CN102902570A - Embedded system register distribution method based on oscillator phase synchronization - Google Patents

Abstract

The invention discloses an embedded system register distribution method based on oscillator phase synchronization and mainly solves the problem of relatively long distribution time of an embedded system register. The realization process comprises the following steps of: (1) drawing a mutual interference graph of intermediate variables; (2) taking a complement graph of the interference graph of the intermediate variables; (3) solving a phase value of an oscillator by utilizing nodes of the oscillator corresponding to the complement graph; (4) obtaining the phase synchronization condition of the oscillator according to the phase value of the oscillator at time t; (5) storing the corresponding nodes to a temporary register; (6) and unloading the intermediate variables in the temporary register to a system register to complete embedded system register distribution. By utilizing the embedded system register distribution method, a better embedded system register distribution result can be obtained in a short time. The embedded system register distribution method can be used for register distribution to the intermediate variables in the compilation process of an embedded system.

Description

Method for distributing register in embedded system based on oscillator phase synchronization

Technical field

The invention belongs to field of computer technology, particularly compilation process is distributed the register of middle variable, can be used for embedded system.

Background technology

Along with the development of information network technique, more and more higher to the requirement of performance, real-time and reliability take computer technology as the embedded system on basis.In embedded system, compiler directly affects system performance, and register distributes the code quality important that compiler is generated.But the execution efficient of therefore distributing the technology Effective Raise programs in embedded system of angle Optimizing Compiler from register.With respect to storer, register manipulation speed is fast but limited amount needs as much as possible effective use.Therefore the register assignment problem is exactly to determine how to optimize the register that uses in the embedded system, reduces the operation to storer in the embedded system as far as possible.Specifically be exactly in the program compilation process as much as possible being kept in the register of intermediate variable that produces reduced the intermediate variable number that is forced to spill into storer, reduce and overflow cost.

Existing method for distributing register in embedded system mainly is based on the method for graph theory, converts the register assignment problem to the graph coloring model, then utilizes the algorithm that solves map colouring problem to obtain the result that register distributes.The heuritic approach OCH based on the graph coloring model early, simplicity of design, the time spent, seldom but distribution effects was poor.HYBRID EVOLUTIONARY ALGORITHMS HEA afterwards, after initialization of population, by the crossover operator CFPX that exempts to conflict the variable in each register is not conflicted, thereby then adjust the number of overflowing that intermediate variable in the individuality reduces intermediate variable by Local Search LSP, reduce the cost of overflowing of register.Although this method can access preferably register allocation result, need a large amount of time.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose a kind of method for distributing register in embedded system based on oscillator phase synchronization, distribute the time to reduce register, thereby improve the execution efficient of embedded system program.

To achieve these goals, technical scheme of the present invention comprises the steps:

(1) intermediate variable in the embedded system compiling is represented with node, connect the corresponding node of intermediate variable of phase mutual interference, obtain interference figure H;

(2) keep the node among the interference figure H constant, remove the limit between connected node among the interference figure H, connect the node that does not connect among the interference figure H, obtain the complement G of interference figure H, generate the adjacency matrix A={a of complement G _Xy, x=1,2 ... N, y=1,2 ... N, wherein N is the interstitial content of complement G;

(3) with the node among the corresponding complement G of oscillator, be designated as respectively 1,2 ..., N, N oscillator initial phase of random generation in [0,2 π], produce at random N oscillator original frequency in [0.1,0.1], calculate the phase change value of oscillator according to following formula:

${\stackrel{\·}{\mathrm{\θ}}}_i\left(t\right)=\left\{\begin{array}{ccc}{\mathrm{\ω}}_i+\frac{k_1}{N}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\sin ({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)& \mathrm{if}& a_{\mathrm{xy}}=1\\ {\mathrm{\ω}}_i-\frac{k_2}{N}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\sin ({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)& \mathrm{if}& a_{\mathrm{xy}}=0\end{array}\right.$

Wherein, i=1,2 ... N, ω _iThe natural frequency of expression oscillator i, k ₁, k ₂The stiffness of coupling of expression oscillator, θ _iThe phase value that represents i oscillator, θ _jRepresent j oscillator phase value, a _XyElement among the expression adjacency matrix A;

(4) according to oscillator initial phase and phase change value in the step (3), obtain constantly oscillator 1,2 of t ..., if the phase place of N is t moment i oscillator and j the cosine value cos (θ that oscillator phase is poor _j-θ _i) 0.99, then i oscillator and j oscillator phase synchronization;

