CN109102062B

CN109102062B - 3D NoC test planning method based on Petri network and chaotic differential firefly algorithm

Info

Publication number: CN109102062B
Application number: CN201810927745.0A
Authority: CN
Inventors: 胡聪; 郑岚; 周甜; 朱爱军; 许川佩; 朱望纯; 万春霆
Original assignee: Guilin University of Electronic Technology
Current assignee: Guilin University of Electronic Technology
Priority date: 2018-08-15
Filing date: 2018-08-15
Publication date: 2020-03-13
Anticipated expiration: 2038-08-15
Also published as: CN109102062A

Abstract

The invention discloses a 3D NoC test planning method based on a Petri network and a chaotic differential firefly algorithm, which can effectively describe the IP core scheduling problem in test planning and simplify a model by adding time delay and a concept with arc suppression on the basis of a prototype Petri network; after the model is established, in order to implement efficient optimization in a transition occurrence sequence set of the Petri network, the basic firefly algorithm is improved in two places, namely, a single-dimensional and multi-dimensional chaotic optimization method is adopted respectively, so that the basic firefly algorithm has fine local optimization capability, and an information sharing mechanism with a differential evolution algorithm is adopted to enhance the global optimization capability of the basic firefly algorithm. The experimental results are compared with the experimental results of other testing methods, and the results show that the testing method of the invention has obvious advantages in the aspects of testing time and program running time.

Description

3D NoC test planning method based on Petri network and chaotic differential firefly algorithm

Technical Field

The invention relates to the technical field of three-Dimensional Network-on-Chip (3D NoC), in particular to a method for testing and planning a 3D NoC based on a Petri Network and a chaotic differential firefly algorithm.

Background

The three-dimensional Network-on-Chip carries out interlayer connection on a two-dimensional Network-on-Chip (NoC) structure Through a Through Silicon Via (TSV) technology, and effectively relieves 'scissors difference' between the manufacturing process level and the design capability. Although the 3D NoC has various advantages such as short interconnection line, high integration level, low power consumption and delay, high expansibility, and strong noise immunity of the circuit, the increase of the number of resource cores and the increase of the structural complexity of the chip system in the unit chip area will bring a new round of examination to the parallel test efficiency of the chip. Therefore, aiming at reducing the test cost, considering the limitations of various constraint conditions such as software and hardware, how to implement efficient parallel transmission and test becomes an NP problem, and meanwhile, the method has great research value.

The Petri network can be used for conveniently describing the phenomena of sequence, synchronization, concurrency, conflict and the like in the distributed system, so that the model is established for the 3D NoC test planning problem through the Petri network, the scheduling process can be depicted through graphs, and the dynamic change of the process is easy to observe. However, when the system scale is continuously enlarged, solving the Petri network through the reachable identifier graph enables the size of the state space matrix to sharply rise exponentially.

Disclosure of Invention

The invention provides a 3D NoC test planning method based on a Petri network and a chaotic differential firefly algorithm, aiming at the problems that the state space of the existing test planning Petri network model is too large and the optimization effect of a test planning algorithm on test time is poor.

In order to solve the problems, the invention is realized by the following technical scheme:

the 3D NoC test planning method based on the Petri network and the chaotic differential firefly algorithm specifically comprises the following steps:

step 1, establishing an augmented delay transition Petri network model according to the test resource requirement of each resource core in the 3D NoC, calculating an input matrix, an output matrix and a state space matrix of the augmented delay transition Petri network model, and determining an initial identifier and a termination identifier;

step 2, initializing two firefly populations with different scales, and respectively allocating populations for the TAM and sequentially allocating the populations, namely randomly generating NP 1D-dimensional TAM allocation individuals to form the TAM allocation population according to a TAM allocation individual coding mode in a (0, M) opening interval; on the basis, allocating individuals for each TAM, sequentially allocating individual coding modes within the (0,1) open interval, and randomly generating NP2 sequentially allocating individuals to form a sequentially allocated population; wherein M, NP1, NP2 and D are set values, M is the number of TAM, D is the number of IP cores, and NP1 is more than or equal to NP 2;

step 3, generating corresponding transition occurrence sequence individuals according to the TAM distribution individuals of the TAM distribution population and the sequence distribution individuals of the sequence distribution population, and calculating the adaptability value of each transition occurrence sequence individual, namely the total transition time delay and the power consumption;

step 4, optimizing and updating the transition occurrence sequence individuals by adopting a chaotic differential firefly algorithm, and finding out the optimal transition occurrence sequence individuals, namely the combination of the optimal TAM distribution individuals and the optimal sequence distribution individuals; namely:

step 4.1, updating the position of the transition occurrence sequence individual by adopting a firefly algorithm to obtain a transition occurrence sequence individual with the minimum fitness value of the firefly algorithm in the iteration, namely the firefly preferred transition occurrence sequence individual;

4.2, updating the positions of the transition occurrence sequence individuals by adopting a differential evolution algorithm to obtain the transition occurrence sequence individuals with the minimum fitness value in the iteration of the differential evolution algorithm, namely, the differential optimization transition occurrence sequence individuals;

4.3, comparing the fitness values of the firefly preferred transition occurrence sequence individual selected in the step 4.1 and the difference preferred transition occurrence sequence individual selected in the step 4.2, and taking the individual with the smaller fitness value as the optimal transition occurrence sequence individual to enter the step 4.4;

4.4, performing single-dimensional and multi-dimensional chaotic disturbance updating on the optimal transition occurrence sequence individual selected in the step 4.3 by adopting a chaotic optimization method to obtain the combination of the optimal TAM distribution individual and the optimal sequence distribution individual of the iteration;

step 5, judging whether the current iteration reaches the maximum iteration number of the chaotic differential firefly algorithm: if not, returning to the step 3, and entering next iteration optimization; and if so, outputting the optimal transition occurrence sequence individual obtained by the current iteration as an optimal TAM distribution and sequence distribution scheme.

