CN113392566A - Simulation optimization design method based on difference - Google Patents

Simulation optimization design method based on difference Download PDF

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CN113392566A
CN113392566A CN202110788921.9A CN202110788921A CN113392566A CN 113392566 A CN113392566 A CN 113392566A CN 202110788921 A CN202110788921 A CN 202110788921A CN 113392566 A CN113392566 A CN 113392566A
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柳培忠
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Abstract

The invention provides a simulation optimization design method based on difference, and relates to the field of EDA tool simulation optimization. The invention introduces a multi-population strategy cooperative mechanism so as to achieve the purpose of multi-physics cooperative optimization. Firstly, setting parameters to be optimized and an optimization target of a chip, initializing a population, adopting a variation strategy of a multi-population mechanism to ensure the individual cooperativity in the evolution process, then properly rotating a target individual and the variation individual by an initialized coordinate system through a covariance learning matrix in the evolution process, using a mixed intersection strategy to achieve better global optimization, simultaneously adopting a self-adaptive parameter regulation mechanism to enhance the diversity and the high efficiency of the population, improving the global optimization capability, realizing the automatic design and optimization of the parameters in the EDA tool simulation, effectively shortening the design cycle of an engineering product, and providing possibility for more effectively solving the problem of modern engineering design.

Description

Simulation optimization design method based on difference
Technical Field
The invention relates to the field of EDA tool simulation optimization, in particular to a simulation optimization design method based on difference.
Background
The Integrated Circuit (IC) industry is the core of the information technology industry, being a strategic, fundamental and precedent industry that supports economic social development and ensures national security. An autonomous high-end, reliable, safe and controllable Electronic Design Automation (EDA) software tool is an important digital infrastructure for developing the integrated circuit industry. Currently, the IC design industry is developing towards the direction of high integration, super large scale, high performance, low power consumption, and in addition, the huge challenge brought to the design by the nano-scale advanced process, powerful EDA tools can help the design engineer to solve various potential problems, improve the reliability of the chip, shorten the design cycle, accelerate the mass production of the chip, and improve the market competitiveness of the product. However, as the application of the EDA technology in the field of electronic information is increased, some deep-level design service problems are faced, a complex product design task flow often needs to use a plurality of different EDA design software tools, and after a plurality of steps are completed cooperatively, design files and data formats used by design tool software of different manufacturers are compatible, and cannot be shared, so that a fully-automatic design flow cannot be formed.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a simulation optimization design method based on difference, which realizes the rapid optimization of parameters, improves the global optimization capability, shortens the design period of engineering products and can more effectively improve the automation degree of modern engineering design.
The invention provides a simulation optimization design method based on difference, which comprises the following steps:
step 1, setting parameters to be optimized and an optimization target of a chip, initializing a population, wherein the parameters comprise a population scale NP, an individual dimension D and an evolution maximum iteration number TMAXCurrent iteration times t;
step 2, calculating the adaptive value f (x) of population individualsi,t)；
Step 3, dividing the whole population P into three sub-populations P1, P2 and P3, wherein the size of the P1 population is larger than that of the P2 and P3;
4, performing mutation operation cooperatively through a plurality of mutation strategies;
step 5, calculating the excellent rate of each generation of sub-populationkAccording to the rate of the next generation evolution initialization stagekNewly assigning the sub-populations for each variation strategy;
step 6, updating the target individual and the variant individual through a characteristic-based cooperative system;
step 7, performing mixed crossing by adopting a mixed crossing strategy;
step 8, selecting a mechanism: calculating test individuals
Figure BDA0003160273070000021
Fitness value of
Figure BDA0003160273070000022
If it is
Figure BDA0003160273070000023
Replacing the current target individual with the test individual; otherwise, keeping the current target individual;
step 9, recombining the three sub-populations into an overall population, and recording the current optimal individual of the population;
step 10, judging whether a termination condition t is met>TMAXAnd if so, outputting the optimal solution, otherwise, returning to the step 2.