(5) oscillator 1,2 ..., the corresponding node of phase locked oscillator is put into same temporary register among the N, until all nodes all are divided into L temporary register TR1 _,TR ₂..., TR _L, L 〉=1 and be integer;

(6) temporary register number L and embedded system register number M are compared, if temporary register number L is less than or equal to embedded system register number M, then with temporary register TR ₁, TR ₂..., TR _LIn node dump to embedded system register R ₁, R ₂..., R _LIn, this moment, embedded system register spilling variable number X was 0, overflowing cost fitness is 0; Otherwise, first with temporary register TR ₁, TR ₂..., TR _LBe divided into TR ₁, TR ₂..., TR _MAnd TR _M+1, TR _M+2..., TR _LTwo parts are then with temporary register TR ₁, TR ₂..., TR _MIn node dump to embedded system register R ₁, R ₂..., R _MIn, again with temporary register TR _M+1, TR _M+2..., TR _LIn node according to the conflict minimum principle join embedded system register R ₁, R ₂..., R _MIn, and use local search approach LSP to embedded system register R ₁, R ₂..., R _MAllocation result be optimized, obtain embedded system register R ₁, R ₂..., R _MNode, embedded system register spilling variable number X and embedded system register spilling cost fitness, finish the embedded system register and distribute.

The present invention has the following advantages compared with prior art:

1, because the present invention takes full advantage of graph theory knowledge, the intermediate variable interference figure of embedded system is set up complement, compare with the former figure that uses in traditional graph coloring method, the relation that the present invention is clearer and more definite between the intermediate variable;

2, because the oscillator phase synchronization method that the present invention adopts belongs to method for parallel processing, can disposable node be assigned in the register, compare HYBRID EVOLUTIONARY ALGORITHMS HEA, need through initialization, intersection, evolution node to be assigned to register, greatly reduced the time that register distributes, thereby accelerated the process of embedded system compiling, the Practical meaning has been arranged.

Description of drawings

Fig. 1 is FB(flow block) of the present invention;

Fig. 2 is the mutual interference figure of intermediate variable in the embodiment of the invention;

Fig. 3 is the complement of the mutual interference figure of intermediate variable in the embodiment of the invention;

Fig. 4 is the time dependent phase diagram of oscillator in the embodiment of the invention;

Fig. 5 is the mutual interference figure of 20 intermediate variables in the l-G simulation test of the present invention;

Fig. 6 is the mutual interference figure of 37 intermediate variables in the l-G simulation test of the present invention.

Embodiment

With reference to Fig. 1, specific implementation step of the present invention is described below:

Step 1. is drawn interference figure H

Embodiments of the invention select concrete embedded system to carry out the register distribution, and 11 intermediate variables of embedded system represent with node, are designated as 1,2 ..., 11, the corresponding node of intermediate variable of connection phase mutual interference is namely respectively with 1 and 2,1 and 4,1 and 7,1 and 9,2 and 3,2 and 6,2 and 8,3 and 5,3 and 7,3 and 10,4 and 5,4 and 6,4 and 10,5 and 8,5 and 9,6 and 11,7 and 11,8 and 11,9 and 11,10 are connected with 11, draw interference figure, as shown in Figure 2.

Step 2. is drawn the complement G of interference figure H

Keep the node among the interference figure H constant, remove the limit between connected node among the interference figure H, connect the node that does not connect among the interference figure H, obtain the complement G of interference figure H, generate the adjacency matrix A={a of complement G _Xy, x, y represents node, x=1,2 ... N, y=1,2 ... N, N are the interstitial content of complement G, if node x, y links to each other, a _Xy=1, otherwise a _Xy=0;

