CN104820872A - Method for optimizing project duration of engineering project based on potential anti-key working procedures - Google Patents

Abstract

The invention discloses a method for optimizing the project duration of an engineering project based on potential anti-key working procedures in the technical field of engineering project duration control technologies. The method comprises the following steps: identifying potential anti-key working procedures in an engineering project based on certain technical characteristics; dividing all working procedures of the project into a potential anti-key working procedure set X and a non-potential anti-key working procedure set Y; coding the execution modes of all the working procedures in the potential anti-key working procedure set X to generate an initial group of which the size is NP, and adopting a mode of fastest execution for all the working procedures in the non-potential anti-key working procedure set Y; calculating the total duration value corresponding to each single body in the group and converting the reciprocal of the total duration value into the adaptation value of the single body; adjusting the start time of non-key working procedures; selecting a parent, and producing a child by a single-point crossover operator and a single-point mutation operator; combining the parent and the child to form a new group; and if the maximum genetic algebra is obtained, stopping calculation and outputting an optimal solution, thus obtaining the optimal duration scheme of the project.

Description

Potential anti-critical process is utilized to carry out the method for project duration optimization in engineering project

Technical field

The invention belongs to project construction period control technology field, particularly relate to a kind of method utilizing potential anti-critical process determination engineering project Optimal Project Duration.

Background technology

The problem to be solved in the present invention has under plurality of optional selects the prerequisite of execution pattern in each operation of supposition, with the Project Scheduling problem of each process efficiency combination of the shortest determination for target of total lever factor and time parameter.Selinger (1980) proposes this problem the earliest and provides dynamic programming method for solving.The method emphasizes that each operation will keep work continuity, does not consider its situation of being interrupted.But as a rule, do not allow operation interruption can limit the optimum results of total lever factor.Russell and Caselton (1988) model to Selinger is expanded, require assuming that operation can break work continuity and in same operation, between adjacent operation, introduce interruption, proposing the shortest limit time problem binary dynamic programming solving model in consideration interruption situation.But this dynamic programming model need supvr just determine before scheduling one selectable break time unbounded set, this requirement may make model try to achieve feasible solution; For this problem, EI-Rayes and Moselhi (2001) proposes the shortest limit time problem dynamic programming model of improvement, this model comprise a dispatching algorithm and one break time generating algorithm.In dispatching algorithm operational process, one group of break time of generating algorithm energy Auto-matching break time, final plan is made to be feasible.These methods above-mentioned all belong to exact algorithm, the advantage of exact algorithm is ensure finally to converge to optimum solution, but along with the expansion of problem scale, exact algorithm often can not obtain optimum solution within tolerable computing time, be therefore only applicable to problem on a small scale.

Genetic algorithm (Genetic Algorithm) is more and more applied in engineering practice because of its fast search and the ability better tackling NP-hard problem.Genetic algorithm is proposed in 1967 first by Holland and Bagley.Genetic algorithm originates from the study of computer simulation of carrying out biosystem, and it has fairly obvious contact with the social phenomenon of birds or the shoal of fish, is one of exemplary process of swarm intelligence.Research in the past shows, genetic algorithm has the advantages such as practicality, efficient and strong robustness.At present, genetic algorithm has well been used on function optimization, constrained optimization, minimax target problem, multi-objective problem and combinatorial optimization problem, and achieves successfully.

Hyari and EI-Rayes (2006) by multiple attribute utility theory complete respectively total lever factor that bridge construction scheme to be evaluated is provided and break time sum evaluation, according to the corresponding weighted value that evaluation result is joined, then by weighted value by minimize total lever factor and break time sum Model for Multi-Objective Optimization transform in order to single goal minimum model, confirm the validity of this conversion from the pareto forward position that genetic algorithm is tried to achieve.For same problem, Liu and Wang (2007) has tried to achieve by constraint plan model the result that comparatively Hyari and EI-Rayes (2006) is more excellent, in order to verify the performance of constraint plan model further, Liu and Wang introduces two block-type operations in original bridge construction project, to trying to achieve the optimal case under shortest limit time and least cost correspondence.But all there is a common shortcoming in above-mentioned intelligent algorithm method: its essence is that between adjacent operation, scheme is searched for all possible break time in the execution pattern selected of all process steps and same operation.For extensive problem, all there is the drawback that calculated amount is large, speed of convergence is slow in these methods.Long and Ohsato (2009) overcomes above-mentioned shortcoming, by the operation man-made division in project for class can be interrupted and can not be interrupted class, then in genetic algorithm implementation, devise forwards algorithms and rear to algorithm, this makes not solve as variable the break time in same operation between adjacent operation, and can minimize on use sum break time while trying to achieve shortest limit time.Elloumi and Fortmps (2010) provides the genetic algorithm of the optimal case searching for corresponding shortest limit time for the Resource-Constrained Projects scheduling problem (MRCPSP) under Multi-processing mode.First, by non-renewable resources constraint is converted into a target to be optimized, MRCPSP is made to be converted into a biobjective scheduling problem by original single-object problem; And then the distribution treating evaluation of programme fitness value is completed by cluster algorithm.Although the method for solving before the method contrast that Long and Elloumi takes has had obvious improvement, still has the decision variable of redundancy in their model solution process.

Summary of the invention

The object of the invention is to, thering is provided a kind of utilizes potential anti-critical process to identify project the technology of shortest limit time, this technology can identify all potential anti-critical processes in advance, and follow-up calculating also only need launch round potential anti-critical process, thus eliminate a large amount of operations that those are not potential anti-critical processes.The optimizing to whole project shortest limit time is completed finally by genetic algorithm.