In the step 1, the established extended delay transition Petri network model endows each transition with time delay and power consumption on the basis of a prototype Petri network, and adds an arc suppressor which has a control function from a library to the transition.

In step 2, the TAM assigned individual coding mode adopts a real number coding mode, that is: the fractional part is discarded when TAM allocation individuals are randomly initialized, and an idle TAM which is not allocated with an IP core is ensured to be absent, or the IP core is allocated to a TAM number which is not present in the system, and the initialization is carried out again if not.

In the step 2, the sequentially assigned individual coding mode adopts a two-dimensional matrix coding mode, that is:

firstly, determining which TAM each IP core is divided into through TAM distribution individuals;

secondly, randomly initializing the test sequence of the IP cores on each TAM by using decimal numbers in the interval (0,1) under the condition of fixed TAM distribution;

finally, the order of the IP cores is rearranged according to an ascending order, resulting in a certain number of sequentially assigned individuals for each TAM assigned individual.

The fitness value calculation process of the transition occurrence sequence individuals in the step 3 is as follows:

step 3.1, dispatching the first transition distributed to the first TAM by the test, marking the TAM as the busy state under test, and marking the transition as the transition under the excitation state;

step 3.2, searching for the TAM in the idle state, and judging whether the unexcited transition on the TAM has the excitation condition or not according to the input matrix, the output matrix and the transition occurrence criterion:

if the transition meets the excitation condition, calculating the state identifier of the augmented delay transition Petri network model, the transition delay, namely the test time, and the test power consumption, marking the transition as the transition in the excitation state, marking the TAM as the busy state in the test, and returning to the step 3.2 to start searching the TAM in the next idle state;

if the transition does not meet the excitation condition, continuing to search the next unexcited transition on the same TAM, judging whether the unexcited transition has the excitation condition, and if all the unexcited transitions on the TAM do not have the excitation condition, returning to the step 3.2 to start searching the next TAM in an idle state;

step 3.3, after traversing and searching all TAMs, waiting for a transition to finish excitation, namely, an IP core to finish testing, updating the state flag, the transition delay and the test power consumption, marking the transition flag which finishes excitation as the excited transition, marking the TAM which is just released, and judging whether all transitions on the TAM where the transition is located are in the excited state: if yes, marking the TAM as a test completion state; otherwise, marking the TAM as an idle state;

and 3.4, judging whether the termination identifier is reached, namely judging whether all transitions in the transition occurrence sequence are excited transitions: if yes, outputting the total transition time delay and power consumption of the transition generation sequence individuals; otherwise, go to step 3.2.

The unexcited transition having an excitation condition means that: and the transmission paths of the test data packets have no conflict, and the transmission power consumption simultaneously meets the layer power consumption and the total power consumption constraint.

The specific process of the step 4.4 is as follows:

step 4.4.1, setting maximum chaos local search times M_sInitially, the number k of chaotic local search is 1;

step 4.4.2, judging the parity of the chaotic local search times k:

if the chaotic local search times k are odd numbers, performing chaotic disturbance on a certain dimension of the optimal transition occurrence sequence individuals to obtain 1 chaotic individual, and storing the chaotic individual into a chaotic population;

if the chaotic local search times k are even numbers, performing chaotic disturbance on each dimension of the optimal transition occurrence sequence individuals to obtain 1 chaotic individual, and storing the chaotic individual into a chaotic population;

step 4.4.3, judging whether the chaotic local search times k reach the maximum chaotic local search times M_sIf yes, go to step 4.4.4; otherwise, adding 1 to k, and turning to the step 4.4.2;

4.4.4, selecting the chaotic individual with the minimum fitness value in the current chaotic population as a preferred chaotic individual;

4.4.5, if the fitness value of the optimized chaotic individual is smaller than the fitness value of the optimal transition occurrence sequence individual, replacing the original optimal transition occurrence sequence individual by the optimized chaotic individual; otherwise, keeping the original optimal transition occurrence sequence individual unchanged;

and 4.4.6, taking the current optimal transition occurrence sequence individual as the combination of the optimal TAM distribution individual and the optimal sequence distribution individual of the current iteration.

Compared with the prior art, the invention has the following characteristics:

1. the invention adopts an Extended Time Transition Petri Net (ETTPN) to establish a planning model for 3D NoC test, the model endows Time delay and power consumption for each Transition on the basis of a prototype Petri Net, and adds a restraining arc which is led from a library to the Transition and has a control function, thereby effectively describing the IP core scheduling problem in test planning, enhancing the simulation capability of the Petri Net, and simultaneously reducing the dimensionality of rows in an input matrix and an output matrix and the dimensionality of columns in a state space by introducing the restraining arc, thereby simplifying the model and improving the test efficiency.

