CN104809890A - Traffic signal timing optimization method based on principal component analysis and local search improvement orthogonality genetic algorithm - Google Patents

Abstract

Provided is a traffic signal timing optimization method based on principal component analysis and a local search improvement orthogonality genetic algorithm. The algorithm is provided by analyzing internal relation among the genetic algorithm, image processing and mode recognition and can be used for solving various function optimization problems. By means of the algorithm, an improvement orthogonality cross operator based on principal component analysis is provided. The operator first conducts PCA projection on the population before cross, individual length is reduced during cross, orthogonal cross operation is implemented on the projection area, the projection is projected to the original space after cross, redundant individual number and calculation expenses caused by redundancy are reduced, algorithm convergence speed is further improved, and the local search strategy is further introduced. The algorithm is applied to single-crossing signal timing optimization. By means of testing comparison with the existing algorithm, the method improves algorithm generality and efficiency, effective timing time is acquired, and the number of the queuing vehicles in front of a crossing is reduced.

Description

The Traffic Signal Timing optimization method of Orthogonal Genetic Algorithm is improved based on principal component analysis (PCA) and Local Search

Technical field

The invention belongs to the optimization problem of municipal traffic control signal timing.The algorithm (being specifically related to Orthogonal Genetic Algorithm, principal component analysis (PCA) PCA and local searching strategy) of Orthogonal Genetic Algorithm and biometrics identification technology crossing domain is used to realize controlling city Single Intersection signal timing dial.

Background technology

Along with the fast development of China's economy, urbanization process is constantly accelerated, and vehicle guaranteeding organic quantity also increases thereupon fast, and traffic trip amount increases greatly, and transportation supplies wretched insufficiency, disparities between supply and demand highlight.For Beijing, current Beijing vehicle guaranteeding organic quantity has broken through 2,000,000, and urban road annual growth rate is 3%, and vehicle growth rate is 15%, and vehicle flowrate annual growth rate reaches 18%.

As the important component part of city traffic network, crossing be the bottleneck of road passage capability and traffic jam and accident multiplely.The traffic congestion in city, major part is that this causes, and wagon flow is interrupted, accident increases because the traffic capacity of crossing is not enough or do not make full use of and cause, incurs loss through delay seriously.Motor vehicle in big city in intown running time about 1/3rd for level-crossing; And U.S.'s traffic hazard about has and over halfly occurs in crossing.As can be seen here, management crossing being carried out to science with control to be the important subject of traffic control engineering, being ensure the traffic safety of crossing and give full play to the important measures of the traffic capacity of crossing, is the effective way of solution urban transport problems.

At present, the signal controller of most domestic crossing derives from SCOOT (the Split Cycle andOffset Optimization Teclmiquel) system of Britain, SCAT (the Sydney CoordinatedAdaptive Traffic) system of Australia and Japanese capital three system, all adopts timing controlled and adaptive control.These methods are being widely used after improving.

At present, the control system of China's signal is based on single-point control, so have a lot to the signal timing dial research of Single Intersection: the multiphase traffic signal real-time control method based on state demarcation that the people such as He Zhaocheng propose, the Webster split algorithm that the people such as Zhang Cuicui adopt is optimized control to model, and Mu Haibo etc. propose the control method etc. based on Petir net.Due to non-linear, ambiguity and the uncertainty of traffic, the optimization problem of intersection signal timing generally can be summed up as the nonlinear problem of non-convex, traditional optimization method often adopts algebraic method and graphical method etc., these methods can not find its globally optimal solution well, and genetic algorithm is a kind of search technique based on natural selection and evolution, be widely used in optimization problem, therefore genetic algorithm is also widely used in the signal timing optimization problem of traffic control.The human hairs such as Song Xuehua understand the Single Intersection signal timing optimization method based on genetic algorithm, the genetic algorithm adopted in this invention is standard genetic algorithm, wherein selection strategy adds optimum reserved strategy, but standard genetic algorithm local search ability is not strong, is easily absorbed in early Convergent Phenomenon.

For this problem, the present invention analyzes the internal relation between genetic algorithm and the ultimate principle of feature extraction, propose a kind of orthogonal crossover operator based on principal component analysis (PCA), before intersecting, first PCA projection is carried out to population, reduce individual lengths when intersecting, again projecting to luv space after having intersected, reducing because intersecting the individual number of redundancy and computing cost that produce.In order to improve convergence of algorithm speed further, also introduce local searching strategy.City Single Intersection signal timing dial control problem is solved with this.

