CN109960834A - A kind of analog circuit multi-objective optimization design of power method based on multi-objective Bayesian optimization - Google Patents
A kind of analog circuit multi-objective optimization design of power method based on multi-objective Bayesian optimization Download PDFInfo
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Abstract
The invention belongs to analog circuit parameters Automatic Optimal Design fields in IC design, and in particular to a kind of multi-objective Bayesian optimization method based on Gaussian process model.The method of the present invention constructs Gaussian process model in each iteration, to each performance indicator, and then constructs low confidence interval function, carries out the point of circuit simulation next time by the multiple-objection optimization selection to low confidence interval function.International main stream approach, the method for the present invention can substantially reduce circuit simulation number, obtain high-precision Pareto forward position at present relatively.
Description
Technical field
The invention belongs to technical field of integrated circuits, it is related to Analog Circuit Design parameter automatic optimization side in IC design
Method, and in particular to one kind is based on Gaussian process model (Gaussian Process), optimizes (Multi- using multi-objective Bayesian
Objective Bayesian Optimization) algorithm circuit optimization method, this method can be greatly decreased in optimization process
The simulation times of circuit obtain the Analog Circuit Design parameter for meeting performance requirement.
Background technique
It is continuously increased with the continuous promotion of IC process node, and to high-performance, the demand of low consumption circuit, IC simulation
The hand-designed of circuit becomes increasingly difficult.According to data, analog circuit automated design engineering has attracted a large amount of both at home and abroad
Research work.Substantially, analog circuit the Automation Design problem can be converted into nonlinear optimal problem.Mature optimization algorithm
The computing resource constantly enhanced to solve complicated analog circuit optimization problem.
It is asked currently, dimensionally-optimised problem (sizing) is converted single object optimization by most of analog circuit optimization methods
Topic.But in actual design, analog circuit usually has several conflicting performance indicators, and being difficult to find an overall target makes
It is optimal to obtain all properties index.This field knows that method a kind of intuitive and being widely used is known using the priori of designer
Know, assigns a weight for each performance indicator to constitute a weighted target function, convert single object optimization for problem and ask
Topic is solved, but the difficult point of this processing processing method is to determine that suitable weight is more difficult, and the weight of mistake
Distribution may result in improper design.
Think in the industry, Multipurpose Optimal Method is not optimization single target to seek globally optimal solution, and is attempt to find
One group of equally distributed Pareto optimality (Pareto-optimal) design point carrys out the Pareto forward position (Pareto of approaching to reality
Front,PF)；Pareto forward position represents optimal solution of all properties index under different weights；It is specifically chosen which kind of weight, then
It is voluntarily selected by designer.In addition, circuit unit rank PF can be used as the behavior model of unit, for the system-level excellent of stratification
Change.
The multi-objective optimization question of analog circuit is defined as follows in the prior art:
minimizef1(x) ..., fm(x) (1)
Wherein,For design variable, fi(x) i-th of performance indicator, i ∈ { 1...m } are represented, such as is amplified
Gain, bandwidth of device etc..
In multi-objective optimization question, usually not unique globally optimal solution.The target of multiple-objection optimization is to find one
Group Pareto optimal solution.In multi-objective optimization question, a design x1It referred to as dominates (dominate) and designs x2, and if only iffi(x1)≤fi(x2), andSo that fj(x1) < fj(x2).One design point is referred to as
Pareto optimality, and if only if not having any other design point that can dominate it in design space.All Pareto optimalities
The set that design point is constituted, referred to as Pareto forward position.Pareto forward position can regard the continuous curve surface in parameter space as.Multiple target is excellent
The purpose of change exactly finds one group of Pareto optimality point as equally distributed as possible on Pareto forward position, with approximate true
Pareto forward position.