Further, the population is initialized in step 1 by using the following formula:
Figure BDA0003160273070000024
wherein, i is 1,2, is, NP, T is 1,2, TMAXJ ═ 1,2, ·, D; NP represents the number of population individuals; d represents the dimension of the solution; wherein the content of the first and second substances,
Figure BDA0003160273070000025
vector representing a feasible solution in the problem search space and representable as a D-dimension
Figure BDA0003160273070000026
t is the number of iterations,
Figure BDA0003160273070000027
is the maximum value of the search space and,
Figure BDA0003160273070000028
is the minimum value of the search space, and rand (0, 1) represents a range of [0,1 ]]Uniformly distributed random decimal fractions are fit for.
Further, the step 3 of dividing the whole population P into three sub-populations P1, P2 and P3 is performed by using the following formula:
Figure BDA0003160273070000029
wherein, PkDenotes the kth sub-population, NPkDenotes the population size, σ, of the kth sub-populationkThe scale proportion of the kth sub-population is shown, and the scale proportion relation is sigma1＞σ2＝σ3And sigmak∈[0,1]。
Further, the scaling factor F is calculated as follows:
Figure BDA0003160273070000031
wherein formula N (0.5,0.15) represents a Gaussian distribution, f (u)i,t) Represents the test vector ui,tFitness of (a), f (x)i,t) Representing a target individual xi,tIs within the range of 0,1]；
Figure BDA0003160273070000032
Is a global optimal individual; r is1，r2，r3Is the number of three individuals randomly selected from the population and satisfies i ≠ r1 ≠ r2 ≠ r3,
Figure BDA0003160273070000033
Figure BDA0003160273070000034
respectively represent a quilt r1，r2，r3Three individuals select a vector for performing mutation operation, also called a target vector, and a mutation vector obtained by differential mutation operation
Figure BDA0003160273070000035
Referred to as the contribution vector to individual i.
Further, the plurality of mutation strategies include "best/1", "current-to-rand/1", and "rand/2":
best/1：
Figure BDA0003160273070000036
current-to-rand/1：
Figure BDA0003160273070000037
rand/2：
Figure BDA0003160273070000038
wherein F is a scaling factor, and K is in the range of 0,1]，
Figure BDA0003160273070000039
Is a global optimal individual; r is1，r2，r3Is the number of three individuals randomly selected from the population and satisfies i ≠ r1 ≠ r2 ≠ r3,
Figure BDA00031602730700000310
respectively represent a quilt r1，r2，r3Three individuals select a vector for performing mutation operation, also called a target vector, and a mutation vector obtained by differential mutation operation
Figure BDA00031602730700000311
Referred to as the contribution vector to individual i.
Further, the sub-population yield in step 5 is calculated as follows:
counting the number of good individual dimensions of the sub-population which are reserved after each population evolution as bestnumkObtaining the sub-population excellent rate according to the dimension D of the population individualkThe sub-population yield is expressed by the formula
Figure BDA0003160273070000041
Wherein, NPkThe population size of the kth sub-population is shown.
Further, the hybrid crossing strategy in step 7 specifically includes:
Figure BDA0003160273070000042
where θ represents the broad value of the mixed crossover probability and the test vector
Figure BDA0003160273070000043
Calculated by a binomial intersection method, intersected according to the following formula and rotated back to the original coordinate system:
Figure BDA0003160273070000044
further, the step 6 further comprises: calculating covariance C of the sub-population through the sub-population information, solving an eigenvector matrix R of the covariance, and performing updating operation by adopting the following formula:
Figure BDA0003160273070000045
the invention has the advantages that:
by taking the minimization of some parameters of the chip, such as the highest temperature value of the radiating fin in the chip, as an optimization target, the optimal solution is obtained by carrying out the optimization design on the structural parameters of the radiating fin of the chip according to the method, the performance of the radiating fin of the chip can be improved, and the optimization of the design of a chip product is realized.
The population structure of a multi-population mechanism is adopted, the individual cooperativity in the evolution process is guaranteed by combining each sub-population with a corresponding variation strategy, a properly rotating coordinate system is established for cross operation through the covariance learning among the populations, and the global search capability is improved through adopting a mixed cross strategy, so that the accuracy of data is improved, and the automation capability of the EDA is improved.