Summary of the invention

The object of the invention is to propose the control of a kind of improvement Orthogonal Genetic Algorithm (HPOGA) based on principal component analysis (PCA) and Local Search for city Single Intersection signal timing dial, carry out signal timing optimization with the queuing vehicle number before crossing for optimization aim, realize the optimal control of traffic signals.

Improvement Orthogonal Genetic Algorithm (HPOGA) based on principal component analysis (PCA) and Local Search of the present invention, first PCA projection is carried out to population before it is characterized in that intersecting, reduce individual lengths when intersecting, again projecting to luv space after having intersected, reducing because intersecting the individual number of redundancy and computing cost that produce.In order to improve convergence of algorithm speed further, also introduce local searching strategy.

Improve a traffic signal optimization timing method for Orthogonal Genetic Algorithm based on principal component analysis (PCA) and Local Search, comprise the following steps:

S1 carries out individual UVR exposure, initialization data, and setup parameter:

Described individuality represents the combination of green time; Use t _irepresent the green time of i phase place, for keeping the validity of the offspring individuals produced, adopt 3 ageings, individual UVR exposure form is: < t ₁t ₂t ₃>, decimally encodes; Described setup parameter comprises: setting crossover probability Pc is 0.8, and mutation probability Pm is 0.01, individual lengths 3;

S2 initialization of population:

N 3 individualities are generated, composition initial population P0 according to following orthogonal initialization of population method;

S2.1 finds the s dimension meeting following formula;

$u_s-l_s=\underset{1\&le;i\&le;N}{\max }\{u_i-l_i\}$

If S2.2 solution space is [l, u], then at s Wei Chu, solution space is divided into S sub spaces [l (1), u (1)], [l (2), u (2)] ... [l (s), u (s)];

$\left\{\begin{array}{c}l\left(i\right)=l+(i-1)\left(\frac{u_s-l_s}{S}\right)I_s\\ u\left(i\right)=u-(S-1)\left(\frac{u_s-l_s}{S}\right)I_s\end{array}\right.i=\mathrm{1,2},...s$

Wherein, I _s=[c _{1, j}] _{1 × N},

S3 generates interim population P ' gen

If gen is evolutionary generation, with Probability p cross, each individuality in colony Pgen is selected, add interim colony P ' gen;

S4 interlace operation

If x _irepresent and elect the body one by one that will carry out intersecting according to crossover probability Pc, then X=[x ₁, x ₂... x _n] representing the population colony that will carry out Orthogonal crossover operator, n represents population size, and the concrete steps of the orthogonal crossover operator of Based PC A are as follows:

X is expressed as matrix Pop by S4.1 _{n × m}=[x ₁ ^t, x ₂ ^t... x _n ^t] ^t, wherein each behavior body one by one, m represents chromosome length.

S4.2 carries out PCA projection to Pop, obtains Pop' _{n × p}=[y ₁ ^t, y ₂ ^t... y _n ^t] ^t, p represents the data dimension in PCA territory, y _irepresent individual x respectively _ithe data obtained after dimensionality reduction.

S4.3 carries out random pair to the individuality in colony Pop', every a pair individual y _iand y _i+1carry out Orthogonal crossover operator, according to the orthogonal arrage construction step structure orthogonal arrage in orthogonal _lM(Q ^f)=[a _i,j] _{m × p}, p is y _iand y _i+1dimension, utilize orthogonal arrage L _m(Q ^f) come y _iand y _i+1carry out orthogonal, M data assemblies will be produced.

The M individuality newly produced is carried out PCA reflection and is mapped to original domain by S4.4, and carry out fitness evaluation to the individuality obtained, the individuality selecting fitness best joins in colony C.

S4.5C is exactly the new progeny population produced after Pop carries out interlace operation.

S5 Local Search

Population P generates new population P' after cluster Local Search.Concrete steps are as follows:

If the scale of S5.1 population P is n, carries out cluster be divided into some sub-populations to the individuality in P according to individual comparability degree, the individual amount in every sub-population is set as m (algorithm arranges middle m=3) herein;

S5.2 performs SPX operation to every the sub-population divided in Step1, produces g offspring individual, i.e. the progeny population (herein g=10 in algorithm) of the sub-population of each division;

S5.3 joins each progeny population in population P'.