In order to improve the performance of optimization algorithm, circuit simulation number needed for optimization process is reduced, in the world for more
Target simulation circuit optimization proposes many methods.It is similar to the optimization of single goal analog circuit, most of existing multiple target electricity
Road optimization method is divided into two major classes: based on model and based on the method for emulation.It will be electric based on the Multipurpose Optimal Method of model
Road performance modeling is analytical function, is then based on these analytical function models and executes multiple-objection optimization.Such as in bibliography
[4] it in-[6], is combined by geometric programming (GP) and with multi-objective Evolutionary Algorithm, handles multiple target circuit optimization problem.It is such
Optimization method based on model, accurate world model are most important.But often based on the circuit performance formula derived by hand
Precision is insufficient.In method based on emulation, optimization process be by circuit simulation tools as SPICE directly drives.Circuit is seen
Make the black box function (black-box function) from design parameter to performance number, circuit simulation is function evaluation, in turn
Multi-objective optimization algorithm is taken to the corresponding black box function of circuit.
Heuristic value is common multiple target circuit optimization algorithm, for example, using in bibliography [7]-[9]
Non-dominated sorted genetic algorithm (NSGA-II) [10].In bibliography in [11], using the multiple target based on decomposition into
Change algorithm (MOEA/D) [12].It is used in bibliography [13] and converts a series of single object optimizations for multi-objective problem and ask
The scalarization scheme of topic.In bibliography [3], the PF of circuit system be generated by reusing the PF of submodule, and
The PF of submodule is still to be generated by evolution algorithm.Optimization method based on emulation needs a large amount of calling circuit simulation, especially
When circuit simulation takes a long time, the calculating cost of this method is very high.
In order to solve the deficiency of existing method, propose in the world in recent years a kind of based on online associated model (online
Surrogate model) circuit optimization method.In this approach, it does not need to construct accurate off-line model in advance, but
A sparse initial model is first constructed, model is constantly updated with the addition of new sampled point in an iterative process.For example,
In GPMOOG [14] methods proposed in 2012, online companion is used as using Gaussian process model (Gaussian Process, GP)
With model, the evolution algorithm MOEA/D [12] [15] of multiple-objection optimization is used as internal multiple-objection optimization kernel.GP model can not only
Enough estimated performances, moreover it is possible to provide the uncertainty estimation of predicted value.In the MOEA/D evolutionary process of every generation, GP model by with
The filial generation performance of generation predicted, if prediction has biggish uncertainty, the emulation tool that then be used directly is obtained
Otherwise the performance of filial generation design replaces time-consuming emulation using GP predicted value.Newly generated design of Simulation point, which is also added to, to be used for
GP model is updated, model accuracy is improved.
The prior art [16] disclose Bayes optimization be it is a kind of for simulation calculation cost dearly based on the excellent of emulation
Change algorithm.In Bayes's optimization, Gaussian process model is used as associated model.In GPMOOG, GP model prediction not really
It is qualitative to be only used for deciding whether to introduce time-consuming emulation, and in multi-objective Bayesian optimization, GP model participates in excellent deeper into ground
Change process；In each iteration, predicted value that function (acquisitionfunction) is provided according to GP model and its not is obtained
Certainty building obtains function and is used for the balance exploration (Exploration) in optimization process and utilizes (Exploitation).
Done in currently known preferable areas adjacent sampling (utilization) or between the area sampling (exploration) not yet furtherd investigate
Tradeoff.
Basis based on the prior art, the invention proposes a kind of multi-objective optimization algorithms based on Bayes's optimization
(Multi-objective Bayesian optimization, MOBO).MOBO algorithm proposed by the present invention and at present in the world
Best GPMOOG algorithm is compared, and can preferably approach Pareto forward position, while substantially reducing circuit simulation number.
Bibliography related to the present invention has:
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Modeling,Optimization,and Synthesis for System-Level Analog and RF Designs,”
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Proceedings of the 43rd annual design automation conference(DAC),2006,pp.31–
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Summary of the invention
It is an object of the invention to the bases based on the prior art, propose a kind of multiple-objection optimization based on Bayes's optimization
Algorithm (Multi-objective Bayesian optimization, MOBO).Multi-objective Bayesian is based on more particularly to one kind
The analog circuit multi-objective optimization design of power method of optimization.