2. The chaos differential firefly algorithm is adopted, namely the differential evolution algorithm shares optimal information with the firefly algorithm in an auxiliary mode, the global optimization capability of the basic firefly algorithm is enhanced, meanwhile, single-dimensional and multidimensional chaos disturbance optimization is carried out on the optimal individual position of each iteration, the local search capability of the basic firefly is enhanced, and the optimization precision is improved, so that the improved chaos differential firefly algorithm is utilized to implement efficient optimization in a transition occurrence sequence set of a Petri network, and finally the optimal test planning scheme of the 3D NoC is obtained.

Drawings

Fig. 1 is a schematic diagram of a 3D Mesh NoC parallel test.

FIG. 2 is a diagram of an ETTPN submodel.

FIG. 3 is a flow chart of the transition occurrence sequence fitness value calculation.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings in conjunction with specific examples.

The invention adopts a new meta-heuristic optimization method, namely a Firefly Algorithm (FA), to search in a transition occurrence sequence set of a Petri network, the FA has the advantages of simple and easily understood concept, high convergence speed, high optimization precision and the like, is increasingly applied to solving NP problems, but the FA still cannot get rid of the common problem that the group intelligent optimization Algorithm is easy to fall into a local optimum value and cannot jump out. Therefore, the invention provides a Chaotic Differential Firefly Algorithm (CDEFA) aiming at the problems, and simultaneously enhances the global optimization capability and the local fine search capability of the basic Firefly Algorithm. And finally, realizing the optimal solution of the 3D NoC test planning problem by combining the extended time delay transition Petri network with the chaotic differential firefly algorithm.

The 3D NoC according to the preferred embodiment of the present invention is a 3D Mesh topology, and as shown in fig. 1, is mainly composed of resource nodes, i.e., resource cores (IP), routing nodes, resource network interfaces, interconnection lines in a horizontal plane (xy direction), and TSVs in a vertical plane (z direction).

1. Test strategy

In order to reduce the hardware overhead of the test, reduce the network congestion and the complexity of the test model, the adopted test strategy is as follows: multiplexing NoC as Test Access Mechanism (TAM), namely, using routing nodes, interconnection lines, TSVs and the like in NoC as path resources for transmitting test vectors of resource cores. And the selection of the transmission path is determined by a deterministic dimensional sequence XYZ routing algorithm, for example, when the core 8 at the third layer in fig. 1 is assigned to TAM2 for testing, a Test vector is Input to the core 4 at the first layer from an Input2 port by an Automatic Test Equipment (ATE), and then is sequentially routed to the core 8 at the third layer along the x, y, and z coordinate directions, and a Test response of the core is finally Output to the ATE through an Output2 port via the core 3 at the first layer in the same manner. In the testing process, a non-preemptive transmission mode is adopted, namely, the IP cores are continuously tested, interruption caused by resource preemption by other IP cores in the testing process is avoided, and each core can be tested only once.

2. Description of the problem

The 3D NoC test planning problem to which the present invention relates can therefore be briefly summarized as: for a 3D NoC, the relevant parameters of N resource kernels are known as: scan chain length and number, number of test vectors, etc. The method comprises the steps of giving M TAMs (namely M pairs of I/O test ports) with fixed bandwidth, a topological structure, a scheduling mode, a routing algorithm and the like, researching how to establish an accurate Petri network model for the test process of each IP core, describing the TAM distribution of the IP core and the test time and test power consumption of the core through elements in the Petri network, solving the Petri network model through a group intelligent optimization algorithm under the conditions that test resources are free of conflict and the power consumption meets the limit, and finally obtaining an optimal transition occurrence sequence, namely an optimal test scheme of the system.

3. Petri net modeling

Aiming at the test planning problem, an IP core-oriented idea is combined with a subtask division mode, and an extended delay transition Petri network model is established aiming at the resources required by the transmission of the test data packet of each core on different TAMs. A model is established through Visual Object Net + + simulation software and the running state of the Petri network system is observed, for example, 3 TAMs of 14 cores to be tested, ETTPN models established for an IP core 3 and an IP core 5 are shown in FIG. 2, and Table 1 and Table 2 respectively list the meanings of each transition and each library in FIG. 2.

TABLE 1 meanings of the transitions in FIG. 2

TABLE 2 meanings of the libraries in FIG. 2

By transition t_0,3For example, the ETTPN model operation rules are briefly described in two aspects, from the perspective of 3D NoC, when IP core 3 is assigned to TAM0 for testingThe source is the

router

1, 3 of the 0 th layer in the topological structure, the

router

1,2, 3 of the 1 st layer, only when these test resources are unoccupied, the test power consumption meets the constraint condition, and at the same time, the IP core 3 can smoothly complete the test work on TAM0 when the IP core 3 is not tested before; from the Petri Net perspective, transition t_0,3Is generated under the conditions of the depot s_0,1、s_0,3、s_1,1、s_1,2、s_1,3The test power consumption meets the constraint condition with identification, and the storehouse S_b3In the case of no mark, the transition t_0,3Can be excited. Transition t_0,3After being activated, the depot S_b3Get an identification, meaning a transition t_1,3And t_2,3Will not satisfy the excitation condition, thereby ensuring three transition t_0,3、t_1,3、 t_2,3Only one of the cores can occur, namely, the core 3 is ensured to be allocated to one TAM (a pair of I/O ports) for single test, so that the simulation capability of the Petri network is enhanced, and the number of libraries for control initiation in the Petri network established for test objects of the same scale is reduced. For example, when a p93791 (containing 32 IP cores) test reference circuit is mapped to a 3D NoC Mesh structure with the scale of 4 × 3, the dimensionality of rows in an input matrix and the dimensionality of columns in a state space can be reduced by introducing a restraining arc, compared with the situation that 32 dimensions are respectively reduced when the restraining arc is not introduced, and therefore the purposes of simplifying a model and improving the test efficiency are achieved.