In the present embodiment, keep the node 1,2 of Fig. 2 ..., 11 is constant, removes the limit between the node that links to each other among Fig. 2, namely respectively with node 1 and 2,1 and 4,1 and 7,1 and 9,2 and 3,2 and 6,2 and 8,3 and 5,3 and 7,3 and 10,4 and 5,4 and 6,4 and 10,5 and 8,5 and 9,6 and 11,7 and 11,8 and 11, limit between 9 and 11,10 and 11 is removed, and the node that does not connect in the connection layout 2 is namely respectively with node 1 and 3,1 and 5,1 and 6,1 and 8,1 and 10,1 and 11,2 and 4,2 and 5,2 and 7,2 and 9,2 and 10,2 and 11,3 and 6,3 and 8,3 and 9,3 and 11,4 and 7,4 and 8,4 and 9,4 and 11,5 and 6,5 and 7,5 and 10,5 and 11,6 and 7,6 and 8,6 and 9,6 and 10,7 and 8,7 and 9,7 and 10,8 and 9,8 and 10,9 are connected with 10, obtain the complement G of Fig. 2, as shown in Figure 3, generate the adjacency matrix of Fig. 3:

$A=\left\{\begin{array}{ccccccccccc}1& 0& 1& 0& 1& 1& 0& 1& 0& 1& 1\\ 1& 1& 0& 1& 1& 0& 1& 0& 1& 1& 1\\ 1& 0& 1& 1& 0& 1& 0& 1& 1& 0& 1\\ 0& 1& 1& 1& 0& 0& 1& 1& 1& 0& 1\\ 1& 1& 0& 0& 1& 1& 1& 0& 0& 1& 1\\ 1& 0& 1& 0& 1& 1& 1& 1& 1& 1& 0\\ 0& 1& 0& 1& 1& 1& 1& 1& 1& 1& 0\\ 1& 0& 1& 1& 0& 1& 1& 1& 1& 1& 0\\ 0& 1& 1& 1& 0& 1& 1& 1& 1& 1& 0\\ 1& 1& 0& 0& 1& 1& 1& 1& 1& 1& 0\\ 1& 1& 1& 1& 1& 0& 0& 0& 0& 0& 1\end{array}\right\}.$

Step 3. is found the solution the oscillator phase changing value

Node with among the corresponding complement G of oscillator is designated as respectively 1,2 ..., N, N oscillator initial phase of random generation produces N oscillator free run frequency setting at random in [0.1,0.1] in [0,2 π], calculates the phase change value of oscillator according to following formula:

${\stackrel{\·}{\mathrm{\θ}}}_i\left(t\right)=\left\{\begin{array}{ccc}{\mathrm{\ω}}_i+\frac{k_1}{N}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\sin ({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)& \mathrm{if}& a_{\mathrm{xy}}=1\\ {\mathrm{\ω}}_i-\frac{k_2}{N}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\sin ({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)& \mathrm{if}& a_{\mathrm{xy}}=0\end{array}\right.,$

Wherein, i=1,2 ... N, ω _iThe natural frequency of expression oscillator i, k ₁, k ₂The stiffness of coupling of two different numerical value of expression oscillator, θ _iThe phase value that represents i oscillator, θ _iRepresent j oscillator phase value, a _XyElement among the expression adjacency matrix A;

In the present embodiment, oscillator is designated as 1,2 ..., 11, its initial phase is respectively 3.029,5.181, and 3.704,1.421,0.758,1.582,3.663,1.825,3.877,1.667,2.417 its natural frequency is respectively 0.060, and-0.022 ,-0.008,0.067,0.098 ,-0.054 ,-0.053,0.015,0.088 ,-0.017,0.065;

According to above-mentioned formula, as oscillator stiffness of coupling k ₁=12, k ₂, calculate the phase change value of oscillator, as shown in Figure 4 at=5 o'clock.

Step 4. is determined the oscillator synchronization situation

According to oscillator initial phase and the phase change value in the step 3, obtain constantly oscillator 1,2 of t ..., the phase value of N, in the present embodiment, oscillator 1,2 during t=10, ..., 11 phase value is respectively 5.137,6.081, and 5.840,5.860,6.073,2.890,2.897,2.914,2.905,2.951,6.101, if t moment i oscillator and j the cosine value cos (θ that oscillator phase is poor _j-θ _i) 0.99, then i oscillator and j oscillator phase synchronization; In the present embodiment, synchronous in twos between 10 by calculating as can be known oscillator 6,7,8,9, oscillator 2,5, synchronous in twos between 11, oscillator 3,4 is synchronous, oscillator 1 not with other oscillator synchronization.

Step 5. is with the same temporary register that deposits in of the corresponding node of phase locked oscillator in the step 4, until all nodes all are divided into L temporary register TR ₁, TR ₂..., TR _L, L 〉=1 and be integer.