Traditional single goal Bayes's optimization method is expanded to multiple-objection optimization, low confidence interval (Lower by the present invention
Confidence bound, LCB) function is chosen as the acquisition function of each target, and it is excellent to carry out multiple target to multiple LCB functions
Change.The present invention is directed to the multiple-objection optimization of more LCB functions, proposes a kind of based on non-dominated ranking (Non-dominated
Sorting multi-objective Evolutionary Algorithm) passes through a kind of improved non-branch after the Pareto forward position for obtaining multiple LCB functions
New data point is selected from the PF obtained with sequence, and carries out circuit simulation, and simulation result is placed into training set for improving
GP model；Our experiments show that MOBO algorithm of the invention can preferably approach Pareto forward position, while it is imitative to substantially reduce circuit
True number.
Specifically, a kind of analog circuit automatic optimizing design method based on multi-objective Bayesian optimization of the invention,
It include: the random uniform sampling in design space；In each iteration, each target is made using resulting data are currently emulated
For training set, Gaussian process model is constructed；For each target, constructs low confidence interval and obtain function；And to low confidence interval
Function carries out multiple-objection optimization, and a click-through is finally selected on the Pareto forward position of the resulting low confidence interval of multiple-objection optimization
Row circuit simulation, subsequently into next iteration, until the circuit simulation number for reaching maximum allowable then exits；Include:
Input parameter:
1. analog circuit netlist, manufacturing process file, circuit emulator；
2. the variation range that Analog Circuit Design parameter and design parameter allow；
3. initial random sampling number Ninit；
4. each performance indicator Yp, p=1 ..., Np, wherein NpFor the quantity of performance indicator；
5. algorithm termination condition, such as maximum allowable circuit simulation number；
Export result:
Design point on one group of Pareto forward position can dominate that is, in this group of design parameter without any one design point
Other design points are dominated by other design points.
Step 1: the uniformly random sampling N in design parameter spaceinitA sample point, and to by calling emulator to obtain
The performance index value Y of all sampled pointsp, p=1 ..., Np；
Step 2: being directed to each performance indicator Yp, the performance indicator obtained by emulation is as training set, building Gaussian process
Regression model；
Step 3: being directed to each Gaussian process model, construct low confidence interval (LCB) as acquisition function；
Step 4: using multi-objective optimization algorithm, multiple-objection optimization is carried out to the LCB function of different performance index；
Step 5: carrying out non-dominated ranking on the resulting Pareto forward position of step 4, and select first point, carry out circuit
Emulation, if termination condition meets, algorithm is terminated, and otherwise, is transferred to step 2.
The present invention constructs Gaussian process model [17] in step 2, using following steps:
Step 2.1: choosing mean function and covariance function used in Gaussian process model, Gaussian process model can be by one
A mean function m (x) characterizes with a covariance function k (x, y).In an embodiment of the present invention, using constant mean letter
Number m (x)=μ0, Gauss covariance function are as follows:
Wherein, Λ=diag (l1..., ld) it is a diagonal matrix, and liIndicate the characteristic length in i-th of dimension
(lengthscale), [1, d] i ∈, μ0,σfAnd Λ is the hyper parameter of GP model；
Step 2.2: Gauss mistake is estimated by maximal possibility estimation (Maximum Likelihood Estimation, MLE)
Hyper parameter vector θ=[μ in journey model0, σf, l1..., ld], it gives training set { X, y }, wherein X={ x1..., xN, y=
(f(x1) ..., f (xN))T, N is the sum of existing simulated point；Log-likelihood function is represented by [17]:
Wherein, Kθ(i, j)=k (xi, xj), by solving the log-likelihood function in maximization formula (3), it can get Gauss
Hyper parameter θ in process model；
The present invention in step 3, using following sub-steps, obtains letter according to the low confidence interval of Gaussian process model construction
