance defined by the repulsion operation, the initial value of the dimension of the repulsion operation, the maximum number of iterations, and the initial DAG graph;

(2) randomly generate the position vectors of N fireworks according to the encoding scheme of the present invention;

(3) Calculate the number of explosion sparks, explosion amplitude and fitness value of fireworks;

(4) Perform explosion operation and Gaussian mutation operation to generate explosion sparks and Gaussian mutation sparks, and map sparks beyond the scope of the feasible region back into the feasible region;

(5) Determine whether the spark produced by the fireworks with the best fitness value needs to be repelled, if necessary, go to step ⑥, if not, go to step (7);

(6) Randomly select the dimension of the spark to perform the repelling operation, and if there is a spark beyond the range of the feasible domain after repulsion, map it back into the feasible domain;

(7) calculate the fitness value of explosion spark and Gaussian variation spark;

(8) Keep the fireworks or sparks with the best fitness value to the next generation, and select the remaining N-1 fireworks according to the roulette rules based on Euclidean distance;

(9) Whether the algorithm termination condition is satisfied and the maximum number of iterations is reached, if it is satisfied, the optimal task scheduling sequence is output, and the algorithm stops; if not, go to step (3).

Particularly,

The encoding method is as follows: the encoding retains the position of each firework, which is a characteristic of a multi-dimensional vector, and only redefines the meaning of each dimension. Use X _i to represent the position vector of fireworks i, namely: X _i =[x ₁ ,x ₂ ,...,x _j ,...,x _m ], where x _j =rand(1,n), n represents the processor core Quantity, rand(1,n) means randomly taking an integer value between 1 and n; m means the number of tasks, and x _j means that the jth task is assigned to the x _j processor core for execution. This encoding method ensures that a task can only be assigned to one processor core for execution, and each processor core can handle multiple tasks.

The repelling operation method is as follows: when the distance between the firework with the best fitness value and the spark it produces is less than the acceptable range, the repelling operation is performed: in Indicates the value of the k-th dimension of the position vector of the spark produced by fireworks i, is the value of the k-th dimension of the spark position vector after repulsion, and Δs is the repulsion operator. Considering the characteristics of CMP task scheduling, the value of repulsion operator applied to CMP task scheduling is: Δs=rand(0,n -1), where n represents the number of processor cores, and rand(0,n-1) is a function that randomly selects an integer between 0 and n-1.

The iterative method of the dimension z of the repelling operation is: z(t)=w*z(t-1), wherein z(t) represents the value of the tth iterative repelling operation dimension, z(t -1) represents the value of the action dimension of the t-1th iteration repulsion operation, w is a nonlinear inertia weight value that decreases with the increase of the number of iterations t, and satisfies: w(t)=(1/2) ^t , where w(t) is the value of w in the tth iteration.

The beneficial effects of the present invention are:

Make full use of the characteristics of fast convergence speed and high solution accuracy of the basic fireworks algorithm, and introduce a repelling operator in the basic fireworks algorithm to perform repelling operations on the fireworks with the best fitness value, so as to avoid sparks that are too close to the fireworks or The waste of computing resources caused by overlapping without practical significance; and adding a nonlinear inertia weight factor to the dimension of the repulsion operator to enhance the global exploration ability of the algorithm in the early stage of iteration, and at the same time strengthen the detailed optimization ability of the algorithm in the later stage of iteration .

Description of drawings

Fig. 1 is the DAG figure of described example one;

Fig. 2 is a schematic diagram of the scheduling process of the first example;

Fig. 3 is a schematic diagram of the optimized scheduling process of the first example;

Fig. 4 is a flowchart of the present invention;

detailed description

The specific embodiment of the present invention will be further described below in conjunction with accompanying drawing:

The invention improves the fireworks algorithm, and applies the improved fireworks algorithm to the task scheduling problem under the CMP framework. The present invention first performs repelling operation on the fireworks with the best fitness value of each generation in the fireworks algorithm to ensure that the sparks generated by them are effective and avoid waste of computing resources due to spark failure; at the same time, nonlinear inertia weight is applied to the dimension of the repelling operation factor, so that the algorithm has a stronger global exploration ability in the early stage of iteration, and can carry out detailed optimization in the later stage of iteration.