There is a one-to-one correspondence between the transition occurrence sequences in the model and the test planning scheme, and there are 3 when 14 IP cores are assigned to 3 TAMs for testing¹⁴Test planning schemes, i.e. from an initial identity M₀Arrival termination identifier M {00000000000000111111111111111111}_fWhen it is 3 { (11111111111111111111111111111111) }¹⁴A transition occurrence sequence

Searching an optimal sequence in a large amount of transition occurrence sequence sigma sets through an algorithm, which is equal to searching an optimal test path selection scheme in a test planning scheme, wherein the test time of the optimal planning scheme is the transition occurrence sequenceAnd finally realizing the transformation from the 3D NoC test planning problem to the Petri net solving problem through the ETTPN model by the sum of all transition time delays DI and the waiting time W in the column sigma.

After the model is established, an input matrix A and an output matrix A are calculated according to a software simulation chart of the model^-And A⁺And determining initial and termination identifications by using the state space matrix, namely all reachable identifications, and establishing a basis for subsequently judging whether the transition has an excitation condition.

4. Method for solving Petri network model through algorithm

In order to solve the ETTPN model established for the 3D NoC test planning problem, a firefly algorithm is adopted to perform optimization in a transition occurrence sequence set of the model.

The firefly algorithm searches an optimal value through the guidance of brightness difference between individuals, for the problem of maximum optimization, firefly individuals with small absolute brightness are always attracted by individuals with larger absolute brightness, the position vectors of the firefly individuals are continuously updated, and local and global optimal solutions in a solution space can be simultaneously obtained through iterative optimization because the brightness induction range of each individual is fixed and the individuals are independent. However, the basic firefly, while addressing the full NP problem of larger size, still has some limitations:

1) because the firefly algorithm is lack of variation rules, the population diversity cannot be ensured in the iterative optimization process, and thus the firefly algorithm is easy to premature and converge;

2) in the later period of iteration, along with the reduction of the distance between the firefly individuals, the individuals oscillate back and forth near the extreme point due to overlarge attraction, so that the convergence rate is low and the optimization precision is low.

Aiming at the two defects, the chaotic Differential firefly Algorithm is provided based on the excellent characteristics of chaos sequence randomness, traversal, initial value sensitivity and the like and the good global search capability of a Differential Evolution Algorithm (DE).

4.1 Algorithm encoding

After an ETTPN model is established and an optimization algorithm is selected, the algorithm needs to be coded, namely, a test planning scheme is expressed into individuals in a firefly algorithm in a proper coding mode, so that the firefly algorithm can be applied to the model to solve the problem, and therefore the following coding modes are set:

assume that the total number of IP cores is N and the number of TAMs is M. The influence of the sequence of the IP core test divided into different TAMs and the IP core test on the same TAM on the test time is cooperatively considered, so that an individual needs to be allocated to the TAM and the individual needs to be coded with the test sequence.

1) TAM assignment Individual codes

And (3) adopting a real number coding mode, when the TAM is randomly initialized to allocate individuals, discarding a decimal part, ensuring that no idle TAM of an IP core is not allocated, or allocating the IP core to a TAM number which does not exist in the system, and otherwise, re-initializing.

TAMs assign individual codes as follows:

X_TAM＝{B₁B₂··· B_N}

in the formula, B_iIndicates that the ith tested IP core is divided into B_iThe TAM is tested, N is the total number of IP cores, i is more than or equal to 1 and less than or equal to N, and B is more than or equal to 1 and less than or equal to B_i≤M。

2) Sequentially assigning individual codes

And (3) adopting a two-dimensional matrix coding mode, firstly determining to which TAM each IP core is divided, determining the sequence of the IP cores on each TAM after the division scheme is determined, randomly initializing by using decimal numbers in the (0,1) interval, and finally rearranging the sequence of the cores according to the ascending sequence.

The sequential assignment of individual codes is as follows:

in the formula, A_bjThe test order of the IP cores representing the corresponding labels on the TAMb is j. 1 is less than or equal to A_bjN is not less than N, b is not less than 1 and not more than M, j is not less than 1 and not more than N, N is the upper limit of the number of cores allocated on each TAM, and N is N-M + 1. An element of 0 in the individual code indicates that the core is absent.

3) Transition generation sequence coding

The method is characterized in that the 3D NoC test planning problem needs to be solved and converted into the ETTPN modelTherefore, it is necessary to convert the IP core TAM assignment individual code and the test sequence assignment individual code into a transition occurrence sequence code corresponding to a combination of the two:

in the formula: t is t_b,jAnd e T represents a test vector containing the jth IP core on the TAM with the label b, j is more than or equal to 1 and less than or equal to N, N is the upper limit of the number of cores allocated on each TAM, N is N-M +1, and b is more than or equal to 0 and less than or equal to M-1. (the formulas in this line are modified)

The total number of IP cores is 10, the number of TAMs is 3 for example, the coding mode is elaborated in detail, and TAMs allocate individuals X_TAMBy { 1002012112 } it is meant that

IP cores

2, 3, 5 are partitioned into TAM0 tests,

IP cores

1, 6, 8, 9 are partitioned into TAM1 tests, and

IP cores

4, 7, 10 are partitioned into TAM2 tests. Test order assignment of individuals

The sequence representing the 3 IP cores that were partitioned to the TAM0 test is: 3 → 2 → 5, the sequence of the 4 cores tested by dividing to TAM1 is: 6 → 9 → 8 → 1, the sequence of the 3 cores tested divided over TAM2 is: 4 → 10 → 7.