Number:
Step 3.1: giving a new data point x, the mean value and variance of its distribution, GP model are predicted according to Gaussian process
To a prediction not instead of scalar value of f (x), one meets the stochastic variable of normal distribution, i.e. f (x)~N (μ (x), σ2
(x)), wherein μ (x) and σ2(x) it is respectively as follows:
Wherein, KθDefinition and formula (3) unanimously, k (x, X)=(k (x, x1) ..., k (x, xN))T, k (X, x)=k (x, X
)T.In formula (4), μ (x) can regard Gaussian process as and return the anticipation function value provided, σ2It (x) is then the measurement of uncertainty in traffic；
Step 3.2: LCB, which is constructed, for each objective function obtains function:
LCB1(x) ..., LCBm(x),
Wherein, LCBi(x), it indicates to objective function fi(x) LCB obtains function:
LCBi(x)=μi(x)-kiσi(x), i=1..m
The present invention carries out multiple target to LCB function based on improved NSGA-II [10] algorithm in step 4, using one kind
Optimization, as follows step by step:
Step 4.1: the random N number of point of uniform sampling, the original demographic as evolution algorithm in design parameter
(population)；
Step 4.2: according to the variation of differential evolution algorithm [15] (differential evolution, DE)
(mutation) with hybridize (crossover) operation, generate filial generation (children) via current parent (parent) population
Population.
Variation (mutation) operating method of differential evolution is as follows, and enabling parent population design parameter is p1...pN, pass through
Variation generates population m1...mN, firstly, enabling zooming parameter (scalefactor) F~N (0.8,0.2) is from Gaussian Profile N
The stochastic variable sampled in (0.8,0.2), then, for i=1...N, from p1…pNTwo design parameter p of middle random selectionr1
With pr2, then miProduction method is as follows:
mi=pi+F×(pr1-pr2)
The population m generated via variation1…nN, for i=1...N, enable miWith piHybridize (crossover), generates filial generation
Population ci, hybridizing method is as follows: the dimension for enabling design variable is D, and setting hybrid rate (crossover rate, CR) is 0.8, first
An integer r is first randomly selected from 1...Didx, then, for each dimension j=1...D, choose the random number in (0,1)
rcr=rand (0,1), then ciJ-th of variable cijIt is generated via such as under type:
Step 4.3: by the LCB functional value of parent population, the LCB functional value of filial generation population, and having emulated and designed
The design point of performance parameters value is combined, and a new point set is formed；According to the non-dominated ranking (non-in [10]
Dominated sorting) method, which is ranked up；Original non-dominated ranking method includes two steps, mastery row
Sequence and crowding distance (crowding distance) compare, and in this step, the method for mastery sequence is identical as [10],
And when defining crowding distance, the crowding distance of each target is added in [10], and be in the present invention by each mesh
Target crowding distance is multiplied, and this improvement has the case where biggish magnitude differences between can handle different target performance indicator,
Without being normalized；The schematic diagram of non-dominated ranking finds out the point set as shown in Fig. 2, to the point set in Fig. 2 first
In non-domination solution, as red point set is labeled as rank 0, then again concentrates the point of rank 0 from and remove, then find out
The non-domination solution that left point is concentrated, i.e., green point set are labeled as rank 1, and such recurrence divided until all point sets
With an integer rank value, the point with lower rank value is considered better than the point with larger rank value；For with identical
The point of rank value is compared, in the original definition of crowding distance by crowding distance (crowding distance)
[10], the two o'clock of the same rank value adjacent with the point or so need to be found out to each point, crowding distance is this of left and right consecutive points
Tan Na distance, as shown in crowding_distance (A) in Fig. 2；And in the present invention, crowding distance is changed to crowding
The product of distance, therefore this index is known as " crowded volume " by the present invention；In Fig. 2, the crowding distance of point A is L1+
L2, and the crowded volume of point A is defined as L1 × L2.
