CN104376387A - Optimization decision-making method for concrete transportation queuing networks during high arch dam engineering construction - Google Patents

Abstract

The invention belongs to the technical field of engineering management, and discloses an optimization decision-making method for concrete transportation queuing networks during high arch dam engineering construction. The concrete transportation queuing networks can be dynamically optimized by the aid of the optimization decision-making method during high arch dam construction. The method includes steps of A, describing relevant uncertain parameters by the aid of fuzzy random numbers; B, computing system state transition probabilities of the transportation networks; C, building multi-objective and multistage decision-making optimization models; D, equivalently transforming the models to form solvable multistage decision-making optimization models; E, solving the models by the aid of particle swarm optimization algorithms on the basis of paired processes. The optimization decision-making method has the advantage of applicability to improving the construction efficiency and reducing the running cost during high arch dam engineering construction.

Description

Concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction

Technical field

The invention belongs to project management technique field, the concrete transportation queuing network Study on Decision-making Method for Optimization particularly in a kind of induced joint engineering construction.

Background technology

Concrete construction in induced joint engineering construction by concrete production, transport and build three systems and form, as shown in Figure 1.In induced joint engineering construction, often only need a concrete production system (dashed rectangle see in the middle of Fig. 1 bottom).Concrete production system is generally made up of (circle see in Fig. 1 dashed rectangle) multiple concrete batching and mixing plant.Dump truck (see small rectangle white in Fig. 1) is queued up at concrete batching and mixing plant place and is loaded concrete, and heavy haul transport uses (see Fig. 1 upper dotted line square frame) to unloading point (see broken line triangle in Fig. 1) for concrete casting system afterwards.Concrete casting system is made up of the cable transportation be erected at above induced joint and cable machine.Cable machine (i.e. black small rectangle in Fig. 1) at unloading point from dump truck unloading concrete be transported to casting area (see Fig. 1 induced joint dash area) by cable system.When dump truck arrives unloading point, then wait in line cable machine concrete being unloaded into wait, then zero load returns concrete batching and mixing plant and prepares next round transport afterwards.

Generally, a concrete production system is required to be multiple unloading point supply concrete.Each unloading point may correspond to multiple casting area, and is responsible for transport between which by multiple cable machine.Dump truck is divided into multiple squad to work on the transportation route of different connection concrete production systems and corresponding unloading point respectively according to different transport tasks.Fig. 2 illustrates the transport case that a concrete production system is responsible for N number of unloading point, and wherein different transportation route collects at concrete production system and is woven into a conveyance queuing network.Different dump truck squads returns circulation transport again from concrete production system to corresponding unloading point, forms a dynamic conveyance queuing network.

The whole concrete process of construction of induced joint can be divided into 3 stages, is respectively dam foundation concreting, and dam concrete is built and dam facing concreting, as shown in Figure 3.The different concrete types needed for the concreting stage is also different, therefore it is also different to produce concrete efficiency at each stage concrete batching plant, and each casting area concreting intensity is also different.In figure 3, each unloading point all have one independently transportation route lead to concrete production system.In each stage, all available dump trucks are all dispensed to corresponding transportation route and carry out operation.The probability that dump truck and cable machine break down can change with transportation route or the difference in unloading point and stage.Usually, the fault of dump truck and cable machine is often gradually hair style fault.When dump truck or cable machine are after certain one-phase enters malfunction, usually maintenance work can be continued until this stage terminates to be sent to maintenance department's maintenance again.Maintenance due to dump truck and cable machine is a job consuming time, often needs the longer time.After maintenance completes, dump truck and cable machine can return work.The dump truck of dynamic change in this transportation network system and cable machine quantity make decision maker need to carry out multistage decision to optimize dump truck and cable machine task in each stage in transportation network distributes and reaches the object minimizing total operating cost He build the duration.

Multistage decision optimisation technique is a kind of optimisation technique for dynamic decision problem.Its main thought determines the division in stage and the decision variable in each stage and state variable according to the dynamic feature of actual decision problem, and the state transition equation of the constraint condition of difference establishing target function and decision variable and reflection decision variable and state variable relation, form multistage decision Optimized model, and design the technology that corresponding algorithm carries out solving.

In recent years, decision optimization technology is applied in a lot of fields, as stock control, Resourse Distribute, construction site layout etc.Main correlation technique comprises multiobiective decision optimum, multiple attribute decision making (MADM) optimization and multilevel policy decision optimization etc.These decision optimization technology effectively can solve staticaccelerator decision problem, but for multistage dynamic decision problem, not yet form optimisation technique problem and the method for solving of system.

Summary of the invention

Technical matters to be solved by this invention is: propose the concrete transportation queuing network Study on Decision-making Method for Optimization in a kind of induced joint engineering construction, solves concrete transportation queuing network optimization problems in high arch dam construction.

The technical solution adopted for the present invention to solve the technical problems is: the concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction, comprises the following steps:

A. fuzzy stochastic number is adopted to describe relevant uncertain parameter;

B. transportation network system state transition probability calculates;

C. multi-object and multi-phase decision Optimized model is built;

D. equivalence conversion is carried out to model, form the multistage decision Optimized model that can separate;

E. the particle swarm optimization algorithm based on Dual Method is adopted to solve model.

Concrete, in steps A, described relevant uncertain parameter comprises:

1) monthly effective working day: affect by weather condition, these uncertain factors of accident and there is fuzzy and stochastic feature, be expressed as

2) transport of dump truck and the stand-by period: affect by transportation range, driver technology and these factors of road conditions, dump truck is used along path i respectively in stage k heavy duty and unloaded haulage time with represent, its time waited in unloading point i and concrete production system at stage k is used respectively with represent, then dump truck at stage k along total two-way time of path i is: ${\stackrel{\widetilde{\‾}}{T}}_i\left(k\right)={\stackrel{\widetilde{\‾}}{T}}_h^i\left(k\right)+{\stackrel{\widetilde{\‾}}{T}}_e^i\left(k\right)+{\stackrel{\widetilde{\‾}}{T}}_u^i\left(k\right)+{\stackrel{\widetilde{\‾}}{T}}_c\left(k\right),\∀i,k;$

3) dump truck arrival rate: use represent that a dump truck is in the arrival rate of stage k in unloading point i, its computing formula is as follows: ${\stackrel{\widetilde{\‾}}{\mathrm{\λ}}}_i\left(k\right)=\frac{1}{{\stackrel{\widetilde{\‾}}{T}}_i\left(k\right)}=\frac{1}{{\stackrel{\widetilde{\‾}}{T}}_h^i\left(k\right)+{\stackrel{\widetilde{\‾}}{T}}_e^i\left(k\right)+{\stackrel{\widetilde{\‾}}{T}}_u^i\left(k\right)+{\stackrel{\widetilde{\‾}}{T}}_c\left(k\right)},\∀i,k;$

4) cable machine service rate: use e _ik () represents the cable machine quantity being allocated in unloading point i operation at stage k, be a cable machine at the service rate of stage k in unloading point i operation, be engraved in when a certain unloading point i unload concrete and etc. dump truck quantity to be unloaded when being j, unloading point i is at the service rate of this stage k can be calculated as:

${\stackrel{\widetilde{\‾}}{\mathrm{\μ}}}_i^j\left(k\right)=\left\{\begin{array}{c}j{\stackrel{\widetilde{\‾}}{\mathrm{\μ}}}_i\left(k\right),j=\mathrm{0,1},...,e_i\left(k\right)-1\\ e_i\left(k\right){\stackrel{\widetilde{\‾}}{\mathrm{\μ}}}_i\left(k\right),j=e_i\left(k\right),e_i\left(k\right)+1,...,v_i\left(k\right).\end{array}\right.$