The transition occurrence sequence corresponding to the combination of the TAM distribution individual and the test sequence distribution individual is as follows:

4.2 chaos difference firefly algorithm position updating criterion

Establishing an ETTPN model, determining an algorithm coding scheme, initializing a firefly population according to the coding scheme, taking 10 IP cores and 3 TAMs as examples, randomly generating the TAM with the scale of 100 and the dimension of 10 within a (0,3) division interval, and distributing the firefly population, and generating the sequence with the scale of 30 within the (0,1) division interval. And after the initialization is finished, generating a corresponding transition occurrence sequence individual according to the TAM allocation individual and the sequence allocation individual generated by the initialization. For example by X_TAMAnd (1002012112) } and

generating

For this transition occurrence sequence, its fitness value is calculated as follows (see fig. 3):

(note: there are three TAM states in the calculation process: busy state under test, idle state in non-test stage and complete test state; transition also has three states: unexcited state, complete excited state and excited state just excited but not completed.)

Step 1: scheduling test assignment to first transition, e.g., t, on first TAM_0,3And marks the TAM as the busy state under test, and marks the transition as the transition in the excited state.

Step 2: searching for a TAM in an idle state, and judging whether an unexcited transition on the TAM has an excitation condition or not according to an input matrix, an output matrix and a transition occurrence criterion (namely judging whether a transmission path of a test data packet conflicts or not and whether transmission power consumption simultaneously meets layer power consumption and total power consumption constraints or not), and entering a step 3 if the transition meets the occurrence condition; and if the transition does not meet the occurrence condition, continuously searching the next unexcited transition on the same TAM, repeating the judgment, and if all the transitions on the TAM do not meet the occurrence condition, repeating the step 2 to start searching the next idle TAM.

And step 3: and (3) calculating the state identification, the transition time delay (namely the test time) and the test power consumption of the ETTPN model, marking that the transition is in the excited state transition and the TAM is in the busy state under test, and then turning to the step (2) to start searching for the next idle TAM.

And 4, step 4: after traversing and searching all the TAMs, waiting for the completion of the excitation of a certain transition (namely, the completion of the test of a certain IP core), marking the transition which is completely excited as the excited transition, marking the TAM which is just released, judging whether all the transitions on the TAM where the transition is located are in an excited state, if so, marking the TAM as a complete test state, otherwise, marking the TAM as an idle state, and updating the state identification, the transition time delay and the power consumption.

And 5: judging whether a termination mark is reached, namely judging whether all transitions are excited transitions, and if so, outputting the total transition time delay and power consumption of a transition occurrence sequence; otherwise, go to step 2.

After the fitness values of all the transition occurrence sequences are obtained through calculation in the steps, the transition occurrence sequence individuals are optimized and updated according to the following firefly algorithm and differential evolution algorithm. And finally, comparing the optimization results of the two algorithms to obtain the individual position with the best fitness value in the iteration. The differential evolution algorithm can share the optimal information with the firefly population through the independent optimization searching auxiliary mode, and the population diversity and the global optimization searching capability of the basic firefly algorithm are indirectly enhanced.

1) Basic firefly algorithm location update criterion

In the firefly algorithm, an objective function is subjected to individual position vector

The fitness value of (A) is taken as the absolute brightness I of the firefly I_iI.e. by

If the absolute brightness of firefly i is greater than firefly j, the attraction of i to j is calculated by:

in the formula, β₀Represents the maximum attractive force, gamma is the light absorption coefficient, r_ijThe distance between two fireflies is expressed by the following formula:

in the formula, x_i,kAnd x_j,kRespectively representing the k-th dimension in the position vectors of the firefly individual i and the individual j.

Firefly individual j approaches i by updating its location according to the following formula due to its attraction to it.

Wherein t represents the number of iterations and α is [0,1]]The constant value in the interval is constant,

representing a random number vector.

2) Differential evolution algorithm location update criterion

The differential evolution algorithm mainly comprises the following three operations:

a. mutation operation

Generating any one target vector in solution space by mutation operation of the following formula

(G is evolution algebra, NP is population size) corresponding to the given vector

Wherein r1, r2 and r3 are integers which are not equal to i in the interval [1, NP ] and are independent of each other, and F epsilon [0.4,1] represents a mutation operator.

b. Crossover operation

Diversity is enhanced by replacing some of the target vectors with corresponding dimensions of the donor vectors, the intersection process producing trial vectors as follows:

where D is the vector dimension, randb (j) represents the random number between the [0,1] ranges, CR ∈ [0,1] is the crossover operator, rnbr (i) epsilon (1,2, ·, D) is a dimension in the vector.

c. Selection operation

And selecting an individual with a better fitness value from the target vector and the test vector according to a greedy criterion for subsequent iteration:

in the formula (I), the compound is shown in the specification,

and

the target function values are respectively corresponding to the test vector and the target vector.