S6 mutation operation

To arbitrary individual pi=(pi, 1, pi, 2 in population Pgen ... pi, N), i ∈ 1,2 ... n}, participates in mutation operation with probability P mutation: produce a decimal r ∈ [0,1], and a random integers j ∈ [1, N]; Make pi, j=lj+r* (uj-lj), variation is carried out to colony P ' gen and produces new population Ggen.

S7 selects operation

In order to keep population diversity, first choose from population (Pgen+Cgen+Lgen+Ggen) the best individuality of individual fitness value adds population Pgen+1 of future generation, then from population (Pgen+Cgen+Lgen+Ggen) remaining individuality, random selecting individuality joins population Pgen+1 [28] of future generation.

S8 end condition judges

Reach stop algebraically or continuous 50 generation optimal value constant or find globally optimal solution, stop evolving and Output rusults, otherwise turn S3.

Obtain effective traffic signal optimization timing thus.

Compared with prior art, the present invention has following beneficial effect.

Based on the improvement Orthogonal Genetic Algorithm (HPOGA) of principal component analysis (PCA) and Local Search, before intersecting, first PCA projection is carried out to population, reduce individual lengths when intersecting, again projecting to luv space after having intersected, reducing because intersecting the individual number of redundancy and computing cost that produce.In order to improve convergence of algorithm speed further, also introduce local searching strategy.By the test in Single Intersection signal timing optimization problem, demonstrate versatility and the validity of algorithm, obtain the effective timing time, reduce the queuing vehicle number before crossing.

Accompanying drawing explanation

Fig. 1 is the wagon flow distribution plan of Single Intersection;

Fig. 2 is the Signal Phase Design figure applying Single Intersection in the present invention, in figure: first phase is that East and West direction is kept straight on and turned right; Second phase is that East and West direction is turned left; Third phase is keep straight on and turn right in north-south; 4th phase place is turn left in north-south;

Fig. 3 is the process flow diagram of method therefor of the present invention.

Fig. 4 is principal component analysis (PCA) (PCA) orthogonal crossover operator figure.

Concrete enforcement

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.

The present invention adopts four phase places, three lanes method for designing, the wagon flow distribution plan of Single Intersection as shown in Figure 1, the Signal Phase Design figure of Single Intersection as shown in Figure 2, the process flow diagram of the improvement Orthogonal Genetic Algorithm based on principal component analysis (PCA) and Local Search that the present invention proposes as shown in Figure 3, whole flow process is the orthogonal crossover operator of Based PC A, the population that will carry out intersecting projects to the subspace of PCA, then on PCA transform domain, Orthogonal crossover operator is carried out to population, the individuality produced after intersecting passes through PCA back projection again to original domain, carries out fitness evaluation.Wherein, principal component analysis (PCA) (PCA) orthogonal crossover operator as shown in Figure 4.

Composition graphs 3 is described in detail implementation process of the present invention.Embodiments of the invention are being implemented premised on technical solution of the present invention, give detailed embodiment and concrete operating process, but protection scope of the present invention are not limited to following embodiment.

Embodiment selects Single Intersection signal timing dial to be optimized problem to the innovatory algorithm proposed (HPOGA) and classical genetic algorithm (SGA), test based on minimum spanning tree cluster genetic algorithm (CGA) and classic method and compare herein.By the performance of algorithms of different in the different problem of process relatively can be found out.These algorithms all adopt optimum maintaining strategy.

In this embodiment, by solve objective function (with on track of letting pass after respective phase state the queuing vehicle of letting pass on track add up to performance index) obtain the signal timing dial of current period, namely the green time under each phase place, so individuality here represents the combination of green time.Use t _irepresent the green time of i phase place, simultaneously in order to keep the validity of the offspring individuals produced, adopt 3 ageings, individual UVR exposure form is: < t ₁t ₂t ₃>, encodes with scale-of-two.