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The invention will be further described with reference to the following examples with reference to the accompanying drawings.
FIG. 1 is an execution flow chart of a simulation optimization design method based on difference according to the present invention.
Detailed Description
As shown in fig. 1, the simulation optimization design method based on difference of the present invention includes:
step 1, setting parameters to be optimized and an optimization target of a chip, initializing a population, wherein the parameters comprise a population scale NP, an individual dimension D and an evolution maximum iteration number TMAXCurrent iteration times t; preferably, the population is initialized in step 1 by using the following formula:
Figure BDA0003160273070000051
wherein, i is 1,2, is, NP, T is 1,2, TMAXJ ═ 1,2, ·, D; NP represents the number of population individuals; d represents the dimension of the solution; wherein the content of the first and second substances,
Figure BDA0003160273070000052
vector representing a feasible solution in the problem search space and representable as a D-dimension
Figure BDA0003160273070000053
t is the number of iterations,
Figure BDA0003160273070000054
is the maximum value of the search space and,
Figure BDA0003160273070000055
is the minimum value of the search space, and rand (0, 1) represents a range of [0,1 ]]Uniformly distributed random decimal fractions are fit for.
Step 2, calculating the adaptive value f (x) of population individualsi,t) (ii) a The calculation formula of the adaptive value is as follows:
f(xi,t)＝0.1/(0.1+1/|lgf(xi,t)|),0≤f(xi,t)≤10-λ
in the formula, λ is determined by the calculation accuracy of the computer, and in one embodiment, λ is 8.
Step 3, dividing the whole population P into three sub-populations P1, P2 and P3, wherein the size of the P1 population is larger than that of the P2 and P3; preferably, the step 3 of dividing the whole population P into three sub-populations P1, P2 and P3 is performed by using the following formula:
Figure BDA0003160273070000056
wherein, PkDenotes the kth sub-population, NPkDenotes the population size, σ, of the kth sub-populationkThe scale proportion of the kth sub-population is shown, and the scale proportion relation is sigma1＞σ2＝σ3And sigmak∈[0,1]。
Step 4, performing mutation operation cooperatively through multiple mutation strategies, specifically, each population corresponds to one mutation strategy, and the multiple mutation strategies include "best/1", "current-to-rand/1", and "rand/2":
best/1：
Figure BDA0003160273070000057
current-to-rand/1：
Figure BDA0003160273070000061
rand/2：
Figure BDA0003160273070000062
wherein F is a scaling factor, and K is in the range of 0,1]，
Figure BDA0003160273070000063
Is a global optimal individual; r is1，r2，r3Is the number of three individuals randomly selected from the population and satisfies i ≠ r1 ≠ r2 ≠ r3,
Figure BDA0003160273070000064
are respectively provided withIs represented by1，r2，r3Three individuals select a vector for performing mutation operation, also called a target vector, and a mutation vector obtained by differential mutation operation
Figure BDA0003160273070000065
Referred to as the contribution vector to individual i; wherein, the calculation formula of the scaling factor F is as follows:
Figure BDA0003160273070000066
wherein formula N (0.5,0.15) represents a Gaussian distribution, f (u)i,t) Represents the test vector ui,tFitness of (a), f (x)i,t) Representing a target individual xi,tIs within the range of 0,1]；
Figure BDA0003160273070000067
Is a global optimal individual; r is1，r2，r3Is the number of three individuals randomly selected from the population and satisfies i ≠ r1 ≠ r2 ≠ r3,
Figure BDA0003160273070000068
Figure BDA0003160273070000069
respectively represent a quilt r1，r2，r3Three individuals select a vector for performing mutation operation, also called a target vector, and a mutation vector obtained by differential mutation operation
Figure BDA00031602730700000610
Referred to as the contribution vector to individual i; if the current fitness is better, the parameter F in the last iteration is continuously reservedi,tOtherwise, a gaussian distribution N (0.5,0.15) is satisfied, with an expected value of 0.5 and a variance of 0.15.