In the present embodiment, deposit the corresponding node of phase locked oscillator in temporary register TR ₁, TR ₂, TR ₃, TR ₄In, i.e. TR ₁={ 6,7,8,9,10}, TR ₂={ 2,5,11}, TR ₃={ 3,4}, TR ₄={ 1}.

Step 6. compares temporary register number L and embedded system register number M, if L≤M, then with temporary register TR ₁, TR ₂..., TR _LIn node dump to embedded system register R ₁, R ₂..., R _LIn, this moment, embedded system register spilling variable number X was 0, overflowing cost fitness is 0; Otherwise, first with temporary register TR ₁, TR ₂..., TR _LBe divided into TR ₁, TR ₂..., TR _MAnd TR _M+1, TR _M+2..., TR _LTwo parts are then with temporary register TR ₁, TR ₂..., TR _MIn node dump to embedded system register R ₁, R ₂..., R _MIn, again with temporary register TR _M+1, TR _M+2..., TR _LIn node according to the conflict minimum principle join embedded system register R ₁, R ₂..., R _MIn.

In the present embodiment, temporary register number L=4, embedded system register number M=3, L≤M is first with temporary register TR ₁, TR ₂, TR ₃, TR ₄Be divided into TR ₁..., TR ₃And TR ₄Two parts are then with temporary register TR ₁..., TR ₃In node dump to embedded system register R ₁, R ₂, R ₃In, again with temporary register TR ₄In node according to the conflict minimum principle join embedded system register R ₂In.

Step 7. uses local search approach LSP to embedded system register R ₁, R ₂..., R _MAllocation result be optimized, obtain embedded system register R ₁, R ₂..., R _MNode.

7a) calculate embedded system register R ₁, R ₂..., R _MEach node u's in the allocation result overflows factor S _ Factor (u)=S_Cost (u) * CF (u, m), u=1,2...N, 1≤m≤M, N is the node number, M is the register number, and wherein S_Cost (u) overflows cost, CF (u for node u, m) be to link to each other with node u among the interference figure H, and be stored in the register R at node u place _mIn the node number, be u with the node sequencing postscript from big to small according to the factor S _ Factor that overflows of each node ₁, u ₂... u _N

In the present embodiment, calculate according to above-mentioned formula, node 1 overflow factor S _ Factor (1)=3, node 4 overflow factor S _ Factor (4)=1, it is 0 that all the other nodes overflow the factor, the ordering postscript is Isosorbide-5-Nitrae, 2,3,5,6,7,8,9,10,11;

7b) according to 7a) ranking results u ₁, u ₂... u _N, the node u of calculation overflow factor maximum ₁The register Rk at place is comprising node u ₁With remove node u ₁The time to overflow cost poor $\mathrm{\Δfitness}\left(k\right)={\mathrm{fitness}}_{u_1\∈R_k}\left(k\right)-{\mathrm{fitness}}_{u_1\∉R_k}\left(k\right),$ 1≤k≤M, wherein, For comprising node u ₁The time register R _kOverflow cost,

For removing node u ₁The time register R _kOverflow cost,

In the present embodiment, calculate according to above-mentioned formula, overflow the register R at node 1 place of factor maximum ₂To overflow cost poor for Δ fitness (2)=2;

7c) utilize above-mentioned formula to calculate other registers R _eComprising node u ₁With remove node u ₁The time overflow the poor Δ fitness of cost (e), e=1,2...M, and e ≠ k,

In the present embodiment, calculate according to above-mentioned formula, node 1 is at other registers R ₁, R ₃In to overflow cost poor for Δ fitness (1)=3, Δ fitness (3)=1;

7d) from 7c) other registers R of calculating _eOverflow and find out minimumly among the poor Δ fitness of cost (e), be designated as Δ fitness _Min, with Δ fitness _MinWith 7b) middle node u ₁The register R at place _kThe poor Δ fitness of cost (k) that overflows compare, if Δ fitness _Min＜Δ fitness (k) is with node u ₁Adjust to Δ fitness _MinIn the corresponding register, otherwise, node u ₁Do not adjust,

In the present embodiment, according to above-mentioned steps, with node 1 from register R ₂Adjust to register R ₃

7e) with reference to 7b)-7d), determine successively node u ₂... u _NThe adjustment situation after, again obtain embedded system register R ₁, R ₂..., R _MNode,

In the present embodiment, according to above-mentioned steps, all the other nodes all do not adjust;