To achieve these goals, the technical scheme key step that the present invention proposes comprises:

Step 1: to the operation A of project _idivide, the operation meeting potential anti-critical process decision condition is put into potential anti-critical process set X, the operation not meeting potential anti-critical process decision condition is put into non-potential anti-critical process set Y;

Wherein, A _ifor i-th operation of project, i=1,2 ..., M;

M is the quantity of project operation;

Step 2: encode to the execution pattern of all process steps in potential anti-critical process set X, generate initial population, Population Size is N _p, then the fastest execution pattern is adopted to all process steps in non-potential anti-critical process set Y;

Step 3: use dispatching algorithm to calculate individual corresponding chief engineer's time value in population, the inverse of total lever factor is converted into individual fitness value; Then adjustment algorithm is adopted to adjust start time of non-key operation, in order to minimize sum and be interrupted the number of times occurred break time;

Step 4: adopt roulette selection parent, and produce filial generation by single-point crossover operator and single-point mutation operator, the number of filial generation is N _p;

Step 5: merge parent and filial generation by fitness value, form new population, new Population Size is still N _p; If now reach maximum genetic algebra, then stop calculating and exporting optimum solution; Otherwise, return step 3.

Described potential anti-critical process decision condition is:

If (a) operation A _ithe continuity that do not work requirement, then operation A _iexist with precedence activities and start-terminate SF or end-end FF type precedence relationship retrains, and exist with successor activities and start-terminate SF or beginning-beginning SS type precedence relationship retrains;

If (b) operation A _ido not exist with precedence activities and start-terminate SF or end-end FF type precedence relationship retrains, or do not exist with successor activities and start-terminate SF or beginning-beginning SS type precedence relationship retrains, and operation A _imeet the requirement of work continuity.

Described use dispatching algorithm calculates individual corresponding chief engineer's time value in population and comprises following sub-step:

Sub-step A1: calculate sub-operation a _i,jduration D _i,j; Wherein, a _i,jfor operation A _iin jth sub-operation, j=1,2 ... N, N are the quantity of operation;

Sub-step A2: calculate sub-operation a _i,jstart time S _i,jwith end time F _i,j, specifically:

A () is as operation A _iwith its precedence activities A _hmeet precedence relationship SS _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (S _h,j+ β _h,j, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=S _{h, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(S_{h,j}-\underset{k=1}{\overset{j-1}{\mathrm{\Σ}}}{D}_{i,k}+{\mathrm{\β}}_{h,i});$

B () is as operation A _iwith its precedence activities A _hmeet precedence relationship SF _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (S _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=S _{h, 1}-D _{i, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin requirement work continuous print situation, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(S_{h,j}-\underset{k=1}{\overset{j}{\mathrm{\Σ}}}{D}_{i,k}+{\mathrm{\β}}_{h,i});$

C () is as operation A _iwith its precedence activities A _hmeet precedence relationship FS _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (F _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=F _{h, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(F_{h,j}-\underset{k=1}{\overset{j-1}{\mathrm{\Σ}}}{D}_{i,k}+{\mathrm{\β}}_{h,i});$

D () is as operation A _iwith its precedence activities A _hmeet precedence relationship FF _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (F _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=F _{h, 1}-D _{i, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(F_{h,j}-\underset{k=1}{\overset{j}{\mathrm{\Σ}}}{D}_{i,k}+{\mathrm{\β}}_{h,i});$

Wherein, β _h,ifor operation A _iwith its precedence activities A _hkey restrain;

SS _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-starting the constraint of SS type precedence relationship;

SF _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-terminating the constraint of SF type precedence relationship;

FS _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-starting the constraint of FS type precedence relationship;

FF _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-terminating the constraint of FF type precedence relationship;

Sub-step A3: according to formula calculate total lever factor.

The described break time sum of minimizing comprises following sub-step:

Sub-step B1: make i=M, M are the quantity of project operation;

Sub-step B2: if operation A _ibe do not require the successional operation of work, then perform sub-step B3; Otherwise, make i=i-1, perform sub-step B6;

Sub-step B3: make j=N-1, N are the quantity of sub-operation;

Sub-step B4: as operation A _iwith its successor activities A _tmeet precedence relationship SS _i,t=β _i,ttime, make S _i,j=min (S _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its successor activities A _tmeet precedence relationship SF _i,t=β _i,ttime, make S _i,j=min (F _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its successor activities A _tmeet FS _i,t=β _i,ttime, make F _i,j=min (S _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j;

As operation A _iwith its successor activities A _tmeet FF _i,t=β _i,ttime, make F _i,j=min (F _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j;

Wherein, β _i,tfor operation A _iwith successor activities A _tkey restrain;

SS _i,trepresent operation A _iwith its successor activities A _tbetween for starting-starting the constraint of SS type precedence relationship;

SF _i,trepresent operation A _iwith its successor activities A _tbetween for starting-terminating the constraint of SF type precedence relationship;

FS _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-starting the constraint of FS type precedence relationship;

FF _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-terminating the constraint of FF type precedence relationship;

Sub-step B5: make j=j-1, if j >=1, then returns sub-step B4; If j<1, then perform sub-step B6;

Sub-step B6: if i >=1, then return sub-step B2; If i<1, then terminate.

The described number of times being interrupted appearance that minimizes comprises following sub-step:

Sub-step C1: make i=1;

Sub-step C2: if operation A _ibe do not require the successional operation of work, then perform sub-step C3; Otherwise, make i=i-1, perform sub-step C6;

Sub-step C3: make j=2;

Sub-step C4: as operation A _iwith its precedence activities A _hmeet precedence relationship SS _h,i=β _h,itime, make S _i,j=max (S _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its precedence activities A _hmeet precedence relationship SF _h,i=β _h,itime, make S _i,j=max (S _h,j-D _i,j+ β _{h, i,}f _{i, j-1}), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its precedence activities A _hmeet precedence relationship FS _h,i=β _h,itime, make S _i,j=max (F _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its precedence activities A _hmeet precedence relationship FF _h,i=β _h,itime, make S _i,j=max (F _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _w,j;

Wherein, β _h,ifor operation A _iwith its precedence activities A _hkey restrain;

SS _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-starting the constraint of SS type precedence relationship;

SF _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-terminating the constraint of SF type precedence relationship;

FS _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-starting the constraint of FS type precedence relationship;

FF _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-terminating the constraint of FF type precedence relationship;

Sub-step C5: make j=j+1, if j≤N, then returns sub-step C4; If j>N, then perform sub-step C6;

Sub-step C6: if i≤M, then return sub-step C2; If i>M, then terminate.

