Based on Gene regulation fast simulated annealing algorithm
Technical field
The invention belongs to technical field of bioengineering, and in particular to one kind is based on Gene regulation fast simulated annealing algorithm.
Background technique
In the presence of the microorganism that can convert glycerol into 1,3-PD, mainly several bacteriums in nature.Such as:
Klebsiella, Citrobacters, Enterobacter and Clostridia etc., wherein klebsiella
(Klebsiella pneumoniae) and with higher turn of clostridium butyricum (Clostridium butyricum)
Rate and 1,3-PD production capacity, thus more paid close attention to.Early in nineteen fifty-three, annealing algorithm has been introduced into control field,
Annealing thought is successfully introduced into Combinatorial Optimization field by nineteen eighty-three, S.Kirkpatrick etc..1,3-PD production was controlled
Journey can solve the random optimization problem that strategy is iteratively solved based on Monte-Carlo using annealing algorithm, and starting point is to be based on
Similitude in physics between the annealing process of solid matter and general combinatorial optimization problem.Simulated annealing is from a certain higher
Initial temperature is set out, and with the continuous decline of temperature parameter, join probability kick characteristic finds objective function at random in solution space
Globally optimal solution can be jumped out probabilityly in locally optimal solution and finally tend to global optimum.Simulated annealing is a kind of
General optimization algorithm, theoretically algorithm has the global optimization performance of probability, is applied in engineering at present, such as
The fields such as VLSI, production scheduling, control engineering, machine learning, neural network, signal processing.With simulated annealing theory
, there is the fast simulated annealing algorithm of numerous species in research, this speed for allowing for calculating greatly is promoted, due to asking
Topic includes 26112 system continuous parameters and 9217 path discrete parameters, and calculation amount is very huge, only on serial computer
It can not solve the problems, such as.
Summary of the invention
For overcome the deficiencies in the prior art, a kind of fast simulated annealing calculation continuously fermented based on Gene regulation is proposed
Method, algorithm optimization method solves control problem encountered, using the concentration of extracellular 1,3-PD as performance indicator
Mix dynamical system according to fast simulated annealing algorithm solution is non-linear.
The technical solution of the present invention is as follows: being based on Gene regulation fast simulated annealing algorithm, the algorithm solves the micro- life of glycerol
Object ferment control problem, function x (t) are set as the concentration in the glycerol microbial fermentation controlling element of t moment: that is,
X (t)=(x1(t),x2(t),…,x14(t)) I, is enabledN={ 1,2 ..., N }, N are test number (TN), and W is path set, | W
| it is number of path, t
For reaction time, t ∈ [0, T], T ∈ R+,For state variable, j
∈IN,k∈I|W|Indicate that controlling element is in the concentration of t moment when jth time test kth paths;DjFor the glycerol dilution rate of jth time test,For the glycerol initial concentration j ∈ I of jth time testN, under 37 DEG C, PH=7 anaerobic condition, each point of state vector x
Amount control is in the range of the lower bound of state vector x and the upper bound provide, the lower bound of state vector x and the upper bound are as follows:
x*=(0.0001,0.01,0,0,0,0,0,0,0,0,0,0,0,0)T,
x*=(10,2039,939.5,1026,360.9,2039,200,939.5,30,30,30,30,30,3 0)T,
Then feasible set is expressed asMeanwhile the feasible set of system parameter u are as follows:
If the interval of glycerol dissimilation production 1,3-PD is respectively [0, t with the time range continuously fermentedb] and [tb, T], then
To j ∈ IN,k∈I|W|Glycerol biology dismutation can be described as following the non-linear of enzymatic and gene regulation and mix power
System HNDS (j, k):
Wherein f=(f1,f2,...,f14)T, uk∈R30, [0, T] ∈ R+, this System describe is glycerol elder generation batch fermentation
(1) continuously ferment after the process of (2), tbFor the end time of batch fermentation, D in Batch fermentation processj=0. sets glycerol dissimilation life
It produces the interval of 1,3-PD and the time range continuously fermented is respectively [0, tb] and [tb, T], wherein 0 < tb< T <+∞ is to giving