Concrete, in step B, the quantity of the dump truck that described transportation network system state is stopped by each unloading point is determined, its change affects at the service rate of each unloading point for the arrival rate of each unloading point and cable machine by dump truck, use represent stage k when unloading point i place have j dump truck unload concrete or etc. to be unloaded time network subsystem i state, use expression state (j=0,1 ..., v _i(k)) probability of happening, if derive each state probability of happening computing formula as follows:

$p_i^0\left(k\right)={[\underset{j=0}{\overset{e_i\left(k\right)-1}{\mathrm{\Σ}}}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!j!}{\left({\stackrel{\widetilde{\‾}}{\mathrm{\ρ}}}_i\left(k\right)\right)}^j+\underset{j=e_i\left(k\right)}{\overset{v_i\left(k\right)}{\mathrm{\Σ}}}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!e_i\left(k\right)!e_i{\left(k\right)}^{j-e_i\left(k\right)}}{\left({\stackrel{\widetilde{\‾}}{\mathrm{\ρ}}}_i\left(k\right)\right)}^j]}^{-1}$

$p_i^j\left(k\right)=\left\{\begin{array}{c}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!j!}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j{p}_i^0\left(k\right),1\&le;j<e_i\left(k\right)\\ \frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!e_i\left(k\right)!e_i{\left(k\right)}^{j-e_i\left(k\right)}}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j{p}_i^0\left(k\right),e_i\left(k\right)\&le;j\&le;v_i\left(k\right).\end{array}\right.$

Concrete, in step C, described structure multi-object and multi-phase decision Optimized model, comprising:

C1. model state system of equations is built:

Use A _v(k) and A _ek () is illustrated respectively in the quantity of the adjustable dump truck of stage k and cable machine:

$A_V\left(k\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{v}_i\left(k\right)$ With $A_E\left(k\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}_i\left(k\right);$

Represent with ζ the number of stages that maintenance is used, use ψ _i(k) and φ _ik () represents the dump truck that is dispensed to subsystem i and the cable machine rate of breakdown at stage k respectively, then the equations of state that can build model is as follows:

$A_V(k+1)=A_V\left(k\right)-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_i\left(k\right)v_i\left(k\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_i(k-\mathrm{\&zeta;})v_i(k-\mathrm{\&zeta;})+R_V(k+1)$

$A_E(k+1)=A_E\left(k\right)-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i\left(k\right)e_i\left(k\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i(k-\mathrm{\&zeta;})e_i(k-\mathrm{\&zeta;})+R_E(k+1)$

Wherein, when k-ζ≤0, ψ _i(k-ζ) v _i(k-ζ) and φ _i(k-ζ) e _i(k-ζ) value is 0;

C2. model starting condition is built:

Use α ₁and β ₁be illustrated respectively in the quantity that the starting stage can supply dump truck and the cable machine allocated, build model starting condition:

A _v(1)=α ₁and A _e(1)=β ₁;

C3. model constrained condition is built:

The quantity of the dump truck and cable machine that are dispensed to subsystem i at stage k should be no less than 0 and be no more than and for the quantity of the dump truck of allotment and cable machine, can build model constrained condition as follows in this stage:

0≤v _i(k)≤A _v(k) and 0≤e _i(k)≤A _e(k),

C4. model objective function is built:

Target according to decision maker builds as follows about minimizing the objective function of building duration and operating cost:

1) build the duration: the working time representing dump truck with t, H represents the charging capacity of dump truck, represent at the concrete actual placing intensity of stage k in casting area i, ξ _ik () represents the service rate of cable machine at stage k unloading point i; Due to ξ _ik () is stochastic variable, according to law of great numbers, calculate its expectation value as follows:

$E\left({\mathrm{\&xi;}}_i\left(k\right)\right)=\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right),\&ForAll;i,k$

Thus can the actual placing intensity of concrete of calculation stages k casting area i as follows:

$I_i^d\left(k\right)=\mathrm{tHE}\left({\mathrm{\&xi;}}_i\left(k\right)\right)=\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right),\&ForAll;i,k$

With represent at the concrete actual placing intensity of stage k in casting area i, Q _ik () represents the plan concreting amount at stage k casting area i, D _ik () represents and builds the duration the concrete of stage k casting area i is actual, its computing formula is as follows:

$D_i\left(k\right)=\frac{Q_i\left(k\right)}{I_i^m\left(k\right)}=\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}{I}_i^d\left(k\right)}=\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)},\&ForAll;i,k$

In pouring construction process, only all casting area of current generation all complete build after could start the pouring construction of next stage, use represent and build total lever factor,

Wherein x=(v ₁(), v ₂() ..., v _n(), e ₁(), e ₂() ..., e _n()),

$\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}}=(\stackrel{\widetilde{\&OverBar;}}{w},{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_1(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_2(\&CenterDot;),...,{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_N(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_1(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_2(\&CenterDot;),...,{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_N(\&CenterDot;)),$

Then its computing formula is as follows:

$f_d(x,\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}})=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i}{\max }\left\{D_i\left(k\right)\right\}=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i}{\max }\left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)}\right\}$

2) operating cost: use C _brepresent the unit operating cost of 1 concrete batching and mixing plant, C _vrepresent the unit operating cost of 1 dump truck, C _erepresent the unit operating cost of a cable machine, represent the total operating cost of concreting; Because the time span of stage k is and the operating cost of concrete batching and mixing plant, dump truck and cable machine can middlely within the whole duration occur, therefore the length of total lever factor can affect the total operating cost of concreting; Represent the quantity of concrete batching and mixing plant with M, then can calculate as follows:

$f_c(x,\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}})=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\stackrel{\widetilde{\&OverBar;}}{w}(C_{b}M+C_v{A}_V\left(k\right)+C_e{A}_E\left(k\right))\&times;\underset{i}{\max }\left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}{\mathrm{tH\&Sigma;}}_{j=0}^{v_i\left(k\right)}{p}_i^j\left(k\right){\mathrm{\&mu;}}_i^j\left(k\right)}\right\};$

C5. based on the integrated formation multi-object and multi-phase decision Optimized model of equations of state, starting condition, constraint condition, objective function:

Concrete, in step D, describedly equivalence conversion is carried out to model, the multistage decision Optimized model that formation can be separated, specifically comprise:

Suppose that the longest permissible total lever factor of building is D, be then converted into following constraint condition by minimizing the objective function of building total lever factor:

$\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i}{\max }\left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}{\mathrm{tH\&Sigma;}}_{j=0}^{v_i\left(k\right)}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)}\right\}\&le;D$

The multistage decision Optimized model solved after conversion is as follows:

Concrete, realize comprising step based on the particle swarm optimization algorithm of Dual Method described in step e:

E1. particle structure design step is carried out for multistage decision Optimized model:

Suppose decision phase number K=3, the position encoded vector being 2N × 3 and tieing up of each particle, with a bit in representation space; Each particle is divided into 3 parts, represents the decision variable v in 3 stages respectively _i(k) and e _i(k), as follows:

P _l(τ)＝[p _l1(τ),p _l2(τ),…,p _l(2N×3)(τ)]＝[Y _l ¹(τ),Y _l ²(τ),Y _l ³(τ)]，

${Y_l}^k\left(\mathrm{\&tau;}\right)=[y_{l1}^k\left(\mathrm{\&tau;}\right),y_{l2}^k\left(\mathrm{\&tau;}\right),\&CenterDot;\&CenterDot;\&CenterDot;,y_{l\left(2N\right)}^k\left(\mathrm{\&tau;}\right)]\&DoubleLeftRightArrow;[v_1\left(k\right),v_2\left(k\right),\&CenterDot;\&CenterDot;\&CenterDot;,v_N\left(k\right),e_1\left(k\right),e_2\left(k\right),\&CenterDot;\&CenterDot;\&CenterDot;,e_N\left(k\right)]$