Beneficial effect of the present invention is: first, by the elasticity theory of all types of critical process, only using the execution pattern of potential anti-critical process as variable, and other operation is not re-used as variable, greatly reduce the variable number of operation execution pattern, potential anti-critical process is fewer, then the simplification of this algorithm to solution procedure is more obvious; The second, by adjustment algorithm, automatically determine the start time of each operation, thus automatically determine the break time between each operation, make also no longer become variable break time, compared with existing algorithm, decrease variable number, the unit number of project is more, simplifies effect more obvious.

Accompanying drawing explanation

Fig. 1 is Project duration schematic diagram;

Fig. 2 is the operation corresponding relation figure in RSM in operation and GPRs network;

Fig. 3 is that RSM and GPRs network transforms schematic diagram;

Fig. 4 is operation A _ido not require work continuity schematic diagram;

Fig. 5 is operation A _irequirement work continuity schematic diagram;

Fig. 6 is the engineering information tables of data of repeated project;

Fig. 7 is optimal scheduling tables of data;

Fig. 8 is general solution and methods and results curve comparison figure provided by the invention; Wherein, (a) is general solution result curve figure, and (b) is methods and results curve map provided by the invention.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.It is emphasized that following explanation is only exemplary, instead of in order to limit the scope of the invention and apply.

Embodiment 1

Below in conjunction with example, the present invention is further described.Embodiment 1 is set forth principle of the present invention.

Suppose that a repeated project is made up of M operation, each operation will repeat in N number of unit.Operation A _i(i=1 ..., M) have Ω ⁱplant execution pattern, wherein the work efficiency of kth kind execution pattern is assuming that operation A _i(i=1 ..., M) require to keep the constraint of resource constancy, so as operation A _iafter selected a kind of execution pattern, just must with this execution pattern work to this operation terminates.With a _i,jrepresent operation A _isub-operation in a jth unit, Q _i,jrepresent corresponding workload, so sub-operation a _i,jduration D _i,jcan be drawn by formula (1).

$D_{i,j}=\frac{Q_{i,j}}{\underset{k=1}{\overset{{\mathrm{\&Omega;}}^i}{\mathrm{\&Sigma;}}}{B}_i^k\&times;P_i^k}\&ForAll;i=1,...,M;j=1,...,N---\left(1\right)$

for 0-1 variable, represent operation A _ihave selected kth kind execution pattern, otherwise mean do not have selected.In order to meet the constant requirement of resource, formula (2) must be met.

$\underset{k=1}{\overset{{\mathrm{\&Omega;}}^i}{\mathrm{\&Sigma;}}}{B}_i^k=1,\&ForAll;i=1,...,M---\left(2\right)$

Respectively with C _sS, C _sF, C _fSand C _fFrepresent the operation set meeting the constraint of corresponding precedence relationship, such as, if (i, j, β _i,j) ∈ C _sS, then operation A is represented _ias operation A _jprecedence activities, with A _jlife period constraint SS _i,j=β _i,j.Make S _i,jand F _i,jrepresent operation a respectively _i,jstart time and the end time, so repeated project shortest limit time problem can be described as with operation A _iexecution pattern with operation a _i,jstart time S _i,jfollowing planning problem P for variable:

$P:\min \left(T_p\right)=\min \left(\underset{j=1,...,N}{\underset{i=1,...,M}{\max }}\left(F_{i,j}\right)\right)=\min \left(\underset{j=1,...,N}{\underset{i=1,...,M}{\max }}(S_{i,j}+D_{i,j})\right)---\left(3\right)$

$S_{i,j+1}=S_{i,j}+D_{i,j},F_{i,j+1}=S_{i,j+1}+D_{i,j+1},i\&Element;W,\&ForAll;j=1,...,N-1---\left(4\right)$

$S_{i,j+1}\&GreaterEqual;S_{i,j}+D_{i,j},F_{i,j+1}=S_{i,j+1}+D_{i,j+1},i\&Element;\stackrel{\&OverBar;}{W},\&ForAll;j=1,...,N-1---\left(5\right)$

S _t,j≥S _i,j+β _i,t，(i,t,β _i,t)∈C _SS(6)

F _t,j≥S _i,j+β _i,t，(i,t,β _i,t)∈C _SF(7)

S _t,j≥F _i,j+β _i,t，(i,t,β _i,t)∈C _FS(8)

F _t,j≥F _i,j+β _i,t，(i,t,β _i,t)∈C _FF(9)

$\underset{i\&Element;\stackrel{\&OverBar;}{W}}{\mathrm{\&Sigma;}}\underset{j=1}{\overset{N-1}{\mathrm{\&Sigma;}}}(S_{i,j+1}-F_{i,j})=\min \left(\underset{i\&Element;\stackrel{\&OverBar;}{W}}{\mathrm{\&Sigma;}}\underset{j=1}{\overset{N-1}{\mathrm{\&Sigma;}}}(S_{i,j+1}-F_{i,j})\right),S_{i,j}\&GreaterEqual;{\mathrm{ES}}_{i,j}---\left(10\right)$

Wherein, the objective function that formula (3) is planning problem P, namely minimizes repeated Project duration.In formula (4), in set W, all process steps all requires maintenance work continuity constraint, and its essence is at sub-operation a _i,jand a _{i, j+1}between apply simultaneously minimum time constraint FS=0 and maximum time constraint FS=0, i.e. sub-operation a _i,jterminate latter 0 day, sub-operation a _{i, j+1}could start, simultaneously sub-operation a _i,jafter end 0 day at the most, sub-operation a _{i, j+1}must start.In formula (5), set middle all process steps does not all require work continuity constraint, is namely equivalent to sub-operation a _i,jand a _{i, j+1}between only exist minimum time constraint FS=0.To formula (9), formula (6) ensures that all operations meet given precedence relationship, β _i,tfor corresponding to operation A _iand A _tbetween precedence relationship amount of restraint, the constraint of precedence relationship that the present invention discusses all belongs to minimum time constraint.Formula (10) requires to try to achieve under the shortest total lever factor prerequisite, makes sub-operation a _i,jwith sub-operation between summation break time minimum, ES _i,jrepresent operation a _i,jearliest start time.