Provide the explanation of each detailed problem involved in this invention technical scheme below in detail:

S1 carries out individual UVR exposure, initialization data, and setup parameter:

Described individuality represents the combination of green time; Use t _irepresent the green time of i phase place, for keeping the validity of the offspring individuals produced, adopt 3 ageings, individual UVR exposure form is: < t ₁t ₂t ₃>, decimally encodes; Described setup parameter comprises: setting crossover probability Pc is 0.8, and mutation probability Pm is 0.01, individual lengths 3;

S2 initialization of population:

N 3 individualities are generated, composition initial population P0 according to following orthogonal initialization of population method;

S2.1 finds the s dimension meeting following formula;

$u_s-l_s=\underset{1\&le;i\&le;N}{\max }\{u_i-l_i\}$

If S2.2 solution space is [l, u], then at s Wei Chu, solution space is divided into S sub spaces

[l(1),u(1)],[l(2),u(2)]...[l(s),u(s)]；

$\left\{\begin{array}{c}l\left(i\right)=l+(i-1)\left(\frac{u_s-l_s}{S}\right)I_s\\ u\left(i\right)=u-(S-1)\left(\frac{u_s-l_s}{S}\right)I_s\end{array}\right.i=\mathrm{1,2},...s$

Wherein, I _s=[c _{1, j}] _{1 × N},

S3 generates interim population P ' gen

If gen is evolutionary generation, with Probability p cross, each individuality in colony Pgen is selected, add interim colony P ' gen;

S4 interlace operation

If x _irepresent and elect the body one by one that will carry out intersecting according to crossover probability Pc, then X=[x ₁, x ₂... x _n] representing the population colony that will carry out Orthogonal crossover operator, n represents population size, and the concrete steps of the orthogonal crossover operator of Based PC A are as follows:

X is expressed as matrix Pop by S4.1 _{n × m}=[x ₁ ^t, x ₂ ^t... x _n ^t] ^t, wherein each behavior body one by one, m represents chromosome length.

S4.2 carries out PCA projection to Pop, obtains Pop' _{n × p}=[y ₁ ^t, y ₂ ^t... y _n ^t] ^t, p represents the data dimension in PCA territory, y _irepresent individual x respectively _ithe data obtained after dimensionality reduction.

S4.3 carries out random pair to the individuality in colony Pop', every a pair individual y _iand y _i+1carry out Orthogonal crossover operator, according to the orthogonal arrage construction step structure orthogonal arrage L in orthogonal _m(Q ^f)=[a _i,j] _{m × p}, p is y _iand y _i+1dimension, utilize orthogonal arrage L _m(Q ^f) come y _iand y _i+1carry out orthogonal, M data assemblies will be produced.

The M individuality newly produced is carried out PCA reflection and is mapped to original domain by S4.4, and carry out fitness evaluation to the individuality obtained, the individuality selecting fitness best joins in colony C.

S4.5C is exactly the new progeny population produced after Pop carries out interlace operation.

S5 Local Search

Population P generates new population P' after cluster Local Search.Concrete steps are as follows:

S5.1 supposes that the scale of population P is n, carries out cluster be divided into some sub-populations to the individuality in P according to individual comparability degree, and the individual amount in every sub-population is set as m (algorithm arranges middle m=3) herein;

S5.2 performs SPX operation to every the sub-population divided in Step1, produces g offspring individual, i.e. the progeny population (herein g=10 in algorithm) of the sub-population of each division;

S5.3 joins each progeny population in population P'.

S6 mutation operation

To arbitrary individual pi=(pi, 1, pi, 2 in population P ' gen ... pi, N), i ∈ 1,2 ... n}, participates in mutation operation with probability P mutation: produce a decimal r ∈ [0,1], and a random integers j ∈ [1, N]; Make pi, j=lj+r* (uj-lj), variation is carried out to colony P ' gen and produces new population Ggen.

S7 selects operation

In order to keep population diversity, first choose from population (Pgen+Cgen+Lgen+Ggen) the best individuality of individual fitness value adds population Pgen+1 of future generation, then from population (Pgen+Cgen+Lgen+Ggen) remaining individuality, random selecting individuality joins population Pgen+1 [28] of future generation.

S8 end condition judges

Reach stop algebraically or continuous 50 generation optimal value constant or find globally optimal solution, stop evolving and Output rusults, otherwise turn S3.

Detailed description experimental result of the present invention below:

In order to prove the validity of the method for the invention in Single Intersection signal timing dial controls, adopt HPOGA (algorithm in the present invention), SGA (Standard GeneticAlgorithm respectively, standard genetic algorithm), CGA (based on minimum spanning tree cluster genetic algorithm) and classic method be optimized Single Intersection signal timing dial, each optimizing process calculates the timing in 10 cycles.Experimental result is as shown in table 1.