Wherein l represent particle numbering (l=1,2 ..., L); L is population scale; τ be iterations (τ=0,1 ..., T); T is maximum iteration time; P _l(τ)=[p _l1(τ), p _l2(τ) ..., p _{l (2N × 3)}(τ) position of particle l in τ generation] is represented; Y _l ^k(τ) the kth part of particle l in τ generation is represented; for q tie up component (q=1 ..., 2N); Because all dump trucks for allotment and unloading equipment are all dispensed to work in every when each stage starts, therefore have:

$\underset{q=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_v\left(k\right),\&ForAll;k$ With $\underset{q=N+1}{\overset{2N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_e\left(k\right),\&ForAll;k$

$\underset{q=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_v\left(k\right),\&ForAll;k$ With $\underset{q=N+1}{\overset{2N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_e\left(k\right),\&ForAll;k;$

E2. dual formula particle step of updating:

1. particle initialization:

1) establish k=1, wherein, k represents the kth part in particle;

2) establish q=1, wherein, q represents q element in the kth part in particle;

3) at interval [1, A _v(k)-N+q] in stochastic generation positive integer with initialization make q=q+1 subsequently;

4) in interval middle stochastic generation positive integer is with initialization make q=q+1 subsequently;

5) if q<N, the 4th is returned) step; Otherwise, if q=N, initialization make q=q+1 subsequently;

6) at interval [1, A _e(k)-2N+q] in stochastic generation positive integer with initialization make q=q+1 subsequently;

7) in interval middle stochastic generation positive integer is with initialization make q=q+1 subsequently;

8) if q<2N, the 7th is returned) step; Otherwise, if q=2N, initialization

9) if end condition meets, i.e. k=3, then complete the initialization of particle; Otherwise, make k=k+1 and return the 2nd) and step;

2. pair Particle velocity initialization:

3 parts are divided into the speed of each particle as follows:

$V_l\left(\mathrm{\&tau;}\right)=[v_{l1}\left(\mathrm{\&tau;}\right),v_{l2}\left(\mathrm{\&tau;}\right),\&CenterDot;\&CenterDot;\&CenterDot;,v_{l(2N\&times;3)}\left(\mathrm{\&tau;}\right)]=[Z_l^1\left(\mathrm{\&tau;}\right),Z_l^2\left(\mathrm{\&tau;}\right),Z_l^3\left(\mathrm{\&tau;}\right)]$

Wherein V _l(τ)=[v _l1(τ), v _l2(τ) ..., v _{l (2N × 3)}(τ) speed of particle] is represented; represent the kth part of τ for medium-rate l, the vector representation that 3 parts of each speed are a 2N dimension is as follows:

$Z_l^k\left(\mathrm{\&tau;}\right)=[z_{l1}^k\left(\mathrm{\&tau;}\right),z_{l2}^k\left(\mathrm{\&tau;}\right),\&CenterDot;\&CenterDot;\&CenterDot;,z_{l\left(2N\right)}^k\left(\mathrm{\&tau;}\right)]$

Wherein for q tie up element (q=1 ..., 2N);

Following three conditions need be met when carrying out speed initialization:

1) in speed, the value of each element must be integer;

2) in speed following element with must be zero, namely with wherein k=1,2,3;

3) in speed, the absolute value of each element can not exceed (q=1,2 ..., N) and (q=N+1, N+2 ..., 2N),

Wherein A _v(k) and A _ek () is respectively the quantity that each stage can supply dump truck and the unloading equipment allocated;

3. define the positive and negative dual element in Particle velocity:

Due to the element of the kth part in the speed of particle may be positive number or non-positive number, positive element or antielement can be defined as; Each part of speed is all containing the positive antielement of two classes: wherein, q=1, and 2 ..., N is a class, represents the decision variable v of dump truck _i(k); Q=N+1, N+2 ..., 2N is another kind of, represents the decision variable e of unloading equipment _i(k);

To the positive antielement of each class, if then may be defined as positive element, on the contrary, if then antielement can be defined as; In the positive antielement of each class, if the quantity of positive element is O, then the quantity of known antielement is N-O;

If (k=1,2,3; G=1,2) be the set of the positive element in the positive antielement of g class in kth part in the speed of particle or correspondence, for the set of the antielement in the positive antielement of g class in kth part in the speed of particle or correspondence;

If be a positive element, then have if be an antielement, then have correspondingly, for the element in particle if had then for positive element; If had then known for antielement;

4. adopt antithesis update mechanism to upgrade particle:

1) in particle renewal process, the positive and negative cycling of elements in each speed is absolute value and adopts following formula to be normalized to number between [0,1] respectively:

${\mathrm{Po}}_{\mathrm{lq}}^k=\frac{z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{Or}}_g^k}{z}_{\mathrm{lj}}^k\left(\mathrm{\&tau;}\right)},\&ForAll;z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{Or}}_g^k,{\mathrm{Pa}}_{\mathrm{lq}}^k=\frac{z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{An}}_g^k}{z}_{\mathrm{lj}}^k\left(\mathrm{\&tau;}\right)},\&ForAll;z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{An}}_g^k,$

Wherein for the probable value obtained after positive element normalizing, for the probable value obtained after antielement normalizing;

2) establish update times m=1, the higher limit of update times is

3) to the positive antielement of each class in particle, once the probability that a certain positive element obtains by its normalization selected, then (namely 1 is added to it ); Meanwhile, to the positive antielement of each class of particle, according to the probability that normalization obtains select a certain antielement, subsequently (namely 1 is subtracted to it ); To above-mentioned if then the above-mentioned operation aligning antielement is cancelled, and enters the 4th) step; Otherwise, directly enter the 4th) and step;

4) if end condition meets, namely then the renewal of the kth Partial Elements of particle l in τ generation is completed; Otherwise, make m=m+1 and return the 3rd) and step.

The invention has the beneficial effects as follows: solve concrete transportation queuing network optimization problems in high arch dam construction, thus improve arch dam construction efficiency, reduce total operating cost.

Accompanying drawing explanation

Fig. 1 is concrete production, transport and casting system in induced joint construction project;

Fig. 2 is concrete transportation queuing network in induced joint construction project;

Fig. 3 is the multi-stage optimization of concrete transportation network;

Fig. 4 is the state migration procedure of transportation network subsystem i;

Fig. 5 is the multistage decision modeling technique flow process for concrete transportation queuing network optimization problem in induced joint construction project;

Fig. 6 is stochastic variable probability density function;

Fig. 7 is fuzzy random variable be converted into (r, σ)-trapezoidal fuzzy variable process;

Fig. 8 is the structural design of particle;

Fig. 9 is dual formula particle more new principle;

Figure 10 be dual formula particle more new technological process compare with conventional particle update method.

Embodiment

Technical scheme of the present invention is described in detail below in conjunction with drawings and Examples:

The present invention solves the concrete transportation queuing network optimization problem in above-mentioned induced joint engineering construction, and propose following multistage decision modeling technique, concrete steps are as follows:

(1) uncertain parameters calculates.Because induced joint engineering construction is unconventional engineering construction, there is one-time construction feature, lack similar engineering construction data for referencial use, related data information need be obtained by expert investigation analysis.Here fuzzy stochastic number is adopted to describe relevant uncertain parameter.These uncertain parameter mainly comprise:

1) monthly effective working day: there is fuzzy and stochastic feature by the uncertain factor such as weather condition, accident affects.Be expressed as

2) transport of dump truck and the stand-by period: affect by factors such as transportation range, driver technology and road conditions.Dump truck is used along path i respectively in stage k heavy duty and unloaded haulage time with represent, its time waited in unloading point i and concrete production system at stage k is used respectively with represent.Then dump truck at stage k along total two-way time of path i is: ${\stackrel{\widetilde{\&OverBar;}}{T}}_i\left(k\right)={\stackrel{\widetilde{\&OverBar;}}{T}}_h^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_e^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_u^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_c\left(k\right),\&ForAll;i,k$