In critical path method (CPM) network, the length of critical path determines the total lever factor of project, critical path comprises critical process and connects the key restrain of two critical processes.Similar, in repeated schedule item (RSM), Project duration is determined by the length of critical path, critical path comprises critical process and connects the key restrain of two critical processes.Critical path is represented, then R={R with Pc _i,t| (i, t, β _i,t) ∈ C _sSor (i, t, β _i,t) ∈ C _sFor (i, t, β _i,t) ∈ C _fSor (i, t, β _i,t) ∈ C _fFrepresent the set that all precedence relationships retrain.Then Project duration _tpcan be expressed as:

$T_p=\underset{a_{i,j}\&Element;\mathrm{Pc}}{\mathrm{\&Sigma;}}{D}_{i,j}+\underset{R_{i,t}\&Element;\mathrm{Pc}}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_{i,t}---\left(11\right)$

Key restrain β _i,tby the defined of engineering project own, not by operation a _i,joperation patterns affect.If operation a _i,jpositive critical process, then D _i,jget positive sign; Otherwise, if operation a _i,janti-critical process, then D _i,jget negative sign.For a critical process, D _i,jget 0.Such as shown in Fig. 1, the precedence relationship between operation is ${\mathrm{FF}}_{A_1,A_2}={\mathrm{\&beta;}}_{\mathrm{1,2}},{\mathrm{SS}}_{A_2,A_3}={\mathrm{\&beta;}}_{\mathrm{2,3}}$ With ${\mathrm{SS}}_{A_3,A_4}={\mathrm{\&beta;}}_{\mathrm{3,4}},$ And operation A ₁, A ₃and A ₄requirement work continuity, in Fig. 1, heavy black line represents critical path, so total lever factor T _pcan be expressed as:

$T_p=(\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}{D}_{1,j}+D_{\mathrm{4,3}}-D_{\mathrm{2,3}})+({\mathrm{\&beta;}}_{\mathrm{1,2}}+{\mathrm{\&beta;}}_{\mathrm{2,3}}+{\mathrm{\&beta;}}_{\mathrm{3,4}})---\left(12\right)$

From formula (11), the total lever factor of project is determined by the amount of restraint of critical process duration and key restrain, for same project, the amount of restraint of key restrain equals determined value, therefore only needs to pay close attention to the impact of critical process duration change on total lever factor.

In order to try to achieve shortest limit time, under existing resource condition, first consider by all process steps all according to the fastest possible execution pattern arrangement, and all process steps all start in earliest start time, obtain an initial schedule scheme thus, obviously this is a feasible solution of former problem.In initial schedule scheme, because all critical processes have been all the fastest execution patterns, therefore total lever factor cannot be made shorter by improving its work efficiency.If now there is not anti-critical process in critical path, the total lever factor of then now trying to achieve is the shortest total lever factor, if critical path exists anti-critical process, from formula (11), by the duration of selecting slower execution pattern to extend positive critical process, some critical process or non-key operation, total lever factor all can not be made to reduce, only extend the duration of anti-critical process in initial scheme, total lever factor just can be made to shorten.After duration of this anti-critical process is extended, new anti-critical process may be produced, now need to carry out new one and take turns optimization, until there is not anti-critical process or the duration not by extending anti-critical process shortens total lever factor further.In this change procedure, controlled is that those likely produce the operation of anti-critical process all the time, and namely meet the necessary condition that anti-critical process exists, the present invention is defined as potential anti-critical process.Notice, the solution obtained by said process is not optimum solution, because it does not minimize sum break time under the prerequisite meeting shortest limit time, for this reason, Long and Ohsato (2009) is being terminated-is starting the forwards algorithms of design under the constraint of FS precedence relationship and be generalized to whole four kinds of precedence relationships constraint to algorithm afterwards by the present invention, namely start-start SS, beginning-end SF, end-beginning FS and end-end FF, to reach the object minimizing sum break time.

In sum, the general thought solving project shortest limit time problem is, find out potential anti-critical processes all in project, using its execution pattern as variable, then the fastest execution pattern is adopted to other operations, the algorithm designed by the present invention tries to achieve the optimum execution pattern of each operation and the optimum start time of operation fast, make corresponding total lever factor and break time sum minimum.

In RSM, operation A _i(i=1 ..., M) be decision condition (or the operation A of potential anti-critical process _ithe middle necessary condition that there is anti-critical process) be:

Condition (1) is if operation A _ithe continuity that do not work requirement, then operation A _ithere is SF or FF type precedence relationship with precedence activities to retrain, and there is SF or SS type precedence relationship with successor activities and retrain.

Condition (2) is if operation A _ithere is not SF or FF type precedence relationship with precedence activities to retrain, or there is not SF or SS type precedence relationship with successor activities and retrain, so operation A _imeet the requirement of work continuity.