The invention proposes a kind of Fast simulation circuit Multipurpose Optimal Methods based on multi-objective Bayesian optimization, will pass
Single goal Bayes's optimization method of system expands to multiple-objection optimization, low confidence interval (Lower confidence bound,
LCB) function is chosen as the acquisition function of each target, and carries out multiple-objection optimization to multiple LCB functions；Our experiments show that this
Inventive method constructs Gaussian process model in each iteration, to each performance indicator, and then constructs low confidence interval function, leads to
Cross the point that the selection of the multiple-objection optimization to low confidence interval function carries out circuit simulation next time.Relatively current international mainstream
Method, this method can substantially reduce circuit simulation number, obtain high-precision Pareto forward position.
Advantages of the present invention has: (1) can provide the Pareto forward position of the multiple performances of circuit automatically；(2) reaching same
Under conditions of precision, optimize required circuit simulation number less than current main stream approach.
Detailed description of the invention
Fig. 1 is the flow chart of multi-objective Bayesian optimization algorithm of the present invention.
Fig. 2 is non-dominated ranking schematic diagram.
Fig. 3 is hypervolume (hypervolume) schematic diagram in Pareto forward position.
Fig. 4 is optimum results of MOBO, GPMOOG and the MOEA/D algorithm on ZDT1 and ZDT2 function.
Fig. 5 is three exponent arithmetic(al) amplifier circuit figures in example 2.
Fig. 6 is transformer domain to be optimized in example 3.
Fig. 7 is the Pareto forward position that multiple-objection optimization generation is carried out to transformer that MOBO, GPMOOG and MOEA/D are generated.
Specific embodiment
By the implementation process of specific example, the method for the present invention is described in further detail.
The present invention by the MOBO algorithm of proposition with based on emulation MOEA/D algorithm [11] and GPMOOG algorithm [14] progress
Compare, GPMOOG algorithm equally also uses online associated model method, ZDT1 and ZDT2 function is as first test case
[24], the PF of ZDT1 and ZDT2 has analytic solutions, therefore, ZDT1 and ZDT2 function can with verification algorithm obtain Pareto forward position with
Difference between true Pareto forward position；In addition, ZDT function also can verify that the correctness that MOEA/D and GPMOOG is realized, because
The two functions also use in [14]；Then, three real circuits/devices are tested, including a three-stage operational
Amplifier, a job work in the transformer of 60GHz and one in the power amplifier of 2.5GHz.
Based on having proposed a large amount of evaluation index in the world at present for comparing the performance [25] of multi-objective optimization algorithm,.
The present invention uses hypervolume difference measurement (Hypervolume Difference Metric)It is more proposed by the present invention
The performance of MOBO method and existing GPMOOG method and MOEA/D [11] method；
The hypervolume (Hypervolume) of given one group of non-domination solution P, P are defined as by the space of P-domination
Lebesgue estimates, as shown in figure 3, the area of the shadow region in Fig. 3 is the super body in Pareto forward position for two target problems
Product；In order to calculate hypervolume, a reference point is needed, in the present invention, after by the combination of all sampled datas, chooses every individual character
The worst-case value of energy index, forms a reference point, in order to obtain superb bulking value, the point in P must be close to true Pareto
Forward position, and need certain dispersibility (diversity), that is, it is distributed relatively uniform each portion with true Pareto forward position
Divide all relatively, and cannot converge on a bit；
The approximate point set P in a given Pareto forward position, P'sMeasurement is defined as real Pareto forward position P*With P's
Difference between hypervolume, it may be assumed that
Wherein, HV (P*) indicate real Pareto forward position P*Hypervolume, and HV (P) indicates the approximate point set P that provides of algorithm
Hypervolume.