3) dump truck arrival rate: use represent that a dump truck is in the arrival rate of stage k in unloading point i, its computing formula is as follows: ${\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_i\left(k\right)=\frac{1}{{\stackrel{\widetilde{\&OverBar;}}{T}}_i\left(k\right)}=\frac{1}{{\stackrel{\widetilde{\&OverBar;}}{T}}_h^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_e^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_u^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_c\left(k\right)},\&ForAll;i,k;$

As shown in Figure 3, network subsystem i is by unloading point i, and transportation route i, and concrete production system composition, and each network subsystem is intersected in concrete production system.In transportation network system, in each network subsystem, always to reach rate relevant with the two-way time of its each dump truck in this subsystem for the dump truck of unloading point.Due to the inverse of each dump truck two-way time, therefore total arrival rate of each unloading point dump truck also with relevant.Use v _ik () represents the dump truck number distributing to network subsystem i at stage k.If at a time there be j dump truck unload concrete at unloading point i and wait in line, then those dump trucks (the i.e. v not at unloading point i in network subsystem i _i(k)-j) will the source of unloading point i vehicle arrival be become.With represent stage k when unloading point i have j dump truck unloading concrete or etc. to be unloaded time this unloading point the total arrival rate of dump truck, its computing formula is as follows:

${{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_i}^j\left(k\right)=(v_i\left(k\right)-j){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_i\left(k\right),\&ForAll;i,k$

Because in conveyance queuing network whole in each stage, the sum of dump truck and the sum of cable machine are metastable, therefore after each discontinuous running starts, can tend towards stability gradually in the dump truck queue of concrete production system.The dump truck departure rate of concrete production system also will tend towards stability.But for different transportation routes, the departure rate of dump truck depends on the quantity of the dump truck that each subsystem distributes.Because Decision of Allocation is not very remarkable on the impact of each transportation subsystem, above-mentioned computing method are acceptable in engineering.

4) cable machine service rate: use e _ik () represents the cable machine quantity being allocated in unloading point i operation at stage k, be that a cable machine is at the service rate of stage k in unloading point i operation.Be engraved in when a certain unloading point i unload concrete and etc. dump truck quantity to be unloaded when being j, unloading point i this stage k service rate (namely ) can be calculated as:

${\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)=\left\{\begin{array}{c}j{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i\left(k\right),j=\mathrm{0,1},...,e_i\left(k\right)-1\\ e_i\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i\left(k\right),j=e_i\left(k\right),e_i\left(k\right)+1,...,v_i\left(k\right)\end{array}\right.$

(2) transportation network system state transition probability calculates.The quantity of the dump truck that the state of transportation network system is stopped by each unloading point is determined, its change is because dump truck is for the arrival rate of each unloading point and the cable machine service rate at each unloading point.With represent stage k when unloading point i place have j dump truck unloading concrete or etc. to be unloaded time network subsystem i state.The visible table 1 of all possible state.Each state all by arrive or Service events generation or complete and be transferred to adjacent state; Fig. 4 illustrates the state migration procedure of unloading point i.

Table 1: the state table that transportation network system is possible

Above-mentioned state transfer has 2 character: one is, any state is transferred to another state; Two are, all possible status number is limited.The probability of state transfer carrys out the randomness of comfortable each stage dump truck unloading and waiting number.Because network transport system tends towards stability state after effect starts, the probability of state transfer also will be restrained.According to law of great numbers, the frequency approximate evaluation that the probability that things occurs can be occurred by event when great many of experiments.With expression state (j=0,1 ..., v _i(k)) probability of happening.According to the markovian character of continuous time, these probability should meet Ke Ermogenuofu system of equations.If derive each state probability of happening computing formula as follows:

$p_i^0\left(k\right)={[\underset{j=0}{\overset{e_i\left(k\right)-1}{\mathrm{\&Sigma;}}}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!j!}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j+\underset{j=e_i\left(k\right)}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!e_i\left(k\right)!e_i{\left(k\right)}^{j-e_i\left(k\right)}}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j]}^{-1}$

$p_i^j\left(k\right)=\left\{\begin{array}{c}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!j!}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j{p}_i^0\left(k\right),1\&le;j<e_i\left(k\right)\\ \frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!e_i\left(k\right)!e_i{\left(k\right)}^{j-e_i\left(k\right)}}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j{p}_i^0\left(k\right),e_i\left(k\right)\&le;j\&le;v_i\left(k\right)\end{array}\right.$

(3) model state system of equations builds: use A _v(k) and A _ek () is illustrated respectively in the quantity of the adjustable dump truck of stage k and cable machine.Due to when each stage starts, all dump trucks for allotment and cable machine are all dispensed to each subsystem work, can obtain following equation:

$A_V\left(k\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{v}_i\left(k\right)$ With $A_E\left(k\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}_i\left(k\right)$

Because gradually hair style fault may occur at work for dump truck and cable machine, and can terminate to be sent to maintenance again in fault generation rear continuous firing to the stage.The number of stages that maintenance is used is represented with ζ.After maintenance completes, dump truck and cable machine can return work.Use ψ _i(k) and φ _ik () represents the dump truck that is dispensed to subsystem i and the cable machine rate of breakdown at stage k respectively, then the equations of state that can build model is as follows:

$A_V(k+1)=A_V\left(k\right)-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_i\left(k\right)v_i\left(k\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_i(k-\mathrm{\&zeta;})v_i(k-\mathrm{\&zeta;})+R_V(k+1)$

$A_E(k+1)=A_E\left(k\right)-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i\left(k\right)e_i\left(k\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i(k-\mathrm{\&zeta;})e_i(k-\mathrm{\&zeta;})+R_E(k+1)$

Wherein, when k-ζ≤0, ψ _i(k-ζ) v _i(k-ζ) and φ _i(k-ζ) e _i(k-ζ) value is 0.

(4) model starting condition builds: use α ₁and β ₁be illustrated respectively in the quantity that the starting stage can supply dump truck and the cable machine allocated, build model starting condition as follows:

A _v(1)=α ₁and A _e(1)=β ₁

(5) model constrained condition builds: the quantity of the dump truck and cable machine that are dispensed to subsystem i at stage k should be no less than 0 and be no more than and for the quantity of the dump truck of allotment and cable machine, can build model constrained condition as follows in this stage:

0≤v _i(k)≤A _v(k) and 0≤e _i(k)≤A _e(k),

(6) model objective function builds: the target according to decision maker builds as follows about minimizing the objective function of building duration and operating cost:

1) build the duration: the working time representing dump truck with t (hour/day), H (cubic meter /) represents the charging capacity of dump truck, (cubic meter/sky) represents at the concrete actual placing intensity of stage k in casting area i, ξ _ik () (/ hour) represents the service rate of cable machine at stage k unloading point i.Due to ξ _ik () is stochastic variable, according to law of great numbers, calculate its expectation value as follows:

$E\left({\mathrm{\&xi;}}_i\left(k\right)\right)=\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right),\&ForAll;i,k$

Thus can the actual placing intensity of concrete of calculation stages k casting area i as follows:

$I_i^d\left(k\right)=\mathrm{tHE}\left({\mathrm{\&xi;}}_i\left(k\right)\right)=\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right),\&ForAll;i,k$

With (cubic meter/moon) represents at the concrete actual placing intensity of stage k in casting area i, Q _ik () (cubic meter) represents the plan concreting amount at stage k casting area i, D _ik represent by () (moon) and build the duration the concrete of stage k casting area i is actual, its computing formula is as follows:

$D_i\left(k\right)=\frac{Q_i\left(k\right)}{I_i^m\left(k\right)}=\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}{I}_i^d\left(k\right)}=\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)},\&ForAll;i,k$

In pouring construction process, only have when all casting area of current generation all complete build after could start the pouring construction of next stage.With total lever factor is built in (moon) expression,

Wherein x=(v ₁(), v ₂() ..., v _n(), e ₁(), e ₂() ..., e _n()),

$\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}}=(\stackrel{\widetilde{\&OverBar;}}{w},{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_1(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_2(\&CenterDot;),...,{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_N(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_1(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_2(\&CenterDot;),...,{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_N(\&CenterDot;))$