2) Chaotic optimization algorithm updating criterion

After a firefly algorithm is combined with a differential evolution algorithm to carry out one-time iteration optimization on a transition occurrence sequence, obtaining an optimal transition occurrence sequence individual of the iteration, corresponding to an optimal TAM distribution and sequence distribution scheme, namely the position of the optimal firefly individual, applying a chaotic sequence to the optimal firefly individual, generating a series of chaotic individuals in a certain neighborhood of the position of the optimal firefly individual by changing a certain dimension and changing all dimensions in an alternative way, and selecting preferentially from the chaotic individuals, wherein the method comprises the following specific steps:

step 1: randomly selecting initial iteration value y of chaotic sequence₀Setting chaotic local search to carry out M_sThe number of chaotic local searches is accumulated by k, and initially k is 1.

Step 2: from y according to the following cubic mapping function formula_k-1Calculating y_k。

y(n+1)＝4y(n)³-3y(n)

Wherein y (n) e [ -1,1], and y (n) is not equal to 0, n is 0,1,2, ·.

And step 3: judging the parity of the chaotic local search times k:

① if k is odd, then single-dimensional chaotic local search is performed.

In [1, D ]]A random integer D is generated within the range, where D is the solution space dimension. Let tp be p_g，p_gThe global optimal individual position of the firefly of the iteration is obtained by combining a firefly algorithm and a differential evolution algorithm. P according to the formula_gPerforming chaotic disturbance of a certain dimension:

tp_d＝p_gd+(-1)^k(1-(t-1)/T_max)y_k

in the formula, tp_dD-dimension, p, representing tp_gdRepresents p_gD-dimension of (a), T is the number of current iterations of the firefly algorithm, T_maxRepresenting the upper limit of the number of iterations of the firefly algorithm.

② if k is even number, then multi-dimensional chaotic local search is carried out.

Taking D ═ 1,2,. cndot., D, and p_gEach dimension of (a) implements chaotic perturbation according to the above formula.

And 4, step 4: storing the new individual position obtained by the chaotic search for the kth time to the chaotic population individual cx_kI.e. cx_k＝tp。

And 5: if k is less than M_sThen add 1 to k and go to step 2.

Step 6: calculating to obtain a chaotic population cx_k,(k＝1,2,···,M_s) The chaos individual position with the best fitness value is compared with the optimal firefly individual position p in the iteration_gIf the fitness value is good, the replacement is carried out, otherwise, the replacement is not carried out.

Most of the existing chaos optimization methods are multidimensional, namely each dimension of a target vector can be changed in each cycle, but the chaos disturbance in the invention adopts a mode of combining a single dimension with a plurality of dimensions, and the optimizing efficiency and precision can be improved when the optimal solution of the target vector distance is only slightly different.

And performing one-time optimization iteration on transition occurrence sequence individuals, namely TAM distribution and sequence distribution individuals according to the chaotic differential firefly algorithm to obtain the positions of the optimal transition occurrence sequence individuals, recalculating the individual fitness values of the transition occurrence sequences after the positions are updated, performing second-time iteration optimization according to the chaotic differential firefly algorithm, repeating the steps until the preset maximum population iteration times are reached, and finally outputting a TAM distribution and sequence distribution scheme corresponding to the optimal transition occurrence sequence.

Based on the analysis, the invention discloses a 3D NoC test planning method based on a Petri network and a chaotic differential firefly algorithm, which specifically comprises the following steps:

step 1, establishing an ETTPN model according to the test resource requirements of each resource core in the 3D NoC, calculating an input matrix, an output matrix and a state space matrix of the model, and determining an initial identifier and a termination identifier.

Step 2, initializing two firefly populations with scales of NP1 and NP2 respectively, and distributing populations and sequentially distributing populations for TAM respectively, namely randomly generating NP 1D-dimensional TAM distribution individuals to form a TAM distribution population according to a TAM distribution individual coding mode in a (0, M) open interval; on the basis, individuals are allocated to each TAM, the individuals are sequentially allocated in the (0,1) open interval according to the encoding mode, and NP2 sequentially allocated individuals are randomly generated to form a sequentially allocated population. Wherein M, NP1, NP2 and D are all set values, M is the number of TAM, D is the number of IP cores, and NP1 is more than or equal to NP 2.

Taking 3 TAMs of 10 IP cores as an example, randomly initializing in a (0,3) open interval to generate 100 TAM allocation individuals of 10 dimensions, wherein each TAM allocation individual is generated because a test sequence of a core on the same TAM affects test time for the same TAM allocation individual, 30 sequence allocation individuals are randomly generated in the (0,1) interval, that is, each TAM allocation individual corresponds to 30 sequence allocation individuals, IP core numbers allocated to each TAM in the 30 sequence allocation individuals are the same, but test sequences are different, an optimal test sequence under the same TAM allocation mode can be found out first through an algorithm, and then an optimal TAM allocation mode can be found out through the algorithm.

The above coding scheme for combining the firefly algorithm with the practical problem is as follows:

and the TAM allocation individual is used for determining the TAM to which the IP core is allocated for testing, a real number coding mode is adopted, a decimal part is omitted when the TAM allocation individual is randomly initialized, and it is ensured that no idle TAM of the IP core is not allocated, or the IP core is allocated to a TAM number which does not exist in the system, otherwise, the initialization is carried out again.