For Pareto forward position P*Unknown problem closes sampled data of all algorithms in optimization process in the present invention
And obtained Pareto forward position is as true Pareto forward position P*Approximation, although HV (P*) may be still and before true Pareto
The hypervolume on edge has certain gap, but by formula (8) as it can be seen that HV (P*) for the algorithm of all comparisons, it is a constant, because
And P*Selection although will affectThe numerical value of index, but when using in formula (8)Come when comparing two Pareto forward positions, and
It will not influence more resulting superiority and inferiority relationship；
In the present invention, for each problem, each algorithm independently repeats to be disturbed and calculated with mean random for ten timesValue
Statistical data；In addition, testing test GPMOOG's and MOEA/D using double sample student-tDifference between MOBO is
It is no that there is statistical conspicuousness, in double sample student-t test, by MOBO'sValue is carried out with GPMOOG and MOEA/D
Compare, and calculate two corresponding p values, higher p value means the difference between two samples it is more likely that due to becoming at random
Change and generates；In general, if p < 0.05, it may be considered that the difference observed is though statistically significant.
Embodiment 1
This example uses the ZDT1 proposed in [24] and ZDT2 test function to MOBO algorithm and GPMOOG, MOEA/D into
Row test, ZDT1 and ZDT2 are biobjective scheduling problem, and design space is 5 dimension variables；For MOBO algorithm, limit maximum
It is 300 that function, which executes number, and to GPMOOG and MOEA/D, carries out two different tests: firstly, limit GPMOOG with
The maximum simulation times of MOEA/D are 600, and optimum results are compared with MOBO；Then, GPMOOG and MOEA/D is limited
Maximum simulation times be 3600, equally its optimum results is compared with MOBO, every kind of test is repeated 10 times, selection have
There is medianOptimum results, draw its gained Pareto forward position, as shown in Figure 4；
As can be seen that MOBO algorithm only can provide the optimization close to true Pareto forward position with 300 function evaluations
As a result, and GPMOOG and MOEA/D still has larger gap after 600 function evaluations with true Pareto forward position, both calculations
Method can provide the solution close to true Pareto forward position after 3600 function evaluations；The result shows that MOBO algorithm is in speed
Advantage.
Embodiment 2
The low consumed power operational amplifier proposed in [26] is optimized in this example, the circuit is in SMIC 55nm technique
Under be designed and emulate, wherein there is 24 design variables, the value of size, resistance capacitance including transistor, and biasing
The size etc. of electric current, circuit diagram is as shown in Figure 5；
Index to be optimized include gain (Gain), unity gain bandwidth (Unit gain frequency, UGF) and
Phase margin (Phase margin, PM) considers five process corners (TT/FF/SS/SF/FS) when optimizing the circuit, with
And three kinds of temperature conditions (25 DEG C, 40 DEG C, 125 DEG C), therefore to one group of design parameter, need to carry out 15 secondary circuit emulation, to every
Worst-case value of a performance indicator in this 15 times emulation optimizes, it may be assumed that
maximize(Gainc, UGFc, PMc) (9)
Wherein, Gainc, UGFcAnd PMcIndicate least gain under the combination of all techniques/temperature, minimum unit gain
Bandwidth and minimum phase nargin；
To the circuit, when test, limits the maximum circuit simulation number of MOBO as 400 times, including 80 times initially with
Machine sampling；And to other two kinds of algorithms, simulation times are limited as 800 times, and each performance found in multiple-objection optimization is most
The figure of merit andEvery statistical result of index is as shown in table 1.
1 operational amplifier multiple-objection optimization result of table statistics
The results show that the simulation times that MOBO method uses only have the half of GPMOOG and MOEA/D, but gain is obtained
The result of GPMOOG and MOEA/D are superior to unity gain bandwidth；Although MOEA/D has found better phase margin,
The difference of the optimum phase margin value of three kinds of algorithms almost can be ignored, forIndex, MOBO algorithmValue is each
Other two kinds of algorithms are better than in item index.