The Comparative result of table 1 HPOGA and classic method, SGA and CGA

As shown in Table 1, adopt the inventive method each cycle can find timing optimum solution, and SGA and CGA can only find 3 near-optimal solution, classic method then can not find optimum solution.Absolutely prove and the queue length that queue length that the inventive method obtains not only is far smaller than classic method and obtains also be significantly less than the queue length adopting SGA and CGA method to obtain.Therefore, compared with prior art, the present invention can obtain the more effective timing time, reduces the queuing vehicle number before crossing, effectively improves the traffic capacity of Single Intersection.

Claims (2)

1. the Traffic Signal Timing optimization side of Orthogonal Genetic Algorithm is improved based on principal component analysis (PCA) and Local Search

Method, is characterized in that: comprise the steps,

S1 carries out individual UVR exposure, initialization data, and setup parameter;

Described individuality represents the combination of green time; Use t _irepresent the green time of i phase place, for keeping the validity of the offspring individuals produced, adopt 3 ageings, individual UVR exposure form is: < t ₁t ₂t ₃>, decimally encodes; Described setup parameter comprises: setting crossover probability Pc is 0.8, and mutation probability Pm is 0.01, individual lengths 3;

S2 initialization of population,

N 3 individualities are generated, composition initial population P0 according to following orthogonal initialization of population method;

S2.1 finds the s dimension meeting following formula;

$u_s-l_s=\underset{1\&le;i\&le;N}{\max }\{u_i-l_i\}$

If S2.2 solution space is [l, u], then at s Wei Chu, solution space is divided into S sub spaces

[l(1),u(1)],[l(2),u(2)]...[l(s),u(s)]；

$\left\{\begin{array}{c}l\left(i\right)=l+(i-1)\left(\frac{u_s-l_s}{S}\right)I_s\\ u\left(i\right)=u-(S-1)\left(\frac{u_s-l_s}{S}\right)I_s\end{array}\right.i=\mathrm{1,2},...s$

Wherein, $I_s=[c_{1,j}{]}_{1\&times;N},$

S3 generates interim population P ' gen

If gen is evolutionary generation, with Probability p cross, each individuality in colony Pgen is selected, add interim colony P ' gen;

S4 interlace operation

If x _irepresent and elect the body one by one that will carry out intersecting according to crossover probability Pc, then X=[x ₁, x ₂... x _n] representing the population colony that will carry out Orthogonal crossover operator, n represents population size, and the concrete steps of the orthogonal crossover operator of Based PC A are as follows:

X is expressed as matrix Pop by S4.1 _{n × m}=[x ₁ ^t, x ₂ ^t... x _n ^t] ^t, wherein each behavior body one by one, m represents chromosome length;

S4.2 carries out PCA projection to Pop, obtains Pop' _{n × p}=[y ₁ ^t, y ₂ ^t... y _n ^t] ^t, p represents the data dimension in PCA territory, y _irepresent individual x respectively _ithe data obtained after dimensionality reduction;

S4.3 carries out random pair to the individuality in colony Pop', every a pair individual y _iand y _i+1carry out Orthogonal crossover operator, according to the orthogonal arrage construction step structure orthogonal arrage L in orthogonal _m(Q ^f)=[a _i,j] _{m × p}, p is y _iand y _i+1dimension, utilize orthogonal arrage L _m(Q ^f) come y _iand y _i+1carry out orthogonal, M data assemblies will be produced;

The M individuality newly produced is carried out PCA reflection and is mapped to original domain by S4.4, and carry out fitness evaluation to the individuality obtained, the individuality selecting fitness best joins in colony C;

S4.5C is exactly the new progeny population produced after Pop carries out interlace operation;

S5 Local Search

Population P generates new population P' after cluster Local Search; Concrete steps are as follows:

If the scale of S5.1 population P is n, carry out cluster to the individuality in P according to individual comparability degree and be divided into some sub-populations, the individual amount in every sub-population is set as m;

S5.2 performs SPX operation to every the sub-population divided in Step1, produces g offspring individual, i.e. the progeny population of the sub-population of each division;

S5.3 joins each progeny population in population P';

S6 mutation operation

To arbitrary individual pi=(pi, 1, pi, 2 in population P ' gen ... pi, N), i ∈ 1,2 ... n}, participates in mutation operation with probability P mutation: produce a decimal r ∈ [0,1], and a random integers j ∈ [1, N]; Make pi, j=lj+r* (uj-lj), variation is carried out to colony P ' gen and produces new population Ggen;

S7 selects operation

In order to keep population diversity, first choose from population (Pgen+Cgen+Lgen+Ggen) the best individuality of individual fitness value adds population Pgen+1 of future generation, then from population (Pgen+Cgen+Lgen+Ggen) remaining individuality, random selecting individuality joins population Pgen+1 [28] of future generation;

S8 end condition judges

Reach stop algebraically or continuous 50 generation optimal value constant or find globally optimal solution, stop evolving and Output rusults, otherwise turn S3;

Obtain effective traffic signal optimization timing thus.