The present invention will be described in detail below in conjunction with accompanying drawings 1-4.

1. Definition of CMP task scheduling

The CMP task scheduling problem is to schedule tasks to different cores according to a certain algorithm, and make the execution time of all tasks the shortest.

The CMP task scheduling problem can be represented by the triple Π=(P, G, PT). Wherein, P is a set of processor cores. G is a directed acyclic graph (Direct Acyclic Graph, DAG) in graph theory, which represents tasks and dependencies between tasks. PT is a matrix that represents the computing overhead of different tasks on different processor cores, and PT _ip is the computing overhead of task T _i on processor core p.

The DAG diagram representing tasks and inter-task dependencies can be represented by a triple G=(V,S,W), where the meaning of each variable is:

(1) V represents the vertex set of the DAG graph, which consists of all the tasks that the processor needs to process. The i-th task T _i corresponds to the vertex V _i in the DAG graph;

(2) S represents the edge set of the DAG graph, which is composed of communication relationships between tasks. If there is a communication relationship between tasks T _i and T _j , and T _i is the predecessor task of T _j , then there is an edge S in the corresponding DAG graph _ij , the direction of the arrow on the side is from V _i to V _j ;

(3) W is a set of weight values on the edges of the DAG graph, W={W _i1 ,W _i2 ,...,W _ij ,...,W _in }, where m represents the number of tasks with scheduling, and W _ij represents the task The communication overhead between T _i and its predecessor task T _j . When task i and task j are assigned to execute on the same core, the communication overhead is 0.

The CMP task scheduling problem applicable to the present invention requires the use of a standard DAG graph to represent tasks and inter-task dependencies, that is, the DAG graph is required to have a unique entry node and a unique exit node. Accompanying drawing 1 is an example of a task scheduling model of the present invention, T ₁ is the only entry node, T ₉ is the only exit node, and the calculation overhead matrix PT of 4 tasks in this example on 3 processor cores is:

The task scheduling problem with dependencies requires that the execution of T _i can only be started after all the predecessor tasks of task T _i are executed. In a group of task scheduling, the time required for the execution of task T _i is exe[T _i ], and the calculation method is:

exe[T _i ]＝W _ij +PT _ip +max{exe[T _j ]}

T _j ∈ pre(T _i )

Among them, pre(T _i ) represents the set of predecessor tasks of task T _i , W _ij represents the communication overhead between task T _i and task T _j , PT _ip represents the computational overhead of task T _i on processor core p, max{exe[T _j ]} is the time taken for all the predecessor tasks of task T _i to be executed.

Then the mathematical definition of the dependent CMP task scheduling problem is: TS=min{exe[T _last ]}

Among them, exe[T _last ] is the time taken for the last task to be executed, and TS is the task scheduling length, that is, the time taken for all tasks to be executed.

2. Fitness value

The task scheduling method of the present invention retains the characteristics of the firework algorithm to evaluate the quality of fireworks or sparks by the size of the fitness value. The fitness value of fireworks with good quality is small; the fitness value of fireworks with poor quality is large.

Define the size of the task scheduling length TS as the size of the fitness value. When the TS is larger and the time to complete all tasks is longer, the quality of fireworks is worse; on the contrary, when the TS is smaller and the time to complete all tasks is shorter, the quality of fireworks is better.

The fitness value function is:

f(X _i )=TS(X _i )

in

3. Introduce the location update scheme of the repulsion operator

The basic firework algorithm shows good optimization ability in various combinatorial optimization problems, but the explosion radius of the firework with the best fitness value is very small, even 0, resulting in the loss of actual value of the generated sparks and a waste of computing resources of the algorithm. It is also easy to make the algorithm fall into a local optimal solution.

In order to avoid the adverse effects caused by the characteristic of the fireworks algorithm, the present invention introduces a repulsion operator to correct the position of the spark, and when the distance between the fireworks i and the spark it generates is not within an acceptable range, the repulsion takes effect.

The distance between the fireworks and the sparks they produce is measured by the Euclidean distance, and the conditions for the repulsion operation are:

Where X _i represents the position vector of fireworks i, X _h represents the position vector of spark h produced by firework i, and Δr represents the minimum acceptable distance between fireworks i and spark h produced by firework i.