Then its computing formula is as follows:

2) operating cost: use C _b(unit/sky) represents the unit operating cost of 1 concrete batching and mixing plant, C _v(unit/sky) represents the unit operating cost of 1 dump truck, C _e(unit/sky) represents the unit operating cost of a cable machine, (unit) represents the total operating cost of concreting.Because the time span of stage k is and the operating cost of concrete batching and mixing plant, dump truck and cable machine can middlely within the whole duration occur, therefore the length of total lever factor can affect the total operating cost of concreting.Represent the quantity of concrete batching and mixing plant with M, then can calculate as follows: $f_c(x,\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}})=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\stackrel{\widetilde{\&OverBar;}}{w}(C_{b}M+C_v{A}_V\left(k\right)+C_e{A}_E\left(k\right))\&times;\underset{i}{\max }\left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}{\mathrm{tH\&Sigma;}}_{j=0}^{v_i\left(k\right)}{p}_i^j\left(k\right){\mathrm{\&mu;}}_i^j\left(k\right)}\right\}$

(7) equivalence model conversion: then define a multiobject multistage decision Optimized model after above-mentioned equations of state, starting condition, constraint condition, objective function are integrated as follows:

Owing to there is the objective function of different dimension in above-mentioned multi-objective Model, weighted method therefore can not be simply adopted multiple goal to be transformed single goal to facilitate Algorithm for Solving.For this reason, suppose that the longest permissible total lever factor of building is D, then can be converted into following constraint condition by minimizing the objective function of building total lever factor: $\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i}{\max }\left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}{\mathrm{tH\&Sigma;}}_{j=0}^{v_i\left(k\right)}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)}\right\}\&le;D$

The multistage decision Optimized model solved after can transforming like this is as follows:

Fig. 5 illustrates the multistage decision Modeling on Optimal process flow diagram for concrete transportation queuing network problem in induced joint engineering construction.

Based on above-mentioned multistage decision model, the present invention proposes the dual formula particle renewal technology based on particle swarm optimization algorithm.Owing to there is nonlinear objective function and constraint condition in above-mentioned model, therefore in induced joint engineering construction, concrete transportation network multi-rank section decision model is in fact a nonlinear integer programming.Because linear integer programming problem has been proved to be as a NP-difficult problem.Obviously, nonlinear integer programming is than linear integer programming harder problem.Although there is corresponding exact algorithm for some nonlinear integer programming with specific condition, major part effectively can only solve small-scale problem.When in the face of Large-scale Optimization Problems, exact algorithm was difficult to complete calculating within the enough short time.Therefore be necessary that the concrete condition application Heuristic Intelligent Algorithm for problem solves.The Heuristic Intelligent Algorithm be extensively employed at present comprises genetic algorithm, simulated annealing, ant group algorithm etc.Wherein particle swarm optimization algorithm is furtherd investigate in theory, and in control system, decision science, the network optimization, Renewable Energy Development, is used widely in the fields such as data clusters.Its fast study mechanism make it in the practical application of many problems, have more advantage relative to other Heuristic Intelligent Algorithms.The present invention is directed to concrete transportation network multi-rank section decision model in induced joint engineering construction, devise the particle swarm optimization algorithm based on Dual Method, with constraint condition complicated in adaptive model.Introduce its main design thought below.

1. particle structure design: be simplified characterization is the particle structure design that 3 (i.e. K=3) introduce algorithm for decision phase number.Based in the particle swarm optimization algorithm of Dual Method, the position encoded vector being 2N × 3 and tieing up of each particle, with represent in solution space a bit.For ease of understanding, each particle is divided into 3 parts, represents decision variable (the i.e. v in 3 stages respectively _i(k) and e _i(k)), as follows:

P _l(τ)＝[p _l1(τ),p _l2(τ),…,p _l(2N×3)(τ)]＝[Y _l ¹(τ),Y _l ²(τ),Y _l ³(τ)]，

${Y_l}^k\left(\mathrm{\&tau;}\right)=[y_{l1}^k\left(\mathrm{\&tau;}\right),y_{l2}^k\left(\mathrm{\&tau;}\right),\&CenterDot;\&CenterDot;\&CenterDot;,y_{l\left(2N\right)}^k\left(\mathrm{\&tau;}\right)]\&DoubleLeftRightArrow;[v_1\left(k\right),v_2\left(k\right),\&CenterDot;\&CenterDot;\&CenterDot;,v_N\left(k\right),e_1\left(k\right),e_2\left(k\right),\&CenterDot;\&CenterDot;\&CenterDot;,e_N\left(k\right)]$

Wherein l represent particle numbering (l=1,2 ..., L); L is population scale; τ be iterations (τ=0,1 ..., T); T is maximum iteration time; P _l(τ)=[p _l1(τ), p _l2(τ) ..., p _{l (2N × 3)}(τ) position of particle l in τ generation] is represented; Y _l ^k(τ) kth part (the i.e. decision variable v in kth stage of particle l in τ generation is represented _i(k) and e _i(k)).Notice that three parts of each particle are a 2N dimensional vector, wherein for Y _l ^k(τ) q tie up component (q=1 ..., 2N).Because all dump trucks for allotment and unloading equipment are all dispensed to work in every when each stage starts, therefore have:

$\underset{q=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_v\left(k\right),\&ForAll;k$ With $\underset{q=N+1}{\overset{2N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_e\left(k\right),\&ForAll;k$

Fig. 8 illustrate one comprise N number of transportation subsystem, a α dump truck, a β unloading equipment concrete transportation system particle structure express.

2. dual formula particle renewal technology: in traditional PS O algorithm, each dimension in each particle is separate element.Also be separate to the renewal of dimension element each in particle.Position (the i.e. P of particle _l(τ+1)) by speed (the i.e. V of stochastic generation _l(τ+1)) upgrade, the more new formula of its speed and particle is as follows:

V _l(τ+1)＝w(τ)V _l(τ)+c _pr _p(PBest _l-P _l(τ))+c _gr _g(GBest-P _l(τ))， (1)

P _l(τ+1)＝V _l(τ+1)+P _l(τ)， (2)

Wherein V _l(τ)=[v _l1(τ), v _l2(τ) ..., v _{l (2N × 3)}(τ) speed changing particle position] is represented; PBest _l=[pBest _l1, pBest _l2..., pBest _{l (2N × 3)}] be the personal best particle of particle; GBest=[gBest ₁, gBest ₂..., gBest _{2N × 3}] be the global optimum position of population; c _pand c _gfor aceleration pulse, globally optimal solution and individual optimal solution can be balanced to the weighing factor of current particle; r _pand r _git is the random number between 0 to 1; W (τ) can be used for the speed of control previous generation particle to the impact of particle present rate for inertia weight.

Each element of a feasible particle must be positive integer, but traditional speed update method may cause anon-normal or non-integral solution.Therefore, if simple, the fraction part of element each in particle is removed and particle may be made to be difficult to the various constraint conditions met in model, thus cause infeasible solution.Therefore must improve to eliminate to the update mechanism of conventional particle colony optimization algorithm and upgrade and keep conflicting of feasibility.Need the feasibility first ensureing initialization particle for this reason.

(1) particle initialization: for ensureing the feasibility of particle, design following initial method:

1st step establishes k=1 (the kth part of initialization particle).

2nd step establishes q=1 (the element q in the kth part of initialization particle).

3rd step is at interval [1, A _v(k)-N+q] in stochastic generation positive integer with initialization make q=q+1 subsequently.

4th step is in interval middle stochastic generation positive integer is with initialization make q=q+1 subsequently.

If the 5th step q<N, return the 4th step; Otherwise, if q=N, initialization make q=q+1 subsequently.