Step 5, calculating the excellent rate of each generation of sub-populationkAccording to the rate of the next generation evolution initialization stagekRe-dividing into individual variation strategies (i.e.The three mutation strategies "best/1", "current-to-rand/1" and "rand/2") distribute the sub-populations; preferably, the sub-population yield in step 5 is calculated as follows: counting the number of good individual dimensions of the sub-population which are reserved after each population evolution as bestnumkObtaining the sub-population excellent rate according to the dimension D of the population individualkThe sub-population yield is expressed by the formula
Figure BDA0003160273070000071
Wherein, NPkThe population size of the kth sub-population is shown.
Step 6, updating the target individual and the variant individual through a characteristic-based cooperative system; preferably, the step 6 further comprises: calculating covariance C of the sub-population through the sub-population information, solving an eigenvector matrix R of the covariance, and performing updating operation by adopting the following formula:
Figure BDA0003160273070000072
step 7, performing mixed crossing by adopting a mixed crossing strategy; preferably, the hybrid crossing strategy in step 7 specifically includes:
Figure BDA0003160273070000073
where θ represents the broad value of the mixed crossover probability and the test vector
Figure BDA0003160273070000074
Calculated by a binomial intersection method, intersected according to the following formula and rotated back to the original coordinate system:
Figure BDA0003160273070000075
step 8, selecting a mechanism: calculating test individuals
Figure BDA0003160273070000076
Fitness value of
Figure BDA0003160273070000077
If it is
Figure BDA0003160273070000078
Replacing the current target individual with the test individual; otherwise, keeping the current target individual;
step 9, recombining the three sub-populations into an overall population, and recording the current optimal individual of the population;
step 10, judging whether a termination condition t is met>TMAXAnd if so, outputting the optimal solution, otherwise, returning to the step 2.
The variant individuals are individuals subjected to variant operation, the target individuals are individuals selected by a selection mechanism, and the test individuals are individuals subjected to crossing.
The simulation optimization design method based on the difference introduces a multi-population strategy cooperative mechanism so as to achieve the purpose of multi-physical-field cooperative optimization. Firstly, a variation strategy of a multi-population mechanism is adopted to ensure the individual cooperativity in the evolution process, then, in the evolution process, an initialized coordinate system is properly rotated with a target individual and the variation individual through a covariance learning matrix, the global search capability is improved by using a mixed intersection strategy to achieve better global optimization, meanwhile, a self-adaptive parameter regulation mechanism is adopted to enhance the diversity and the high efficiency of the population to a certain extent and improve the overall optimization performance, and finally the obtained solution is applied to the parameter optimization of the product in the EDA tool (such as the optimization of parameters of temperature, voltage and the like of a chip product), so that the design accuracy and the efficiency of the EDA tool can be improved.
Although specific embodiments of the invention have been described above, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, and that equivalent modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which is to be limited only by the appended claims.

Claims (9)

1. A simulation optimization design method based on difference is characterized in that: the method comprises the following steps:
step 1, setting parameters to be optimized and an optimization target of a chip, initializing a population, wherein the parameters comprise a population scale NP, an individual dimension D and an evolution maximum iteration number TMAXCurrent iteration times t;
step 2, calculating the adaptive value f (x) of population individualsi,t)；
Step 3, dividing the whole population P into three sub-populations P1, P2 and P3, wherein the size of the P1 population is larger than that of the P2 and P3;
4, performing mutation operation cooperatively through a plurality of mutation strategies;
step 5, calculating the excellent rate of each generation of sub-populationkAccording to the rate of the next generation evolution initialization stagekNewly assigning the sub-populations for each variation strategy;
step 6, updating the target individual and the variant individual through a characteristic-based cooperative system;
step 7, performing mixed crossing by adopting a mixed crossing strategy;
step 8, selecting a mechanism: calculating test individuals
Figure FDA0003160273060000011
Fitness value of
Figure FDA0003160273060000012
If it is
Figure FDA0003160273060000013
Replacing the current target individual with the test individual; otherwise, keeping the current target individual;
step 9, recombining the three sub-populations into an overall population, and recording the current optimal individual of the population;
step 10,Judging whether a termination condition t is met>TMAXAnd if so, outputting the optimal solution, otherwise, returning to the step 2.