7f) repeating step 7a)-7e), until all overflow the non-zero node of the factor and 7d all do not occur behind certain minor sort) described in Δ fitness _MinDuring＜Δ fitness (k) situation, finish embedded system register R ₁, R ₂..., R _MThe optimization of allocation result,

In the present embodiment, according to above-mentioned steps, all overflow the non-zero node of the factor and are the above-mentioned situation of appearance, and as a result R is optimized ₁={ 6,7,8,9,10}, R ₂={ 2,5,11}, R ₃={ 1,3,4};

Whether the node of each register exists connection at interference figure H in step 8. determining step 7, and if there is no, then embedded system register spilling variable number X=0 overflows cost fitness=0; Overflow the little node of cost in all connected nodes otherwise overflow, add up its number, obtain embedded system register spilling variable number X, again all costs of overflowing of overflowing node are sued for peace, what obtain the embedded system register overflows cost fitness, finishes the embedded system register and distributes

In the present embodiment, register R ₃In node 1 are connected with node and exist connect, because the cost 1 of overflowing of node 4 is overflowed cost 3 less than node 1, so the node of node 4 for overflowing, overflowing the node number is 1, be embedded system register spilling variable number X=1, the cost of overflowing of overflowing node 4 is 1, its embedded system register overflow cost fitness=1, the embedded system register of finishing in the present embodiment distributes.

Effect of the present invention can further specify by following experiment:

1. simulated conditions:

Be that the system of core2 2.4GHZ, internal memory 2G, WINDOWS XP uses Matlab 7.10.0 to carry out emulation at CPU.

2. emulation content:

Choose the embedded system intermediate variable of two kinds of disturbances as experimental subjects, Figure 5 shows that the interference figure of 20 intermediate variables, Figure 6 shows that the interference figure of 37 intermediate variables.Obtain respectively the register allocation result of the embedded system intermediate variable of these two kinds of disturbances with the method that proposes among existing HYBRID EVOLUTIONARY ALGORITHMS HEA and the present invention, and logging program working time, as shown in the table:

Register allocation result and the comparison of working time under two kinds of methods of table 1

As can be seen from Table 1, the method for distributing register in embedded system that the present invention is based on oscillator phase synchronization is suitable with existing HYBRID EVOLUTIONARY ALGORITHMS HEA on effect, but greatly improved the efficient that register distributes, especially when the register negligible amounts that provides, when having variable to overflow, the register allocative efficiency obviously improves, and has accelerated the compilation process of embedded system, and very high practical value is arranged.

Above-mentioned embodiment only is an example of the present invention, does not consist of any limitation of the invention, for example can also be to comprising different intermediate variable numbers with the inventive method, and the embedded system of different register numbers is carried out register and is distributed.

Claims (5)

1. the method for distributing register in embedded system based on oscillator phase synchronization comprises the steps:

(1) intermediate variable in the embedded system compiling is represented with node, connect the corresponding node of intermediate variable of phase mutual interference, obtain interference figure H;

(2) keep the node among the interference figure H constant, remove the limit between connected node among the interference figure H, connect the node that does not connect among the interference figure H, obtain the complement G of interference figure H, generate the adjacency matrix A={a of complement G _Xy, x=1,2 ... N, y=1,2 ... N, wherein N is the interstitial content of complement G;

(3) with the node among the corresponding complement G of oscillator, be designated as respectively 1,2 ..., N, N oscillator initial phase of random generation in [0,2 π], produce at random N oscillator free run frequency setting in [0.1,0.1], calculate the phase change value of oscillator according to following formula:

${\stackrel{\·}{\mathrm{\θ}}}_i\left(t\right)=\left\{\begin{array}{ccc}{\mathrm{\ω}}_i+\frac{k_1}{N}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\sin ({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)& \mathrm{if}& a_{\mathrm{xy}}=1\\ {\mathrm{\ω}}_i-\frac{k_2}{N}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\sin ({\mathrm{\θ}}_j-{\mathrm{\θ}}_i)& \mathrm{if}& a_{\mathrm{xy}}=0\end{array}\right.,$

Wherein, i=1,2 ... N, ω _iThe natural frequency of expression oscillator i, k ₁, k ₂The stiffness of coupling of expression oscillator, θ _iThe phase value that represents i oscillator, θ _jRepresent j oscillator phase value, a _XyElement among the expression adjacency matrix A;