The sequence distribution individuals are used for further determining the test sequence of the IP cores distributed to the same TAM after determining the TAM distribution of the IP cores, a two-dimensional matrix coding mode is adopted, the TAM distribution individual codes are taken as the basis, namely the test sequence of the IP cores distributed to the same TAM can be randomly initialized by using decimal numbers in the (0,1) interval only by determining which TAM each IP core is divided into and determining the division scheme, and finally the test sequence of the cores is rearranged according to the ascending sequence.

And 3, generating a corresponding transition occurrence sequence individual according to the TAM distribution individual generated by initialization and the sequence distribution individual.

And 4, calculating the fitness value of each transition occurrence sequence individual, namely the total transition time delay and the power consumption.

1) Scheduling tests to be assigned to a first transition on a first TAM, and marking the TAM as a busy state under test, and marking the transition as a transition in an excited state.

2) Searching for a TAM in an idle state, and judging whether an unexcited transition on the TAM has an excitation condition or not according to an input matrix, an output matrix and a transition occurrence criterion (namely judging whether a transmission path of a test data packet conflicts or not and whether transmission power consumption simultaneously meets layer power consumption and total power consumption constraints or not), and entering 3 if the transition meets the occurrence condition); if the transition does not meet the occurrence condition, continuing to search the next unexcited transition on the same TAM, repeating the judgment, if all transitions on the TAM do not meet the occurrence condition, turning to the beginning of 2), and starting to search the next idle TAM.

3) Calculating the state identification, transition time delay (namely test time) and test power consumption of the ETTPN model, marking the transition as an excited state transition, marking the TAM as a busy state under test, and then turning to 2) starting to search the next idle TAM.

4) After traversing and searching all the TAMs, waiting for the completion of the excitation of a certain transition (namely, the completion of the test of a certain IP core), marking the transition which is completely excited as the excited transition, marking the TAM which is just released, judging whether all the transitions on the TAM where the transition is located are in an excited state, if so, marking the TAM as a complete test state, otherwise, marking the TAM as an idle state, and updating the state identification, the transition time delay and the power consumption.

5) Judging whether a termination identifier is reached, namely judging whether all transitions are excited transitions, and if so, outputting the total transition time delay and power consumption of the transition occurrence sequence individuals; otherwise, go to 2).

The transition occurrence criteria are: for the transition T ∈ T, if the flags in all the general input libraries of the transition are greater than or equal to 1, and no flag is found in the input library with the arc suppression, that is, the input library with the arc suppression has no flag

And is

Then the transition t is said to have the right to occur and is denoted as M [ t >. And obtaining a new identifier M' after the transition t is excited under the identifier M, wherein the calculation formula is as follows:

the transition delay calculation formula is as follows:

in the formula: m represents the number of TAM, N represents the number of IP cores, W_i,jRepresenting the length of wait at the node when the parallel test constraint is not satisfied, DI_i,jThe total duration of the transmission of the test vector representing IP core i when it is scheduled to be transmitted on TAM j, including the duration T of the test on the IP core itself_coreiAnd testing the routing duration T of the data packet_transiI.e. DI_i,j＝T_{core i}+T_{trans i}. The routing duration of the test packet is calculated by:

T_{trans i}＝nb_{xy i}·T_xy+nb_{z i}·T_z+nb_{r i}·T_r＝T_r+nb_{xy i}·(T_xy+T_r)+nb_{z i}·(T_z+T_r)

in the formula: t is_xy、T_z、T_rRespectively representing unit transmission time of the test vector on the interconnection line, TSV and routing node in the xy coordinate direction, nb_xyi、nb_{z i}、nb_{r i}And respectively representing the number of interconnection lines, TSVs and routing nodes of the test vector passing through the xy coordinate direction.

The layer power consumption constraint and the total power consumption constraint are respectively as follows:

1) at any time slot t, the sum P of the power consumption of the first layer under test core_l ^tThe requirements are satisfied:

in the formula: p_{max_l(l)}Represents the upper limit of power consumption, TS, of the l-th layer_iAnd TE_iWhich are the start and end times of the IP core i test, respectively. P_{test i(l)}Represents the total power consumption distributed in the I-th layer core i, and the power consumption P generated by testing the core_{core i}And power consumption P generated by routing test vectors_{trans i}Is composed of, i.e.

P_{test i}＝P_{core i}+P_{trans i}

In the formula: p_{core i}Supplied by the manufacturer, P_{trans i}The calculation formula is as follows:

P_{trans i}＝nb_{xy i}·P_xy+nb_{z i}·P_z+nb_{r i}·P_r＝P_r+nb_{xy i}·(P_xy+P_r)+nb_{z i}·(P_z+P_r)

in the formula: p_xy、P_z、P_rAnd the transmission power consumption of the test vectors through the xy coordinate direction interconnection line, the TSV and the routing node is represented respectively.

2) At any time slot t, the sum of the power consumptions of all IP cores under test in the topological structure is required

Must be below the upper limit P of the total power consumption_max：

And 5, optimizing and updating the transition occurrence sequence individuals by adopting a chaotic differential firefly algorithm, and searching out the optimal transition occurrence sequence individuals, namely the combination of the optimal TAM distribution individuals and the optimal sequence distribution individuals, namely the optimal test planning scheme.

1) And updating the absolute brightness, attraction and position of the transition occurrence sequence individuals by adopting a firefly algorithm to obtain the transition occurrence sequence individuals with the best fitness value in the iteration.

2) And updating the positions of the individual transition occurrence sequences by mutation, intersection and selection operations by adopting a differential evolution algorithm, thereby obtaining the individual transition occurrence sequences with the best fitness value in the iteration.