Fixed k ∈ IW,j∈IN, it is assumed that system NHDS (j, k) is in moment tsReach approximation steady state, remembers that extracellular approximation steady state concentration is x
(ts;x0,uk,j,wk),i∈I3Enable yj(i),i∈I3When reaching stable state for the extracellular first three substance that jth time test measures
Concentration, the test bit of extracellular substances are defined as with the relative error for calculating data
The robustness of intracellular matter is defined as
Wherein U is the disturbance space of u, u' ∈ Bσ(u), σ > 0 be about u neighborhood ball radius, φ (u'-u) be about
(u'-u) objective function of the probability density function of ∈ U, foundation is as follows:
J (u, j, k)=τ1SSD(u,j,k)+τ2MSD(u,j,k),
Utilize Controlling model
||f(x,uk,j,wk)||≤ξ,
u(j,k)∈U(x0,j,k),
wk∈W
In this algorithm, all variables with opt combination letter for label are expressed as processed variable, and wherein ξ is
One sufficiently small constant greater than zero, the parallel fast simulated annealing algorithm key step of construction are as follows:
Step 1: n is distributed for algorithmpA processor, total number of particles Psize, then the population in each processor isThe following primary data of typing in root processor:
Step 1.1, typing given data u*,u*,x*,x*,T0,Tf, ε, N and each known parameters
Step 1.2, typing path set W,
Step 1.3, typing test data DC,yj(i),i∈I3
Step 1.4 sets k=1, dt=1, T=T0
Step 1.5, takesλ is random between 0 and 1
Number, enables Jopt=J (uopt,j,k),kopt=k
Step 2: by the datacast MPI_Bcast in root processor into each sub-processor
Step 3: in each sub-processorIt is upper to execute following process:
Step 3.1, from UadIn be randomly generatedThe number of a particle, each particle isCalculate the corresponding target function value of each particle
Step 3.2, if n > N, is transferred to Step4.2, otherwise takesIt calculatesWith
If Δ J < 0 orThenIt is no
ThenIt is constant.
Step 4: casting sub-processorOnInto root processor, then execute following steps:
Step 4.1 is calculated
Step 4.2, if Tf> T is then transferred in next step, otherwise T=T δdt, δ is the random number between 0 and 1, goes to step
1.5。
Step 4.3, ifThenOtherwise enter in next step;
Step 4.4, if k > | W |, it is transferred in next step, otherwise k=k+1, is transferred to step3.
Beneficial effect of the present invention
1, the present invention is not required to require the partial derivative of objective function that can find a globally optimal solution, and is easy to be added
Constraint condition, this algorithm weaken the correlation that calculated result quality is chosen with initial point, while also avoiding algorithm in part
The case where optimal solution is without solution;
2, the present invention utilizes approximate stability, intraor extracellular material concentration relative error and the cell for system of continuously fermenting
Biological Robustness of interior material concentration etc. is main constraints, constructs the calculation method of Optimal Control Problem.
Specific embodiment
Algorithm of the present invention solves glycerol microbial fermentation control problem, and function x (t) is set as the glycerol in t moment
The concentration of microbial fermentation controlling element: that is,
X (t)=(x1(t),x2(t),…,x14(t)), x1(t),x2(t),…,x14(t), I is enabledN=1,2 ..., and N }, N is
Test number (TN), W are path set, | W | it is number of path,T is reaction time, t
∈[0,T],T∈R+,For state variable, j ∈ IN,k∈I|W|Table
Concentration of the controlling element in t moment when showing jth time test kth paths;DjFor the glycerol dilution rate of jth time test,For the glycerol initial concentration j ∈ I of jth time testN, under 37 DEG C, PH=7 anaerobic condition, each point of state vector x
Amount control is in the range of the lower bound of state vector x and the upper bound provide, the lower bound of state vector x and the upper bound are as follows:
x*=(0.0001,0.01,0,0,0,0,0,0,0,0,0,0,0,0)T,
x*=(10,2039,939.5,1026,360.9,2039,200,939.5,30,30,30,30,30,3 0)T,
Then feasible set is expressed asMeanwhile the feasible set of system parameter u are as follows:
If the interval of glycerol dissimilation production 1,3-PD is respectively [0, t with the time range continuously fermentedb] and [tb, T],
In 0 < tb< T <+∞, then to j ∈ IN,k∈I|W|Glycerol biology dismutation can be described as following enzymatic and gene regulation
Non-linear mix dynamical system HNDS (j, k):
Wherein f=(f1,f2,...,f14)T, uk∈R30, [0, T] ∈ R+.This System describe is glycerol elder generation batch fermentation
(1) continuously ferment after the process of (2), tbFor the end time of batch fermentation, D in Batch fermentation processj=0.