Embodiment 3
Use the transformer based on TSMC 65nm technological design as example, as shown in fig. 6, the property of the transformer
Electromagnetic Simulation can be carried out by ADS momentum；The transformer has 4 design variables, including metal-8 and metal-9 metal
The width W of layer line circlem8And Wm9And metal-8 and metal-9 metal layer coil radius Rm8And Rm9；
Design object is maximization power transmission efficiency (Power Transfer Efficiency, PTE), and minimum
Change area, it may be assumed that
Minimize (- PTE, area) (11)
For MOBO, maximum Electromagnetic Simulation number is limited as 300 times, including 40 initial random samplings；And for
MOEA/D and GPMOOG method limit maximum simulation times as 350 times；The area that is found in optimization process and efficiency of transmission
Optimal value,Statistical indicator, and the significance being compared with MOBO is as shown in table 2；
The results show that MOBO algorithm realize it is more lower than GPMOOG and MOEA/DMetric, and there is extremely strong system
Significant property is counted, the optimal value of all properties index of MOBO algorithm proposed by the present invention is better than the result of GPMOOG and MOEA/D.
2 transformer multiple-objection optimization result of table statistics
As shown in fig. 7, curve therein is in each algorithmIndex is the Pareto forward position of median, shows MOBO
The Pareto forward position of generation is significantly better than other two kinds of algorithms, the point major part quilt on the Pareto forward position of other two kinds of algorithms
The point on Pareto forward position that MOBO is generated dominates.
Embodiment 4
To use the 2.5GHz operating power amplifier of Taiwan Semiconductor Manufacturing Co.'s 65nm technological design as example, which is one
A design based on array includes 211Repetitive unit, each unit include 4 transistors, which has 5 designs to become
Parameter is measured, as shown in formula (12),
For the power amplifier, it is desirable to maximize its efficiency (Eff) and output power (Pout), while keep its non-linear
It minimizes, it is non-linear to be indicated by total harmonic distortion (Thd), shown in objective design index such as formula (13):
Minimize (- Eff ,-Pout, Thd) (13)
For MOBO method, limits maximum simulation times 300 times, initially sampled immediately including 40 times, and it is right
GPMOOG and MOEA/D, maximum simulation times are limited to 500 times, and correlated results is as shown in table 3, although what MOBO method used
Simulation times are only the 60% of GPMOOG and MOEA/D, but itsIndices be better than other two kinds of algorithms.
Table 3: the multiple-objection optimization statistical result of power amplifier
Claims (4)
1. a kind of analog circuit multi-objective optimization design of power method based on multi-objective Bayesian optimization, characterized in that it comprises:
The random uniform sampling in design space；In each iteration, each target is used and currently emulates resulting data as instruction
Practice collection, constructs Gaussian process model；For each target, constructs low confidence interval and obtain function；And to low confidence interval function
Multiple-objection optimization is carried out, finally selects a point to carry out electricity on the Pareto forward position of the resulting low confidence interval of multiple-objection optimization
Road emulation, subsequently into next iteration, until the circuit simulation number for reaching maximum allowable then exits；Include step:
Input parameter:
1) analog circuit netlist, manufacturing process file, circuit emulator；
2) variation range that Analog Circuit Design parameter and design parameter allow；
3) initial random sampling number Ninit；
4) each performance indicator Yp, p=1 ..., Np, wherein NpFor the quantity of performance indicator；
5) algorithm termination condition, such as maximum allowable circuit simulation number；
Export result:
Design point on one group of Pareto forward position can dominate other that is, in this group of design parameter without any one design point
Design point is dominated by other design points；
Step 1: the uniformly random sampling N in design parameter spaceinitA sample point, and to by calling emulator to be owned
The performance index value Y of sampled pointp, p=1 ..., Np；
Step 2: being directed to each performance indicator Yp, for the performance indicator obtained by emulation as training set, building Gaussian process returns mould
Type；
Step 3: being directed to each Gaussian process model, construct low confidence interval (LCB) as acquisition function；
Step 4: using multi-objective optimization algorithm, multiple-objection optimization is carried out to the LCB function of different performance index；
Step 5: carrying out non-dominated ranking on the resulting Pareto forward position of step 4, and select first point, it is imitative to carry out circuit
Very, if termination condition meets, algorithm is terminated, and otherwise, is transferred to step 2).