2. the Traffic Signal Timing optimization method improving Orthogonal Genetic Algorithm based on principal component analysis (PCA) and Local Search according to claim 1, is characterized in that: the method calculating ideal adaptation angle value in population is as follows,

After terminating using Single Intersection every phase place in one-period, on this phase place clearance track, queuing vehicle sum is as optimization aim, and the objective function namely in genetic algorithm, be also fitness function, its expression formula is

$\begin{array}{c}\hat{S}=\min s\\ =\min \underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{4}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{3}{\mathrm{\&Sigma;}}}{p}_{\mathrm{ijk}}*(s_{\mathrm{ijk}}^l+{\mathrm{\&lambda;}}_{\mathrm{ijk}}*t_i+{\mathrm{\&lambda;}}_{\mathrm{ijk}}*(T-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{t}_i)-p_{\mathrm{ijk}}*u_{\mathrm{ijk}}*t_i-p_{\mathrm{ijk}}*u_{\mathrm{ijk}}*(T-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{t}_i))\end{array}$

$s.t:\left\{,\begin{array}{c}{t}_1+t_2+{\text{t}}_3\text{+}{t}_4=T\\ 6\&le;t_i\&le;T-18\end{array}\right.(i=\mathrm{1,2,3,4})$

In formula, T is the Cycle Length that Single Intersection signal controls; t _irepresent the timing of crossing four phase place, i=1,2,3,4; λ _ijkrepresent the vehicle arriving rate in the i-th k track, phase place j direction, j=1,2,3,4, represent respectively eastwards, westwards, southwards and northwards four Way ins, k=1,2,3, represent left-hand rotation respectively, three tracks of keeping straight on and turn right; u _ijkrepresent the vehicle clearance rate in the i-th k track, phase place j direction; be l week after date, vehicle queue's number in the i-th k track, phase place j direction, expression formula is

$s_{\mathrm{ijk}}^l=\left\{\begin{array}{cc}{s}_{\mathrm{ijk}}^{l-1}+{\mathrm{\&lambda;}}_{\mathrm{ijk}}*t_i-p_{\mathrm{ijk}}*u_{\mathrm{ijk}}*t_i,& s_{\mathrm{ijk}}^{l-1}+{\mathrm{\&lambda;}}_{\mathrm{ijk}}*t_i\&GreaterEqual;u_{\mathrm{ijk}}*t_i\\ 0,& s_{\mathrm{ijk}}^{l-1}+{\mathrm{\&lambda;}}_{\mathrm{ijk}}*t_i<u_{\mathrm{ijk}}*t_i\end{array}\right.$

In formula, p _ijkrepresent release status matrix, its expression formula is:

$p_{\mathrm{ijk}}=\left[\begin{array}{cccc}\{\left(\mathrm{0,1,1}\right)& \left(\mathrm{0,0,0}\right)& \left(\mathrm{0,1,1}\right)& \left(\mathrm{0,0,0}\right)\}\\ \{\left(\mathrm{0,0,0}\right)& \left(\mathrm{0,1,1}\right)& \left(\mathrm{0,0,0}\right)& \left(\mathrm{0,1,1}\right)\}\\ \{\left(\mathrm{1,0,0}\right)& \left(\mathrm{0,0,0}\right)& \left(\mathrm{1,0,0}\right)& \left(\mathrm{0,0,0}\right)\}\\ \{\left(\mathrm{0,0,0}\right)& \left(\mathrm{1,0,0}\right)& \left(\mathrm{0,0,0}\right)& \left(\mathrm{1,0,0}\right)\}\end{array}\right]$

In formula, " 0 " represents that the corresponding track under respective phase is in and forbids release status, and " 1 " represents that the corresponding track under respective phase is in release status.