In view of the possible inhibiting mechanism of 3-HPA, it is assumed that glycerol and 1, it is active transport that 3-PD, which flies transdermal delivery mode,
It is combined with Passive diffusion, to given k ∈ I|W|,j∈IN, it is assumed that system NHDS (j, k) is in moment tsReach approximation steady state, remembers
Extracellular approximation steady state concentration is x (ts;x0,uk,j,wk),i∈I3Y is enabledj(i),i∈I3It is measured for jth time test extracellular
First three substance reaches concentration when stable state, and the test bit of extracellular substances is defined as with the relative error for calculating data
For this purpose, the objective function established is as follows:
J (u, j, k)=τ1SSD(u,j,k)+τ2MSD(u,j,k),
Wherein τ1,τ2It is weight coefficient, is the importance for balanced relative error and robustness, with extracellular 1,3- third
The concentration of glycol is performance indicator, to mix the approximate stability of nonlinear dynamic system, system of continuously fermenting, intracellular foreign object
Biological Robustness of matter concentration relative error and intracellular matter concentration etc. is main constraints, and establishing model is
||f(x,uk,j,wk)||≤ξ,
u(j,k)∈U(x0,j,k),
wk∈W
Wherein ξ is a sufficiently small constant greater than zero, for judging whether service system HNDS (j, k) reaches approximate
Stable state.
In this algorithm, all variables with opt combination letter for label are expressed as processed variable, including variable
kopt, Jopt, uopt, up opt, equally, all variables with current and next combination letter for label are expressed as currently becoming
Amount and next variable, the concrete meaning that all of above variable represents is constant, the parallel fast simulated annealing algorithm that we construct
(SA) key step is as follows:
Step 1: n is distributed for algorithmpA processor, total number of particles Psize, then the population in each processor isThe following primary data of typing in root processor:
Step 1.1, typing given data u*,u*,x*,x*,T0,Tf, ε, N and each known parameters
Step 1.2, typing path set W,
Step 1.3, typing test data DC,yj(i),i∈I3
Step 1.4 sets k=1, dt=1, T=T0
Step 1.5, takesλ is random between 0 and 1
Number, enables Jopt=J (uopt,j,k),kopt=k
Step 2: by the datacast MPI_Bcast in root processor into each sub-processor
Step 3: in each sub-processorIt is upper to execute following process:
Step 3.1, from UadIn be randomly generatedThe number of a particle, each particle isCalculate the corresponding target function value of each particle
Step 3.2, if n > N, is transferred to Step4.2,
Otherwise it takes
It calculatesWith
If Δ J < 0 or
ThenOtherwiseIt is constant.
Step 4: casting sub-processorOnInto root processor, then execute following steps:
Step 4.1 is calculated
Step 4.2, if Tf> T is then transferred in next step, otherwise T=T δdt, δ is the random number between 0 and 1, goes to step
1.5。
Step 4.3, ifThenOtherwise enter in next step.
Step 4.4, if k > | W |, it is transferred in next step, otherwise k=k+1, is transferred to step 3.
The present invention is not required to require the partial derivative of objective function that can find a globally optimal solution, and is easy to be added about
Beam condition, this algorithm weaken the correlation that calculated result quality is chosen with initial point, at the same also avoid algorithm part most
The case where excellent solution is without solution;The present invention using the approximate stability of system of continuously fermenting, intraor extracellular material concentration relative error with
And Biological Robustness of intracellular matter concentration etc. is main constraints, constructs the calculation method of Optimal Control Problem.