2. method according to claim 1, characterized in that in the step 2), construct Gauss mistake using following sub-step
Journey model,
Step 2.1: choosing mean function and covariance function used in Gaussian process model, Gaussian process model can be by one
Value function m (x) and covariance function k (x, a y) characterization；Using constant mean function m (x)=μ0, Gauss covariance function
Are as follows:
Wherein, Λ=diag (l1..., ld) it is a diagonal matrix, and liIndicate the characteristic length in i-th of dimension
(length scale), i ∈ [1, d], μ0,σfAnd Λ is the hyper parameter of GP model；
Step 2.2: Gaussian process mould is estimated by maximal possibility estimation (Maximum Likelihood Estimation, MLE)
Hyper parameter vector θ=[μ in type0, σf, l1..., ld]；It gives training set { X, y }, wherein X={ x1..., xN},y=(f
(x1) ..., f (xN))T, N is the sum of existing simulated point；Log-likelihood function may be expressed as:
Wherein, Kθ(i, j)=k (xi, xj)；By solving the log-likelihood function in maximization formula (2), Gaussian process can get
Hyper parameter θ in model.
3. method according to claim 1, characterized in that in the step 3, using following sub-steps, according to Gauss mistake
The low confidence interval of journey model construction obtains function,
Step 3.1: giving a new data point x, the mean value and variance of its distribution are predicted according to Gaussian process；GP model is to f
(x) a prediction not instead of scalar value, one meets the stochastic variable of normal distribution, i.e. f (x)~N (μ (x), σ2(x)),
Wherein, μ (x) and σ2(x) it is respectively as follows:
Wherein, KθDefinition and formula (2) unanimously, k (x, X)=(k (x, x1) ..., k (x, xN))T, k (X, x)=k (x, X)T；Formula
(3) in, μ (x) can regard Gaussian process as and return the anticipation function value provided, σ2It (x) is then the measurement of uncertainty in traffic；
Step 3.2: LCB, which is constructed, for each objective function obtains function:
LCB1(x) ..., LCBm(x) (4)
Wherein, LCBi(x), it indicates to objective function fi(x) LCB obtains function:
LCBi(x)=μi(x)-κiσi(x), (5) i=1..m.
4. method according to claim 1, characterized in that in the step 4, carried out in the following manner to LCB function
Multiple-objection optimization:
Step 4.1: the random N number of point of uniform sampling in design parameter, the original demographic (population) as evolution algorithm；
Step 4.2: according to the variation (mutation) of differential evolution algorithm (differential evolution, DE) with hybridize
(crossover) it operates, generates filial generation (children) population via current parent (parent) population；
Variation (mutation) operating method of differential evolution are as follows: enabling parent population design parameter is p1...pN, produced by variation
Stranger mouthful m1...mN, firstly, enabling zooming parameter (scale factor) F~N (0.8,0.2) is from Gaussian Profile N (0.8,0.2)
The stochastic variable of middle sampling, then, for i=1...N, from p1...pNTwo design parameter p of middle random selectionr1With pr2, then mi
Production method is as follows:
mi=pi+F×(pr1-pr2)
The population m generated via variation1...mN, for i=1...N, enable miWith piHybridize (crossover), generates filial generation population
ci, hybridizing method are as follows: enable design variable dimension be D, setting hybrid rate (crossover rate, CR) be 0.8, first from
1...D an integer r is randomly selected inidx, then, for each dimension j=1...D, choose the random number r in (0,1)cr=
Rand (0,1), then ciJ-th of variable cijIt is generated via such as under type:
Step 4.3: by the LCB functional value of parent population, the LCB functional value of filial generation population, and having emulated to obtain design parameter
The design point of performance number combines, and forms a new point set；According to non-dominated ranking (non-dominated sorting) side
Method is ranked up the point set；Wherein, when defining crowding distance, the crowding distance of each target is multiplied, to handle difference
There is the case where biggish magnitude differences between target capabilities index, it is not necessary to be normalized；Crowding distance is changed to
The product of crowding distance, the index are known as " crowded volume ".
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