The proof procedure of above-mentioned decision condition is as follows:

Repeated project scheduling (RSM) is carried out corresponding with ordinary priority relation (GPRs) network chart, is converted into network by RSM.The method for transformation of RSM and network model is, any one RSM scheduling scheme can be converted into GPRs network, and critical path, the critical process one_to_one corresponding in critical path, critical process and GPRs in RSM.Arbitrary operation a in RSM _i,jan operation in corresponding GPRs network, represents with two contrary, that flexible strategy are contrary real arrows in direction, as shown in Figure 2.Wherein, D _i,jrepresent operation a _i,jduration.The left end with the arrow of positive flexible strategy value is operation a _i,jstarting point, right-hand member is operation a _i,jend point.If two operations exist minimum time constraint, then connect the obligatory point in an operation and the restrained point in another operation with arrow, and the restrained point of arrow points, the flexible strategy of arrow are the amount of restraint of minimum time constraint; If two operations exist maximum time constraint, same with arrow connection constraints point and restrained point, but now arrow points obligatory point, the flexible strategy of arrow are the opposite number of amount of restraint.Operation A is connected respectively with sink nodes (w) with two virtual source nodes (s) _ithe starting point of middle all process steps and operation A _mthe end point of middle all process steps, like this, RSM is GPRs network chart with regard to equivalent conversion.Such as, in Fig. 1 RSM figure of project, to be converted into after GPRs network chart as shown in Figure 3, black thick line represents critical path.Critical path in Fig. 1 corresponds to the critical path in Fig. 3, the critical process of critical process one_to_one corresponding in Fig. 3.

In GPRs network, operation a _i,jbecome anti-critical process necessary condition be the route (elementary path) of existence one from source point (s) to meeting point (w), make operation a _i,jnegative flexible strategy arrow be positioned on this route.

Critical path is the longest path line connecting source point (s) and meeting point (w), and the feature of anti-critical process is that duration longer total lever factor is shorter, and namely the negative flexible strategy arrow of anti-critical process is positioned on critical path.So, any one operation wants the necessary condition becoming anti-critical process to be: the negative flexible strategy arrow of this operation will be positioned at a route from source point (s) to meeting point (w).

First demonstrate,prove condition (1) to set up.In RSM, the constraint of any operation all comes from two aspects: the constraint of minimum and maximum time 1) produced because there is the requirement of work continuity between adjacent operation in same operation, or the minimum time constraint produced because there is not the requirement of work continuity.2) there is in same unit the minimum time constraint produced between two operations of precedence relationship constraint; In the GPRs network that RSM is corresponding, suppose operation A _iin operation a _i,jfor anti-critical process, so in GPRs, the negative flexible strategy arrow one of this operation is positioned on critical path.Again due to operation A _ido not require work continuity, so operation a _i,jwith a _{i, j+1}(j=1 ..., N-1) between only exist minimum time constraint FS=0, but these constraints can not make operation a _i,jnegative flexible strategy arrow be positioned at any route (elementary path) from source point (s) to meeting point (w), as shown in Figure 4.Therefore, operation a _i,jcan only rely in same unit have precedence relationship constraint two operations between produce minimum time constraint make its negative flexible strategy arrow be positioned on critical path, this just makes operation A _inecessarily by with its precedence activities A _kits end point of precedence relationship effect of contraction, and by with its successor activities A _iits starting point of precedence relationship effect of contraction, namely with precedence activities A _kthere is the constraint of SF or FF type precedence relationship, with successor activities A _ithere is the constraint of SF or SS type precedence relationship.

Demonstrate,prove condition (2) again to set up.Suppose operation A _iin operation a _i,jfor anti-critical process, so in GPRs network chart, the negative flexible strategy arrow one of this operation is positioned on critical path.Operation A again _ithere is not SF or FF type precedence relationship with precedence activities to retrain, or there is not SF or SS type precedence relationship with successor activities and retrain, so operation A _iwith precedence activities A _kwith successor activities A _tprecedence relationship constrained type can be divided three classes: 1) with precedence activities A _kexist FS or SS type precedence relationship constraint, and with successor activities A _tthere is the constraint of FS or FF type precedence relationship; 2) with precedence activities A _kexist FS or SS type precedence relationship constraint, and with successor activities A _tthere is the constraint of SF or SS type precedence relationship; 3) with precedence activities A _kexist SF or FF type precedence relationship constraint, and with successor activities A _tthere is the constraint of FS or FF type precedence relationship.But this three classes situation all can not make operation a _i,jnegative flexible strategy arrow be positioned on any route (elementary path) from source point to meeting point, wherein the first kind is as shown in Figure 5.Therefore, operation a _i,jcan only rely in same operation to retrain between adjacent operation makes its negative flexible strategy arrow be positioned on critical path, so operation A _iin will seek survival between adjacent operation at maximum time constraint FS=0, mean operation A _imeet the requirement of work continuity.

Thus, the decision condition of above-mentioned potential anti-critical process is set up.

According to above-mentioned analysis, the identify project method of shortest limit time of anti-critical process is utilized to comprise the steps:

Step 1: to the operation A of project _idivide, the operation meeting potential anti-critical process decision condition is put into potential anti-critical process set X, the operation not meeting potential anti-critical process decision condition is put into non-potential anti-critical process set Y.

Step 2: encode to the execution pattern of all process steps in potential anti-critical process set X, generate initial population, Population Size is N _p, then the fastest execution pattern is adopted to all process steps in non-potential anti-critical process set Y.

Step 3: use dispatching algorithm to calculate individual corresponding chief engineer's time value in population, the inverse of total lever factor is converted into individual fitness value; Then adjustment algorithm is adopted to adjust start time of non-key operation, in order to minimize sum and be interrupted the number of times occurred break time.

Step 4: adopt roulette selection parent, and produce filial generation by single-point crossover operator and single-point mutation operator, the number of filial generation is N _p;

Step 5: merge parent and filial generation by fitness value, form new population, new Population Size is still N _p; If now reach maximum genetic algebra, then stop calculating and exporting optimum solution; Otherwise, return step 3.