(4) according to oscillator initial phase and phase change value in the step (3), obtain constantly oscillator 1,2 of t ..., if the phase place of N is t moment i oscillator and j the cosine value cos (θ that oscillator phase is poor _j-θ _i) 0.99, then i oscillator and j oscillator phase synchronization;

(5) oscillator 1,2 ..., the corresponding node of phase locked oscillator is put into same temporary register among the N, until all nodes all are divided into L temporary register TR ₁, TR ₂..., TR _L, L 〉=1 and be integer;

(6) temporary register number L and embedded system register number M are compared, if temporary register number L is less than or equal to embedded system register number M, then with temporary register TR1 _,TR ₂..., TR _LIn node dump to embedded system register R ₁, R ₂..., R _LIn, this moment, embedded system register spilling variable number X was 0, overflowing cost fitness is 0; Otherwise, first with temporary register TR ₁, TR ₂..., TR _LBe divided into TR ₁, TR ₂..., TR _MAnd TR _M+1, TR _M+2..., TR _LTwo parts are then with temporary register TR ₁, TR ₂..., TR _MIn node dump to embedded system register R ₁, R ₂..., R _MIn, again with temporary register TR _M+1, TR _M+2..., TR _LIn node according to the conflict minimum principle join embedded system register R ₁, R ₂..., R _MIn, and use local search approach LSP to embedded system register R ₁, R ₂..., R _MAllocation result be optimized, obtain embedded system register R ₁, R ₂..., R _MNode, embedded system register spilling variable number X and embedded system register spilling cost fitness, finish the embedded system register and distribute.

2. method according to claim 1 is overflowed variable number in the wherein said step (6), is the intermediate variable number of the storer of the register spilling from embedded system in the embedded system.

3. method according to claim 1, wherein said step (6) overflow cost, overflow the time of intermediate variable cost for the memory access from embedded system.

4. method according to claim 1, the conflict minimum principle of wherein said step (6) refers in the embedded system register the mutual value minimum of conflicting between the existing intermediate variable in the new intermediate variable that adds and embedded system register.

5. method according to claim 1, wherein the described use local search approach of step (6) LSP is to embedded system register R ₁, R ₂..., R _MAllocation result be optimized, carry out as follows:

6a) calculate embedded system register R ₁, R ₂..., R _MEach node u's in the allocation result overflows factor S _ Factor (u)=S_Cost (u) * CF (u, m), u=1,2...N, 1≤m≤M, N is the node number, M is the register number, and wherein S_Cost (u) overflows cost, CF (u for node u, m) be to link to each other with node u among the interference figure H, and be stored in the register R at node u place _mIn the node number, be u with the node sequencing postscript from big to small according to the factor S _ Factor that overflows of each node ₁, u ₂... u _N

6b) according to 6a) ranking results u ₁, u ₂... u _N, the node u of calculation overflow factor maximum ₁The register Rk at place is comprising node u ₁With remove node u ₁The time to overflow cost poor $\mathrm{\Δfitness}\left(k\right)={\mathrm{fitness}}_{u_1\∈R_k}\left(k\right)-{\mathrm{fitness}}_{u_1\∉R_k}\left(k\right),$ 1≤k≤M, wherein,

For comprising node u ₁The time register R _kOverflow cost,

For removing node u ₁The time register R _kOverflow cost;

6c) utilize above-mentioned formula to calculate other registers R _eComprising node u ₁With remove node u ₁The time overflow the poor Δ fitness of cost (e), e=1,2...M and e ≠ k;

6d) from 6c) other registers R of calculating _eOverflow and find out minimumly among the poor Δ fitness of cost (e), be designated as Δ fitness _Min, with Δ fitness _MinWith 6b) middle node u ₁The register R at place _kThe poor Δ fitness of cost (k) that overflows compare, if Δ fitness _Min＜Δ fitness (k) is with node u ₁Adjust to Δ fitness _MinIn the corresponding register, otherwise, node u ₁Do not adjust;

6e) with reference to 6b)-6d), determine successively node u ₂... u _NThe adjustment situation after, again obtain embedded system register R ₁, R ₂..., R _MNode;

6f) repeat 6a)-6e), until all overflow the non-zero node of the factor and 6d all do not occur behind certain minor sort) described in Δ fitness _MinDuring＜Δ fitness (k) situation, finish embedded system register R ₁, R ₂..., R _MThe optimization of allocation result.

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