6th step is at interval [1, A _e(k)-2N+q] in stochastic generation positive integer with initialization make q=q+1 subsequently.

7th step is in interval middle stochastic generation positive integer is with initialization make q=q+1 subsequently.

If the 8th step q<2N, return the 7th step; Otherwise, if q=2N, initialization

If the 9th step end condition meets, i.e. k=3, then complete the initialization of particle; Otherwise, make k=k+1 and return the 2nd step.

Above-mentioned initial method effectively can ensure the feasibility of particle.In order to keep this feasibility in particle renewal process, following 3 principles need be met to the initialization of the speed of particle.For ease of understanding, it is as follows that the speed of each particle is also divided into 3 parts:

$V_l\left(\mathrm{\&tau;}\right)=[v_{l1}\left(\mathrm{\&tau;}\right),v_{l2}\left(\mathrm{\&tau;}\right),\&CenterDot;\&CenterDot;\&CenterDot;,v_{l(2N\&times;3)}\left(\mathrm{\&tau;}\right)]=[Z_l^1\left(\mathrm{\&tau;}\right),Z_l^2\left(\mathrm{\&tau;}\right),Z_l^3\left(\mathrm{\&tau;}\right)]$

Wherein V _l(τ)=[v _l1(τ), v _l2(τ) ..., v _{l (2N × 3)}(τ) speed of particle] is represented; represent the kth part of τ for medium-rate l.Notice that 3 parts of each speed are the vector representation of 2N dimension as follows:

$Z_l^k\left(\mathrm{\&tau;}\right)=[z_{l1}^k\left(\mathrm{\&tau;}\right),z_{l2}^k\left(\mathrm{\&tau;}\right),\&CenterDot;\&CenterDot;\&CenterDot;,z_{l\left(2N\right)}^k\left(\mathrm{\&tau;}\right)]$

Wherein for q tie up element (q=1 ..., 2N).Provide 3 principle of experience that speed initialization need meet below as follows:

1) in speed, the value of each element must be integer;

2) in speed following element with must be zero, namely with wherein k=1,2,3;

3) in speed, the absolute value of each element can not exceed (q=1,2 ..., N) and (q=N+1, N+2 ..., 2N), be absorbed in infeasible solution after upgrading to avoid particle.

(2) rate constraint: computing can find by experiment, if do not carry out suitable constraint to each element value of speed, the speed of particle may be increased sharply to very large value during evolution very soon.In order to avoid this irregular search behavior, need that certain border is set to each element value of speed and retrain.Be similar to the initial method to speed, in speed, each element (namely ) absolute value be set to and can not exceed (q=1,2 ..., N) and (q=N+1, N+2 ..., 2N), wherein A _v(k) and A _ek () is respectively the quantity that each stage can supply dump truck and the unloading equipment allocated.If each element of speed (namely ) exceed above-mentioned boundary limitation at no point in the update process, namely (q=1,2 ..., N) or (q=N+1, N+2 ..., 2N), then arrange (q=1,2 ..., N) and (q=N+1, N+2 ..., 2N).

(3) positive and negative dual element: can prove if initialization particle is feasible, and initializing rate meets above-mentioned 3 principle of experience, then known according to formula (1), the speed after renewal also will meet principle of experience 2).But each element of the speed after these renewals may be non-integer, its absolute value also may be comparatively large, thus become infeasible solution after causing particle to be upgraded by formula (2).For this reason, the concept introducing positive and negative key element enables particle keep feasibility at no point in the update process to design antithesis update mechanism.In conventional particle colony optimization algorithm, the rate representation calculated by formula (1) be that particle will the distance of movement.The speed with larger absolute value means that particle will move a larger distance.By the speed V that formula (1) calculates _l(τ)=[v _l1(τ), v _l2(τ) ..., v _{l (2N × 3)}(τ) distance between the position of current particle and the global optimum position of its personal best particle and population] is represented.This distance means that particle needs are higher by the degree of evolving more greatly.Therefore, the absolute value of speed can be converted into the probability that selection particle carries out upgrading.Due to the kth part in the speed of particle element (namely ) may be positive number or non-positive number, positive element or antielement can be defined as.Each part of speed is all containing the positive antielement of two classes.One class (i.e. q=1,2 ..., N) and be decision variable (the i.e. v of dump truck _i(k)), and another kind of (i.e. q=N+1, N+2 ..., 2N) and be decision variable (the i.e. e of unloading equipment _i(k)).To the positive antielement of each class, if then may be defined as positive element, on the contrary, if then antielement can be defined as.In the positive antielement of each class, if the quantity of positive element is O, then the quantity of known antielement is N-O.If (k=1,2,3; G=1,2) be the set of the positive element in the positive antielement of g class in kth part in the speed of particle or correspondence, for the set of the antielement in the positive antielement of g class in kth part in the speed of particle or correspondence.Therefore, if be a positive element, then have if be an antielement, then have correspondingly, for the element in particle if had then for positive element; If had then known for antielement.

(4) antithesis more new principle.According to the above discussion, for ensureing particle feasibility during evolution, design antithesis update mechanism as shown in Figure 9, concrete steps are as follows.

1st step: in particle renewal process, is absolute value by the positive and negative cycling of elements in each speed and adopts following formula to be normalized to number between [0,1] respectively:

${\mathrm{Po}}_{\mathrm{lq}}^k=\frac{z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{Or}}_g^k}{z}_{\mathrm{lj}}^k\left(\mathrm{\&tau;}\right)},\&ForAll;z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{Or}}_g^k,{\mathrm{Pa}}_{\mathrm{lq}}^k=\frac{z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{An}}_g^k}{z}_{\mathrm{lj}}^k\left(\mathrm{\&tau;}\right)},\&ForAll;z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{An}}_g^k,$

Wherein for the probable value obtained after positive element normalizing, for the probable value obtained after antielement normalizing.

2nd step: establish update times m=1.Fully upgraded in order to ensure particle, the higher limit of update times is

3rd step: to the positive antielement of each class in particle, once the probability that a certain positive element obtains by its normalization selected, then (namely 1 is added to it ).Meanwhile, to the positive antielement of each class of particle, according to the probability that normalization obtains select a certain antielement, subsequently (namely 1 is subtracted to it ).To above-mentioned if then the above-mentioned operation aligning antielement is cancelled, and enters the 4th step; Otherwise, directly enter the 4th step.

4th step: if end condition meets, namely then the renewal of the kth Partial Elements of particle l in τ generation is completed; Otherwise, make m=m+1 and return the 3rd step.

The mechanism that above-mentioned particle upgrades can automatically by the position control after particle renewal in feasible zone, and by avoiding the search efficiency search in infeasible space effectively being improved to algorithm.Figure 10 represent based on the particle swarm optimization algorithm of Dual Method algorithm flow and with the comparing of conventional particle colony optimization algorithm.