In above-mentioned steps 3, use dispatching algorithm to calculate individual corresponding chief engineer's time value in population and comprise following sub-step:

Sub-step A1: calculation process a _i,jduration D _i,j; Wherein, a _i,jfor operation A _iin a jth operation, j=1,2 ... N, N are the quantity of operation.

Sub-step A2: calculation process a _i,jstart time S _i,jwith end time F _i,j, specifically:

A () is as operation A _iwith its precedence activities A _hmeet precedence relationship SS _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (S _h,j+ β _h,j, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=S _{h, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1}.

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(S_{h,j}-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i}).$

B () is as operation A _iwith its precedence activities A _hmeet precedence relationship SF _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (S _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=S _{h, 1}-D _{i, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1}.

At operation A _iin requirement work continuous print situation, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(S_{h,j}-\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i}).$

C () is as operation A _iwith its precedence activities A _hmeet precedence relationship FS _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (F _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=F _{h, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1}.

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(F_{h,j}-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i}).$

D () is as operation A _iwith its precedence activities A _hmeet precedence relationship FF _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (F _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=F _{h, 1}-D _{i, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1}.

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,...,N}{\max }(F_{h,j}-\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i}).$

Wherein, β _h,ifor operation A _iwith its precedence activities A _hkey restrain.

SS _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-starting the constraint of SS type precedence relationship.

SF _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-terminating the constraint of SF type precedence relationship.

FS _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-starting the constraint of FS type precedence relationship.

FF _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-terminating the constraint of FF type precedence relationship.

Sub-step A3: according to formula calculate total lever factor.

In above-mentioned steps 3, the start time adopting adjustment algorithm to adjust non-key operation comprises two stages, and first stage is used for minimizing sum break time, and second stage is for minimizing the number of times being interrupted and occurring.

The target of first stage is the break time of the scheduling scheme minimized after dispatching algorithm calculates, and therefore only to not requiring that the successional operation of work adjusts, keeps the total lever factor of this scheduling scheme constant in adjustment process.From last operation A _mstart to find forward successively not require the successional operation A of work _i, and according to operation A _iwith its successor activities A _tprecedence relationship constraint to operation A _itime parameter adjust, its essence is fixed work order A _ioperation a in the end in a unit _i,N, and allow operation A _iin all the other operations start at late start time.Its detailed process comprises:

Sub-step B1: make i=M, M are the quantity of project operation.

Sub-step B2: if operation A _ibe do not require the successional operation of work, then perform sub-step B3; Otherwise, make i=i-1, perform sub-step B6.

Sub-step B3: make j=N-1, N are the quantity of operation.

Sub-step B4: as operation A _iwith its successor activities A _tmeet precedence relationship SS _i,t=β _i,ttime, make S _i,j=min (S _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j.

As operation A _iwith its successor activities A _tmeet precedence relationship SF _i,t=β _i,ttime, make S _i,j=min (F _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j.

As operation A _iwith its successor activities A _tmeet FS _i,t=β _i,ttime, make F _i,j=min (S _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j.

As operation A _iwith its successor activities A _tmeet FF _i,t=β _i,ttime, make F _i,j=min (F _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j.

Wherein, β _i,tfor operation A _iwith successor activities A _tkey restrain.

SS _i,trepresent operation A _iwith its successor activities A _tbetween for starting-starting the constraint of SS type precedence relationship.

SF _i,trepresent operation A _iwith its successor activities A _tbetween for starting-terminating the constraint of SF type precedence relationship.

FS _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-starting the constraint of FS type precedence relationship.

FF _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-terminating the constraint of FF type precedence relationship.

Sub-step B5: make j=j-1, if j >=1, then returns sub-step B4; If j<1, then perform sub-step B6.

Sub-step B6: if i >=1, then return sub-step B2; If i<1, then terminate.

Codes implement is:

Subordinate phase minimize on the basis of first stage be interrupted occur number of times, in adjustment process scheduling scheme total lever factor and break time summation all remain unchanged.From first operation A ₁start to find backward successively not require the successional operation A of work _i, and according to operation A _iwith its precedence activities A _kprecedence relationship constraint to operation A _itime parameter adjust, its essence is fixed work order A _ioperation a in first unit _{i, 1}, and allow operation A _iin all the other operations start in earliest start time.Concrete computation process is as follows:

Sub-step C1: make i=1.

Sub-step C2: if operation A _ibe do not require the successional operation of work, then perform sub-step C3; Otherwise, make i=i-1, perform sub-step C6.

Sub-step C3: make j=2.

Sub-step C4: as operation A _iwith its precedence activities A _hmeet precedence relationship SS _h,i=β _h,itime, make S _i,j=max (S _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j.

As operation A _iwith its precedence activities A _hmeet precedence relationship SF _h,i=β _h,itime, make S _i,j=max (S _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j.

As operation A _iwith its precedence activities A _hmeet precedence relationship FS _h,i=β _h,itime, make S _i,j=max (F _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j.

As operation A _iwith its precedence activities A _hmeet precedence relationship FF _h,i=β _h,itime, make S _i,j=max (F _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j.

Wherein, β _h,ifor operation A _iwith its precedence activities A _hkey restrain.

SS _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-starting the constraint of SS type precedence relationship.

SF _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-terminating the constraint of SF type precedence relationship.

FS _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-starting the constraint of FS type precedence relationship.

FF _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-terminating the constraint of FF type precedence relationship.

Sub-step C5: make j=j+1, if j≤N, then returns sub-step C4; If j>N, then perform sub-step C6.

Sub-step C6: if i≤M, then return sub-step C2; If i>M, then terminate.

Codes implement is as follows:

Embodiment 2

Below in conjunction with a concrete example, effect of the present invention is described.As shown in Figure 6, Fig. 6 gives a repeated project, comprise 11 operations and 5 unit, the continuity of operation requires, precedence relationship constrained type and the engineering information such as amount of restraint, possible execution pattern are shown in Fig. 6, seeking a scheduling scheme makes the total lever factor of this project the shortest, and summation break time of correspondence is also minimum.