The exclusion method is:

in Indicates the k-th dimension value of the position vector of spark h, is the k-th dimension value of the position vector of the spark h after the repulsion operation, and Δs is the repulsion operator.

Considering the characteristics of CMP task scheduling, the value of the exclusion operator is: Δs=rand(0,n-1)

Where n represents the number of processor cores, and rand(0,n-1) is a function that randomly selects integers between 0 and n-1.

The repulsion operator does not repel all dimensions of fireworks, but only randomly selects z dimensions for repulsion operation, and z satisfies: z(t)=w*z(t-1)

Among them, z(t) represents the value of the dimension z of the repulsion operation of the tth iteration, z(t-1) represents the value of the dimension z of the repulsion operation of the t-1 iteration, and w is a value that varies with the number of iterations t The increasing and decreasing nonlinear inertia weight value satisfies: w(t)=(1/2) ^t , where w(t) is the value of w in the t-th iteration.

The nonlinear inertia weight value w is relatively large at the initial stage of iteration, which is conducive to the global search of the fireworks algorithm in a larger space; the relatively small value at the later stage of iteration is beneficial to the algorithm at the current optimal A more detailed search is performed around the value.

4. Coding strategy

In order to make the fireworks algorithm with continuous solution space applicable to the discrete CMP task scheduling problem, the invention encodes the fireworks.

The coding scheme described makes each firework or spark in the population represent a possible task scheduling sequence.

In the coding scheme, processor cores are numbered: 1, 2, . . . , n; and tasks to be processed are numbered 1, 2, . . . , m.

Then the position vector X _i of fireworks or spark i can be expressed as:

X _i =[x ₁ ,x ₂ ,...,x _j ,...,x _m ]

x _j = rand(1,n)

Where n represents the number of processor cores, rand(1,n) represents a random integer value between 1 and n; m represents the number of tasks, x _j represents the jth task is assigned to the x _j processor core for execution .

The coding scheme that the present invention adopts has four characteristics:

(1) The coding method is simple and clear, easy to understand and implement;

(2) Satisfy the requirements of the task scheduling problem;

(3) Contains all possible task scheduling schemes;

(4) Realize the unique mapping between the position vector of fireworks or sparks and the task scheduling sequence.

Then the displacement operation of the CMP task scheduling method realized by the present invention is: x _j = x _j +rand(0, R _i )

Among them, x _j indicates that the jth thread is assigned to the x _j processor core for execution, rand(1,R _i ) indicates a random integer value between 1 and R _i , and R _i is the explosion radius of fireworks i.

The mapping rule of the CMP task scheduling method realized by the present invention is: _xj =1+ _xj %(n-1), wherein _xj represents that the jth thread is assigned to the _xj processor core for execution, and n represents the processor number of cores.

The exclusion operation method of the CMP task scheduling method implemented in the present invention is: x _j = x _j +Δs, where x _j indicates that the jth thread is assigned to the x _j processor core for execution, and Δs is an exclusion operator.

Example one:

According to the encoding method described in the present invention, a possible scheduling scheme of Example 1 is: X=[1, 2, 3, 1], as shown in Figure 2, the calculation overhead matrix of Example 1 can be used to calculate the The execution completion time of all tasks in the scheduling sequence is 33.

Example 1 The only optimal scheduling sequence obtained after cyclic iteration of the CMP task scheduling method described in the present invention may be X=[3,1,1,2], according to the calculation overhead matrix of Example 1, all the scheduling sequences can be obtained The thread execution completion time is 10, which is 23 units less than the time required for the scheduling sequence shown in Figure 2 to execute all the threads.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within 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 X_iA position vector representing fireworks i, namely: x_i＝[x₁,x₂,…,x_j,…,x_m]、x_jRand (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, x_jIndicates that the jth task is assigned to x_jExecuting 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>&amp;prime;</mo> <mi>k</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>X</mi> <mi>h</mi> <mi>k</mi> </msubsup> <mo>+</mo> <mi>&amp;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) ═ 1/2^tWhere w (t) is the value of w for the tth iteration.