Claims (6)

1. the concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction, is characterized in that, comprise the following steps:

A. fuzzy stochastic number is adopted to describe relevant uncertain parameter;

B. transportation network system state transition probability calculates;

C. multi-object and multi-phase decision Optimized model is built;

D. equivalence conversion is carried out to model, form the multistage decision Optimized model that can separate;

E. the particle swarm optimization algorithm based on Dual Method is adopted to solve model.

2. the concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction as claimed in claim 1, it is characterized in that, in steps A, described relevant uncertain parameter comprises:

1) monthly effective working day: affect by weather condition, these uncertain factors of accident and there is fuzzy and stochastic feature, be expressed as

2) transport of dump truck and the stand-by period: affect by transportation range, driver technology and these factors of road conditions, dump truck is used along path i respectively in stage k heavy duty and unloaded haulage time with represent, its time waited in unloading point i and concrete production system at stage k is used respectively with represent, then dump truck at stage k along total two-way time of path i is: ${\stackrel{\widetilde{\&OverBar;}}{T}}_i\left(k\right)={\stackrel{\widetilde{\&OverBar;}}{T}}_h^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_e^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_u^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_c\left(k\right),\&ForAll;i,k;$

3) dump truck arrival rate: use represent that a dump truck is in the arrival rate of stage k in unloading point i, its computing formula is as follows: ${\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_i\left(k\right)=\frac{1}{{\stackrel{\widetilde{\&OverBar;}}{T}}_i\left(k\right)}=\frac{1}{{\stackrel{\widetilde{\&OverBar;}}{T}}_h^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_e^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_u^i\left(k\right)+{\stackrel{\widetilde{\&OverBar;}}{T}}_c\left(k\right)},\&ForAll;i,k;$

4) cable machine service rate: use e _ik () represents the cable machine quantity being allocated in unloading point i operation at stage k, be a cable machine at the service rate of stage k in unloading point i operation, be engraved in when a certain unloading point i unload concrete and etc. dump truck quantity to be unloaded when being j, unloading point i is at the service rate of this stage k can be calculated as:

${\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)=\left\{\begin{array}{cc}j{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i\left(k\right)& j=\mathrm{0,1},..,e_i\left(k\right)-1\\ e_i\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i\left(k\right)& j=e_i\left(k\right),e_i\left(k\right)+1,...,v_i\left(k\right)\end{array}\right..$

3. the concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction as claimed in claim 2, it is characterized in that in step B, the quantity of the dump truck that described transportation network system state is stopped by each unloading point is determined, its change affects at the service rate of each unloading point for the arrival rate of each unloading point and cable machine by dump truck, use represent stage k when unloading point i place have j dump truck unload concrete or etc. to be unloaded time network subsystem i state, use expression state (j=0,1 ..., v _i(k)) probability of happening, if derive each state probability of happening computing formula

$p_i^0\left(k\right)={[\underset{j=0}{\overset{e_i\left(k\right)-1}{\mathrm{\&Sigma;}}}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!j!}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j+\underset{j=e_i\left(k\right)}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}\frac{v_i\left(k\right)!}{{(v_i\left(k\right)-j)!e_i\left(k\right)!e_i\left(k\right)}^{j-e_i\left(k\right)}}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j]}^{-1}$

$p_i^j\left(k\right)=\left\{\begin{array}{cc}\frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!j!}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j{p}_i^0\left(k\right),& 1\&le;j<e_i\left(k\right)\\ \frac{v_i\left(k\right)!}{(v_i\left(k\right)-j)!e_i\left(k\right)!e_i{\left(k\right)}^{j-e_i\left(k\right)}}{\left({\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&rho;}}}_i\left(k\right)\right)}^j{p}_i^0\left(k\right),& e_i\left(k\right)\&le;j\&le;v_i\left(k\right)\end{array}\right..$

4. the concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction as claimed in claim 3, it is characterized in that, in step C, described structure multi-object and multi-phase decision Optimized model, comprising:

C1. model state system of equations is built:

Use A _v(k) and A _ek () is illustrated respectively in the quantity of the adjustable dump truck of stage k and cable machine:

$A_V\left(k\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{v}_i\left(k\right)$ With $A_E\left(k\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{e}_i\left(k\right);$

Represent with ζ the number of stages that maintenance is used, use ψ _i(k) and φ _ik () represents the dump truck that is dispensed to subsystem i and the cable machine rate of breakdown at stage k respectively, then the equations of state that can build model is as follows:

$A_V(k+1)=A_V\left(k\right)-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&Psi;}}_i\left(k\right)v_i\left(k\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&Psi;}}_i(k-\mathrm{\&zeta;})v_i(k-\mathrm{\&zeta;})+R_V(k+1)$

$A_E(k+1)=A_E\left(k\right)-\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i\left(k\right)e_i\left(k\right)+\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i(k-\mathrm{\&zeta;})e_i(k-\mathrm{\&zeta;})+R_E(k+1)$

Wherein, when k-ζ≤0, ψ _i(k-ζ) v _i(k-ζ) and φ _i(k-ζ) e _i(k-ζ) value is 0;

C2. model starting condition is built:

Use α ₁and β ₁be illustrated respectively in the quantity that the starting stage can supply dump truck and the cable machine allocated, build model starting condition:

A _v(1)=α ₁and A _e(1)=β ₁;

C3. model constrained condition is built:

The quantity of the dump truck and cable machine that are dispensed to subsystem i at stage k should be no less than 0 and be no more than and for the quantity of the dump truck of allotment and cable machine, can build model constrained condition as follows in this stage:

0≤v _i(k)≤A _v(k) and 0≤e _i(k)≤A _e(k),

C4. model objective function is built:

Target according to decision maker builds as follows about minimizing the objective function of building duration and operating cost:

1) build the duration: the working time representing dump truck with t, H represents the charging capacity of dump truck, represent at the concrete actual placing intensity of stage k in casting area i, ξ _ik () represents the service rate of cable machine at stage k unloading point i; Due to ξ _ik () is stochastic variable, according to law of great numbers, calculate its expectation value as follows:

$E\left({\mathrm{\&xi;}}_i\left(k\right)\right)=\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right),\&ForAll;i,k$

Thus can the actual placing intensity of concrete of calculation stages k casting area i as follows:

$I_i^d\left(k\right)=\mathrm{tHE}\left({\mathrm{\&xi;}}_i\left(k\right)\right)=\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right),\&ForAll;i,k$

With represent at the concrete actual placing intensity of stage k in casting area i, Q _ik () represents the plan concreting amount at stage k casting area i, D _ik () represents and builds the duration the concrete of stage k casting area i is actual, its computing formula is as follows:

$D_i\left(k\right)=\frac{Q_i\left(k\right)}{I_i^m\left(k\right)}=\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}{I}_i^d\left(k\right)}=\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)},\&ForAll;i,k$

In pouring construction process, only all casting area of current generation all complete build after could start the pouring construction of next stage, use f _dtotal lever factor is built in (x, θ) expression,

Wherein x=(v ₁(), v ₂() ..., v _n(), e ₁(), e ₂() ..., e _n()),

$\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}}=(\stackrel{\widetilde{\&OverBar;}}{w},{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_1(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_2(\&CenterDot;),...,{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&lambda;}}}_N(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_1(\&CenterDot;),{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_2(\&CenterDot;),...,{\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_N(\&CenterDot;)),$

Then its computing formula is as follows:

$f_d(x,\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}})=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i}{\max }\left\{D_i\left(k\right)\right\}=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i}{\max }\left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}\mathrm{tH}\underset{j=0}{\overset{v_i\left(k\right)}{\mathrm{\&Sigma;}}}{\text{p}}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j(k\&iexcl;\&curren;)}\right\}$

2) operating cost: use C _brepresent the unit operating cost of 1 concrete batching and mixing plant, C _vrepresent the unit operating cost of 1 dump truck, C _erepresent the unit operating cost of a cable machine, represent the total operating cost of concreting; Because the time span of stage k is and the operating cost of concrete batching and mixing plant, dump truck and cable machine can occur in the whole duration, therefore the length of total lever factor can affect the total operating cost of concreting; Represent the quantity of concrete batching and mixing plant with M, then can calculate as follows:

$f_c(x,\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&theta;}})=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\stackrel{\widetilde{\&OverBar;}}{w}(C_{b}M+C_v{A}_V\left(k\right)+C_e{A}_E\left(k\right))\&times;\underset{i}{\max }\left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}\mathrm{tH}{\mathrm{\&Sigma;}}_{j=0}^{v_i\left(k\right)}{p}_i^j\left(k\right){\mathrm{\&mu;}}_i^j\left(k\right)}\right\};$

C5. based on the integrated formation multi-object and multi-phase decision Optimized model of equations of state, starting condition, constraint condition, objective function:

5. the concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction as claimed in claim 4, is characterized in that carrying out equivalence conversion to model described in step D, forms the multistage decision Optimized model that can separate, specifically comprise:

Suppose that the longest permissible total lever factor of building is D, be then converted into following constraint condition by minimizing the objective function of building total lever factor:

$\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i}{\max \left\{\frac{Q_i\left(k\right)}{\stackrel{\widetilde{\&OverBar;}}{w}\mathrm{tH}{\mathrm{\&Sigma;}}_{j=0}^{v_i\left(k\right)}{p}_i^j\left(k\right){\stackrel{\widetilde{\&OverBar;}}{\mathrm{\&mu;}}}_i^j\left(k\right)}\right\}}\&le;D$

The multistage decision Optimized model solved after conversion is as follows:

6. the concrete transportation queuing network Study on Decision-making Method for Optimization in induced joint engineering construction as claimed in claim 5, is characterized in that, realizes comprising step described in step e based on the particle swarm optimization algorithm of Dual Method:

E1. particle structure design step is carried out for multistage decision Optimized model:

Suppose decision phase number K=3, the position encoded vector being 2N × 3 and tieing up of each particle, with a bit in representation space; Each particle is divided into 3 parts, represents the decision variable v in 3 stages respectively _i(k) and e _i(k), as follows:

P _l(τ)＝[p _l1(τ),p _l2(τ),…,p _l(2N×3)(τ)]＝[Y _l ¹(τ),Y _l ²(τ),Y _l ³(τ)]，

$Y_l^k\left(\mathrm{\&tau;}\right)=[y_{l1}^k\left(\mathrm{\&tau;}\right),y_{l2}^k\left(\mathrm{\&tau;}\right),...,y_{l\left(2N\right)}^k\left(\mathrm{\&tau;}\right)]\&DoubleLeftRightArrow;[v_1\left(k\right),v_2\left(k\right),...,v_N\left(k\right),e_2\left(k\right),...,e_N\left(k\right)]$

Wherein l represent particle numbering (l=1,2 ..., L); L is population scale; τ be iterations (τ=0,1 ..., T); T is maximum iteration time; P _l(τ)=[p _l1(τ), p _l2(τ) ..., p _{l (2N × 3)}(τ) position of particle l in τ generation] is represented; Y _l ^k(τ) the kth part of particle l in τ generation is represented; y _l ^k _q(τ) be Y _l ^k(τ) q tie up component (q=1 ..., 2N); Because all dump trucks for allotment and unloading equipment are all dispensed to work in every when each stage starts, therefore have:

$\underset{q=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_v\left(k\right),\&ForAll;k$ With $\underset{q=N+1}{\overset{2N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_e\left(k\right),\&ForAll;k$

$\underset{q=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_v\left(k\right),\&ForAll;k$ With $\underset{q=N+1}{\overset{2N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=A_e\left(k\right),\&ForAll;k;$

E2. dual formula particle step of updating:

1. particle initialization:

1) establish k=1, wherein, k represents the kth part in particle;

2) establish q=1, wherein, q represents q element in the kth part in particle;

3) at interval [1, A _v(k)-N+q] in stochastic generation positive integer with initialization make q=q+1 subsequently;

4) in interval middle stochastic generation positive integer is with initialization make q=q+1 subsequently;

5) if q<N, the 4th is returned) step; Otherwise, if q=N, initialization make q=q+1 subsequently;

6) at interval [1, A _e(k)-2N+q] in stochastic generation positive integer with initialization make q=q+1 subsequently;

7) in interval middle stochastic generation positive integer is with initialization make q=q+1 subsequently;

8) if q<2N, the 7th is returned) step; Otherwise, if q=2N, initialization

9) if end condition meets, i.e. k=3, then complete the initialization of particle; Otherwise, make k=k+1 and return the 2nd) and step;

2. pair Particle velocity initialization:

3 parts are divided into the speed of each particle as follows:

$V_l\left(\mathrm{\&tau;}\right)=[v_{l1}\left(\mathrm{\&tau;}\right),v_{l2}\left(\mathrm{\&tau;}\right),...,v_{l(2N\&times;3)}\left(\mathrm{\&tau;}\right)]=[Z_l^1\left(\mathrm{\&tau;}\right),Z_l^2\left(\mathrm{\&tau;}\right),Z_l^3\left(\mathrm{\&tau;}\right)]$

Wherein V _l(τ)=[v _l1(τ), v _l2(τ) ..., v _{l (2N × 3)}(τ) speed of particle] is represented; represent the kth part of τ for medium-rate l, the vector representation that 3 parts of each speed are a 2N dimension is as follows:

$Z_l^k\left(\mathrm{\&tau;}\right)=[z_{l1}^k\left(\mathrm{\&tau;}\right),z_{l2}^k\left(\mathrm{\&tau;}\right),...,z_{l\left(2N\right)}^k\left(\mathrm{\&tau;}\right)]$

Wherein for q tie up element (q=1 ..., 2N);

Following three conditions need be met when carrying out speed initialization:

1) in speed, the value of each element must be integer;

2) in speed following element with must be zero, namely with wherein k=1,2,3;

3) in speed, the absolute value of each element can not exceed $\frac{A_V\left(k\right)}{N}(q=\mathrm{1,2},..,N)$ And $\frac{A_E\left(k\right)}{N}(q=N+1,N+2,..,2N),$

Wherein A _v(k) and A _ek () is respectively the quantity that each stage can supply dump truck and the unloading equipment allocated;

3. define the positive and negative dual element in Particle velocity:

Due to the element of the kth part in the speed of particle may be positive number or non-positive number, positive element or antielement can be defined as; Each part of speed is all containing the positive antielement of two classes: wherein, q=1, and 2 ..., N is a class, represents the decision variable v of dump truck _i(k); Q=N+1, N+2 ..., 2N is another kind of, represents the decision variable e of unloading equipment _i(k);

To the positive antielement of each class, if then may be defined as positive element, on the contrary, if then antielement can be defined as; In the positive antielement of each class, if the quantity of positive element is O, then the quantity of known antielement is N-O;

If for the set of the positive element in the positive antielement of g class in kth part in the speed of particle or correspondence, for the set of the antielement in the positive antielement of g class in kth part in the speed of particle or correspondence;

If be a positive element, then have if be an antielement, then have correspondingly, for the element in particle if had then for positive element; If had then known for antielement;

4. adopt antithesis update mechanism to upgrade particle:

1) in particle renewal process, the positive and negative cycling of elements in each speed is absolute value and adopts following formula to be normalized to number between [0,1] respectively:

${\mathrm{po}}_{\mathrm{lq}}^k=\frac{z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{Or}}_g^k}{z}_{\mathrm{lj}}^k\left(\mathrm{\&tau;}\right)},{\&ForAll;z}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{Or}}_g^k,{\mathrm{Pa}}_{\lg }^k=\frac{z_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)}{{\mathrm{\&Sigma;}}_{j\&Element;{\mathrm{An}}_g^k}{z}_{\mathrm{lj}}^k\left(\mathrm{\&tau;}\right)},{\&ForAll;z}_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{An}}_g^k,$

Wherein for the probable value obtained after positive element normalizing, for the probable value obtained after antielement normalizing;

2) establish update times m=1, the higher limit of update times is

3) to the positive antielement of each class in particle, once the probability that a certain positive element obtains by its normalization selected, then 1 is added to it, namely meanwhile, to the positive antielement of each class of particle, according to the probability that normalization obtains select a certain antielement, subsequently 1 is subtracted to it, namely $y_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)=y_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)-1,y_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{An}}_g^k;$ To above-mentioned $y_{\mathrm{lq}}^k\left(\mathrm{\&tau;}\right)\&Element;{\mathrm{An}}_g^k,$ If then the above-mentioned operation aligning antielement is cancelled, and enters the 4th) step; Otherwise, directly enter the 4th) and step;

4) if end condition meets, namely then the renewal of the kth Partial Elements of particle l in τ generation is completed; Otherwise, make m=m+1 and return the 3rd) and step.