According to algorithm steps, first require to divide set X and Y according to the precedence relationship constrained type between operation and work continuity.Operation A ₃, A ₇, A ₈and A ₁₀the decision condition of potential anti-critical process is met, operation A because there is the requirement of work continuity ₅do not require work continuity, but with precedence activities A ₄exist and terminate-terminate the constraint of FF type precedence relationship, and with successor activities A ₆exist and start-start the constraint of SS type precedence relationship, so A ₅also meet the decision condition of potential anti-critical process, all the other operations all do not meet necessary condition, so set X={A ₃, A ₅, A ₇, A ₈, A ₁₀, and gather Y={A ₁, A ₂, A ₄, A ₆, A ₉, A ₁₁.Then with operation A ₃, A ₅, A ₇, A ₈and A ₁₀execution pattern be that variable carries out follow-up calculating.As shown in Figure 7, the shortest limit time of trying to achieve is 31.4 days in the optimal scheduling that algorithm is tried to achieve, corresponding break time and be 4.4 days.

If the algorithm being all used as variable the break time between the execution pattern of all process steps and operation is called general solution, so see Fig. 8 with the results contrast that general solution and method of the present invention solve example respectively.As can be seen from Figure 8, under genetic algorithm parameter arranges identical prerequisite, the time that method provided by the invention converges to needed for optimum solution is only 0.27s, and convergence times was the 10th generation; And the general solution time converged to needed for optimum solution is 10.48s, convergence times was the 395th generation.Fig. 8 shows, method provided by the invention is obviously better than general solution, and in large-scale project, along with the increase of non-potential anti-critical process and unit number, this superiority will be more obvious.

According to the characteristic that anti-critical process and total lever factor oppositely increase, repeated project shortest limit time problem can be regarded as the process utilizing anti-critical process to carry out Time Optimization.The present invention have studied the necessary condition that anti-critical process exists, and find out potential anti-critical processes all in repeated project based on this, using its execution pattern as decision variable, then adopt the fastest execution pattern can obtain corresponding shortest limit time to other operations.In instance analysis, the high efficiency of calculating is embodied.

Method provided by the invention decreases variable number from two aspects.First, by the elasticity theory of all types of critical process, only using the execution pattern of potential anti-critical process as variable, and other operation is not re-used as variable, greatly reduces the variable number of operation execution pattern.The simplification of this process is relevant with the number of potential anti-critical process.Potential anti-critical process is fewer, then the simplification of the present invention to solution procedure is more obvious.The second, by adjustment algorithm, automatically determine the start time of each operation, thus automatically determine the break time between each operation, make also no longer become variable break time, compared with existing algorithm, decrease variable number.The unit number of project is more, simplifies more obvious.

The above; be only the present invention's preferably embodiment, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (5)

1. utilize potential anti-critical process to identify project the method for shortest limit time, it is characterized in that described method comprises:

Step 1: to the operation A of project _idivide, the operation meeting potential anti-critical process decision condition is put into potential anti-critical process set X, the operation not meeting potential anti-critical process decision condition is put into non-potential anti-critical process set Y;

Wherein, A _ifor i-th operation of project, i=1,2 ..., M;

M is the quantity of project operation;

Step 2: encode to the execution pattern of all process steps in potential anti-critical process set X, generate initial population, Population Size is N _p, then the fastest execution pattern is adopted to all process steps in non-potential anti-critical process set Y;

Step 3: use dispatching algorithm to calculate individual corresponding chief engineer's time value in population, the inverse of total lever factor is converted into individual fitness value; Then adjustment algorithm is adopted to adjust start time of non-key operation, in order to minimize sum and be interrupted the number of times occurred break time;

Step 4: adopt roulette selection parent, and produce filial generation by single-point crossover operator and single-point mutation operator, the number of filial generation is N _p;

Step 5: merge parent and filial generation by fitness value, form new population, new Population Size is still N _p; If now reach maximum genetic algebra, then stop calculating and exporting optimum solution; Otherwise, return step 3.

2. method according to claim 1, is characterized in that described potential anti-critical process decision condition is:

If (a) operation A _ithe continuity that do not work requirement, then operation A _iexist with precedence activities and start-terminate SF or end-end FF type precedence relationship retrains, and exist with successor activities and start-terminate SF or beginning-beginning SS type precedence relationship retrains;

If (b) operation A _ido not exist with precedence activities and start-terminate SF or end-end FF type precedence relationship retrains, or do not exist with successor activities and start-terminate SF or beginning-beginning SS type precedence relationship retrains, and operation A _imeet the requirement of work continuity.

3. method according to claim 1 and 2, is characterized in that described use dispatching algorithm calculates individual corresponding chief engineer's time value in population and comprises following sub-step:

Sub-step A1: calculate sub-operation a _i,jduration D _i,j; Wherein, a _i,jfor operation A _iin jth sub-operation, j=1,2 ... N, N are the quantity of operation;

Sub-step A2: calculate sub-operation a _i,jstart time S _i,jwith end time F _i,j, specifically:

A () is as operation A _iwith its precedence activities A _hmeet precedence relationship SS _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (S _h,j+ β _h,j, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=S _{h, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,\&CenterDot;\&CenterDot;\&CenterDot;,N}{\max }(S_{h,j}-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i});$

B () is as operation A _iwith its precedence activities A _hmeet precedence relationship SF _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (S _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=S _{h, 1}-D _{i, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin requirement work continuous print situation, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,\&CenterDot;\&CenterDot;\&CenterDot;,N}{\max }(S_{h,j}-\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i});$

C () is as operation A _iwith its precedence activities A _hmeet precedence relationship FS _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (F _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=F _{h, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,\&CenterDot;\&CenterDot;\&CenterDot;,N}{\max }(F_{h,j}-\underset{k=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i});$