2. The differential-based simulation optimization design method of claim 1, wherein: in step 1, the population is initialized by using the following formula:
Figure FDA0003160273060000014
wherein, i is 1,2, is, NP, T is 1,2, TMAXJ ═ 1,2, ·, D; NP represents the number of population individuals; d represents the dimension of the solution; wherein the content of the first and second substances,
Figure FDA0003160273060000015
vector representing a feasible solution in the problem search space and representable as a D-dimension
Figure FDA0003160273060000016
t is the number of iterations,
Figure FDA0003160273060000017
is the maximum value of the search space and,
Figure FDA0003160273060000018
is the minimum value of the search space, and rand (0, 1) represents a range of [0,1 ]]Uniformly distributed random decimal fractions are fit for.
3. The differential-based simulation optimization design method of claim 1, wherein: in the step 3, the step of dividing the whole population P into three sub-populations P1, P2 and P3 is carried out by adopting the following formula:
Figure FDA0003160273060000021
wherein，PkDenotes the kth sub-population, NPkDenotes the population size, σ, of the kth sub-populationkThe scale proportion of the kth sub-population is shown, and the scale proportion relation is sigma1＞σ2＝σ3And sigmak∈[0,1]。
4. The differential-based simulation optimization design method of claim 1, wherein: the scaling factor F is calculated as follows:
Figure FDA0003160273060000022
wherein formula N (0.5,0.15) represents a Gaussian distribution, f (u)i,t) Represents the test vector ui,tFitness of (a), f (x)i,t) Representing a target individual xi,tIs within the range of 0,1]；
Figure FDA0003160273060000023
Is a global optimal individual; r is1，r2，r3Is the number of three individuals randomly selected from the population and satisfies i ≠ r1 ≠ r2 ≠ r3,
Figure FDA0003160273060000024
Figure FDA0003160273060000025
respectively represent a quilt r1，r2，r3Three individuals select a vector for performing mutation operation, also called a target vector, and a mutation vector obtained by differential mutation operation
Figure FDA0003160273060000026
Referred to as the contribution vector to individual i.
5. The differential-based simulation optimization design method of claim 1, wherein: the multiple variation strategies include "best/1", "current-to-rand/1", and "rand/2":
best/1：
Figure FDA0003160273060000027
current-to-rand/1：
Figure FDA0003160273060000028
rand/2：
Figure FDA0003160273060000029
wherein F is a scaling factor, and K is in the range of 0,1]，
Figure FDA00031602730600000210
Is a global optimal individual; r is1，r2，r3Is the number of three individuals randomly selected from the population and satisfies i ≠ r1 ≠ r2 ≠ r3,
Figure FDA00031602730600000211
respectively represent a quilt r1，r2，r3Three individuals select a vector for performing mutation operation, also called a target vector, and a mutation vector obtained by differential mutation operation
Figure FDA00031602730600000212
Referred to as the contribution vector to individual i.
6. The differential-based simulation optimization design method of claim 1, wherein: the calculation method of the sub-population excellent rate in the step 5 is as follows:
counting the number of good individual dimensions of the sub-population which are reserved after each population evolution as bestnumkObtaining the sub-population excellent rate according to the dimension D of the population individualkThe sub-population yield is expressed by the formula
Figure FDA0003160273060000031
Wherein, NPkThe population size of the kth sub-population is shown.
7. The differential-based simulation optimization design method of claim 1, wherein: the hybrid crossing strategy in the step 7 specifically comprises:
Figure FDA0003160273060000032
where θ represents the broad value of the mixed crossover probability and the test vector
Figure FDA0003160273060000033
Calculated by a binomial intersection method, intersected according to the following formula and rotated back to the original coordinate system:
Figure FDA0003160273060000034
8. the differential-based simulation optimization design method of claim 1, wherein: the step 6 further comprises: calculating covariance C of the sub-population through the sub-population information, solving an eigenvector matrix R of the covariance, and performing updating operation by adopting the following formula:
Figure FDA0003160273060000035
9. the differential-based simulation optimization design method of claim 1, wherein: the chip parameter in the step 1 is the temperature of the heat sink in the chip, and the optimization target is the minimum of the highest temperature value of the heat sink in the chip.
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