3) Comparing the fitness values of two individuals with the optimal transition occurrence sequence in 1) and 2), and selecting better individuals to enter 4).

4) By adopting a chaos optimization method, when the chaos iteration number is odd, a certain dimension of the individual position of the optimal transition occurrence sequence is changed, and when the chaos iteration number is even, all dimensions of the individual position of the optimal transition occurrence sequence are changed, and M is generated in a certain neighborhood of the optimal transition occurrence sequence in such a way_sAnd (4) chaotic individuals.

5) Calculating M_sThe fitness value of the individual chaotic individual,and selecting the individual with the best fitness value (shortest test time) as the optimal individual of the transition occurrence sequence of the iteration.

6) Judging whether the maximum iteration times of the algorithm is reached, otherwise returning to the step 4 to recalculate the fitness value of the transition occurrence sequence, then performing next iteration optimization of the chaotic differential firefly algorithm, and if so, outputting a TAM distribution and sequence distribution scheme corresponding to the optimal transition occurrence sequence individual.

In order to verify the effectiveness of the testing method, 2 systems of an international reference circuit ITC' 02 test benchmarks are selected: simulation experiments were performed with 2 × d695 and p 93791. Compared with other models, the optimization rate of the ETTPN model is between 38.18 and 55.74 percent; compared with the basic firefly algorithm before improvement, the chaos difference firefly algorithm is an algorithm improvement scheme, and the test time optimization rate is 3.14% -8.78%.

The invention discloses a method for solving 3D NoC test planning, in particular to a test method based on an extended delay transition Petri network and a chaotic differential firefly algorithm. The method firstly adds time delay and concept with arc suppression on the basis of a prototype Petri network, can effectively describe the IP core scheduling problem in test planning and simplify the model; after the model is established, in order to implement efficient optimization in a transition occurrence sequence set of the Petri network, the basic firefly algorithm is improved in two places, namely, a single-dimensional and multi-dimensional chaotic optimization method is adopted respectively, so that the basic firefly algorithm has fine local optimization capability, and an information sharing mechanism with a differential evolution algorithm is adopted to enhance the global optimization capability of the basic firefly algorithm. The experimental results are compared with the experimental results of other testing methods, and the results show that the testing method of the invention has obvious advantages in the aspects of testing time and program running time.

It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.

Claims

1. The 3D NoC test planning method based on the Petri network and the chaotic differential firefly algorithm is characterized by comprising the following steps:

step 2, initializing two firefly populations with different scales, and respectively allocating populations for the TAM and sequentially allocating the populations, namely randomly generating NP 1D-dimensional TAM allocation individuals to form the TAM allocation population according to a TAM allocation individual coding mode in a (0, M) opening interval; the TAM allocation individual coding mode adopts a real number coding mode, namely: the decimal part is cut off when TAM allocation individuals are randomly initialized, and the condition that no idle TAM of an unallocated IP core exists is ensured, or the IP core is allocated to a TAM number which does not exist in the system, otherwise, the initialization is carried out again; on the basis, allocating individuals for each TAM, sequentially allocating individual coding modes within the (0,1) open interval, and randomly generating NP2 sequentially allocating individuals to form a sequentially allocated population; the sequential distribution individual coding mode adopts a two-dimensional matrix coding mode, namely: firstly, determining which TAM each IP core is divided into through TAM distribution individuals; secondly, randomly initializing the test sequence of the IP cores on each TAM by using decimal numbers in the interval (0,1) under the condition of fixed TAM distribution; finally, the order of the IP cores is rearranged according to the ascending order, so that a certain number of order distribution individuals are generated for each TAM distribution individual; wherein M, NP1, NP2 and D are set values, M is the number of TAM, D is the number of IP cores, and NP1 is more than or equal to NP 2;

4.4, performing single-dimensional and multi-dimensional chaotic disturbance updating on the optimal transition occurrence sequence individual selected in the step 4.3 by adopting a chaotic optimization method to obtain the combination of the optimal TAM distribution individual and the optimal sequence distribution individual of the iteration; namely:

step 4.4.2, judging the parity of the chaotic local search times k:

step 4.4.3, judging whether the chaotic local search times k reach the maximum chaotic local search times M_sIf yes, go to step4.4.4; otherwise, adding 1 to k, and turning to the step 4.4.2;

step 4.4.6, taking the current optimal transition occurrence sequence individual as the combination of the optimal TAM distribution individual and the optimal sequence distribution individual of the current iteration;

2. The 3D NoC test planning method based on the Petri net and the chaotic differential firefly algorithm according to claim 1, wherein in the step 1, the established extended delay transition Petri net model is based on a prototype Petri net, time delay and power consumption are given to each transition, and a restraining arc with a control effect is added to the transition from a library.

3. The 3D NoC test planning method based on the Petri network and the chaotic differential firefly algorithm according to claim 1, wherein the fitness value calculation process of the transition occurrence sequence individuals in the step 3 is as follows:

step 3.2, searching for the TAM in the idle state, and judging whether the unexcited transition on the TAM in the idle state has the excitation condition or not according to the input matrix, the output matrix and the transition occurrence criterion:

4. The 3D NoC test planning method based on the Petri network and the chaotic differential firefly algorithm according to claim 3, wherein the unexcited transition has an excitation condition that: and the transmission paths of the test data packets have no conflict, and the transmission power consumption simultaneously meets the layer power consumption and the total power consumption constraint.