D () is as operation A _iwith its precedence activities A _hmeet precedence relationship FF _h,i=β _h,itime:

At operation A _iunder not requiring the successional situation of work, S _i,j=max (F _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j, S _{i, 1}=F _{h, 1}-D _{i, 1}+ β _h,i, F _{i, 1}=S _{i, 1}+ D _{i, 1};

At operation A _iin the successional situation of requirement work, f _i,j=S _i,j+ D _i,j, $\mathrm{MAX}=\underset{j=1,\&CenterDot;\&CenterDot;\&CenterDot;,N}{\max }(F_{h,j}-\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{D}_{i,k}+{\mathrm{\&beta;}}_{h,i});$

Wherein, β _h,ifor operation A _iwith its precedence activities A _hkey restrain;

SS _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-starting the constraint of SS type precedence relationship;

SF _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-terminating the constraint of SF type precedence relationship;

FS _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-starting the constraint of FS type precedence relationship;

FF _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-terminating the constraint of FF type precedence relationship;

Sub-step A3: according to formula calculate total lever factor.

4. method according to claim 3, minimizes break time sum and comprises following sub-step described in it is characterized in that:

Sub-step B1: make i=M, M are the quantity of project operation;

Sub-step B2: if operation A _ibe do not require the successional operation of work, then perform sub-step B3; Otherwise, make i=i-1, perform sub-step B6;

Sub-step B3: make j=N-1, N are the quantity of sub-operation;

Sub-step B4: as operation A _iwith its successor activities A _tmeet precedence relationship SS _i,t=β _i,ttime, make S _i,j=min (S _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its successor activities A _tmeet precedence relationship SF _i,t=β _i,ttime, make S _i,j=min (F _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its successor activities A _tmeet FS _i,t=β _i,ttime, make F _i,j=min (S _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j;

As operation A _iwith its successor activities A _tmeet FF _i,t=β _i,ttime, make F _i,j=min (F _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j;

Wherein, β _i,tfor operation A _iwith successor activities A _tkey restrain;

SS _i,trepresent operation A _iwith its successor activities A _tbetween for starting-starting the constraint of SS type precedence relationship;

SF _i,trepresent operation A _iwith its successor activities A _tbetween for starting-terminating the constraint of SF type precedence relationship;

FS _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-starting the constraint of FS type precedence relationship;

FF _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-terminating the constraint of FF type precedence relationship;

Sub-step A3: according to formula calculate total lever factor;

The described break time sum of minimizing comprises following sub-step:

Sub-step B1: make i=M, M are the quantity of project operation;

Sub-step B2: if operation A _ibe do not require the successional operation of work, then perform sub-step B3; Otherwise, make i=i-1, perform sub-step B6;

Sub-step B3: make j=N-1, N are the quantity of sub-operation;

Sub-step B4: as operation A _iwith its successor activities A _tmeet precedence relationship SS _i,t=β _i,ttime, make S _i,j=min (S _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its successor activities A _tmeet precedence relationship SF _i,t=β _i,ttime, make S _i,j=min (F _t,j-β _i,t, S _{i, j+1}-D _i,j), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its successor activities A _tmeet FS _i,t=β _i,ttime, make F _i,j=min (S _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j;

As operation A _iwith its successor activities A _tmeet FF _i,t=β _i,ttime, make F _i,j=min (F _t,j-β _i,t, S _{i, j+1}), S _i,j=F _i,j-D _i,j;

Wherein, β _i,tfor operation A _iwith successor activities A _tkey restrain;

SS _i,trepresent operation A _iwith its successor activities A _tbetween for starting-starting the constraint of SS type precedence relationship;

SF _i,trepresent operation A _iwith its successor activities A _tbetween for starting-terminating the constraint of SF type precedence relationship;

FS _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-starting the constraint of FS type precedence relationship;

FF _i,trepresent operation A _iwith its successor activities A _tbetween for terminating-terminating the constraint of FF type precedence relationship;

Sub-step B5: make j=j-1, if j >=1, then returns sub-step B4; If j < 1, then perform sub-step B6;

Sub-step B6: if i >=1, then return sub-step B2; If i < 1, then terminate.

5. method according to claim 3, minimizes the number of times being interrupted appearance and comprises following sub-step described in it is characterized in that:

Sub-step C1: make i=1;

Sub-step C2: if operation A _ibe do not require the successional operation of work, then perform sub-step C3; Otherwise, make i=i-1, perform sub-step C6;

Sub-step C3: make j=2;

Sub-step C4: as operation A _iwith its precedence activities A _hmeet precedence relationship SS _h,i=β _h,itime, make S _i,j=max (S _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its precedence activities A _hmeet precedence relationship SF _h,i=β _h,itime, make S _i,j=max (S _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its precedence activities A _hmeet precedence relationship FS _h,i=β _h,itime, make S _i,j=max (F _h,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j;

As operation A _iwith its precedence activities A _hmeet precedence relationship FF _h,i=β _h,itime, make S _i,j=max (F _h,j-D _i,j+ β _h,i, F _{i, j-1}), F _i,j=S _i,j+ D _i,j;

Wherein, β _h,ifor operation A _iwith its precedence activities A _hcontrol constraints;

SS _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-starting the constraint of SS type precedence relationship;

SF _h,irepresent operation A _iwith its precedence activities A _hbetween for starting-terminating the constraint of SF type precedence relationship;

FS _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-starting the constraint of FS type precedence relationship;

FF _h,irepresent operation A _iwith its precedence activities A _hbetween for terminating-terminating the constraint of FF type precedence relationship;

Sub-step C5: make j=j+1, if j≤N, then returns sub-step C4; If j > is N, then perform sub-step C6;

Sub-step C6: if i≤M, then return sub-step C2; If i > is M, then terminate.