CN104820872B

CN104820872B - The method for carrying out project duration optimization using potential anti-critical process in engineering project

Info

Publication number: CN104820872B
Application number: CN201510227469.3A
Authority: CN
Inventors: 张立辉; 邹鑫; 乞建勋; 熊俊; 邵利洁
Original assignee: North China Electric Power University
Current assignee: North China Electric Power University
Priority date: 2015-05-06
Filing date: 2015-05-06
Publication date: 2019-04-02
Anticipated expiration: 2035-05-06
Also published as: CN104820872A

Abstract

The invention discloses the methods that one of project construction period control technology field determines engineering project Optimal Project Duration using potential anti-critical process.It include: by the potential anti-critical process in certain technical characteristic recognitive engineering project；Project all process steps are divided into potential anti-critical process set X and anti-critical process set Y non-potential accordingly；The execution pattern of all process steps in potential anti-critical process set X is encoded, initial population, Population Size N are generated_P, most fast execution pattern is then used to all process steps in anti-critical process set Y non-potential；The corresponding chief engineer's time value of individual in population is calculated, converts the inverse of total construction period to the fitness value of individual；Then at the beginning of adjusting non-key process；Parent is selected, and filial generation is generated by single point crossing operator and single-point mutation operator；Merge parent and filial generation by fitness value, forms new population；If reaching maximum genetic algebra at this time, stop calculating and exporting optimal solution, obtains the Optimal Project Duration scheme of project.

Description

The method for carrying out project duration optimization using potential anti-critical process in engineering project

Technical field

The invention belongs to project construction period control technology fields more particularly to a kind of potential anti-critical process of utilization to determine The method of engineering project Optimal Project Duration.

Background technique

The problem to be solved in the present invention is under the premise of it is assumed that each process has various selectable execution pattern, with total The Project Scheduling problem of duration most short determination each process efficiency combination and time parameter for target.Selinger (1980) is earliest It proposes this problem and provides Dynamic Programming method for solving.This method emphasizes that each process will keep work continuity, does not examine The case where considering its interruption.But in most cases, process interruption is not allowed to will limit the optimum results of total construction period.Russell The model of Selinger is extended with Caselton (1988), it is assumed that process can break work continuity require and Interruption is introduced in the same process between adjacent process, proposes the shortest limit time problem binary Dynamic Programming considered in the case of interruption Solving model.But the dynamic programming model needs manager to determine that a selectable break time is unbounded before scheduling Collection, this requirement may make model that can not acquire feasible solution；For this problem, EI-Rayes and Moselhi (2001) are proposed Improved shortest limit time problem dynamic programming model, the model include dispatching algorithm and a break time generating and calculating Method.In dispatching algorithm operational process, one group of break time of break time generating algorithm energy Auto-matching, so that final scheme is It is feasible.These above-mentioned methods belong to exact algorithm, and the advantage of exact algorithm, which is can guarantee, finally converges to optimal solution, but With the expansion of problem scale, exact algorithm tends not to obtain optimal solution within the tolerable calculating time, therefore is only applicable in In small-scale problem.

Genetic algorithm (Genetic Algorithm) is due to the ability of its fast search and preferably reply NP-hard problem It is increasingly used in engineering practice.Genetic algorithm was put forward for the first time by Holland and Bagley in 1967.Heredity is calculated Method originates from the study of computer simulation that is carried out to biosystem, and the social phenomenon of it and birds or the shoal of fish has fairly obvious Connection, is one of exemplary process of swarm intelligence.In the past studies have shown that genetic algorithm has practical, efficient and strong robustness The advantages that.It is asked currently, genetic algorithm has been used in function optimization, constrained optimization, minimax target problem, multiple target well In topic and combinatorial optimization problem, and achieve success.

Hyari and EI-Rayes (2006) have been respectively completed by multiple attribute utility theory to bridge construction scheme to be evaluated Then the evaluation of the total construction period and the sum of break time of offer pass through weighted value according to the corresponding weighted value that evaluation result is matched By the Model for Multi-Objective Optimization conversion for minimizing the sum of total construction period and break time in order to which single goal minimizes model, calculated from heredity The forward position pareto that method acquires confirms the validity of the conversion.For same problem, Liu and Wang (2007) pass through constraint rule Model is drawn to have acquired compared with Hyari and EI-Rayes (2006) more preferably as a result, in order to further verify the property of constraint plan model Can, Liu and Wang introduce two block type processes in original bridge construction project, to acquire shortest limit time and it is minimum at Optimal case under this correspondence.But above-mentioned intelligent algorithm method all have the shortcomings that one it is common: its essence is to all process steps Optional execution pattern and the same process between adjacent process all possible break time scheme scan for.For big All there is drawback computationally intensive, that convergence rate is slow in scale issue, these methods.Long and Ohsato (2009) overcomes above-mentioned Process man-made division in project is that can be interrupted class and can not be interrupted class, then in genetic algorithm implementation procedure by disadvantage Devise forwards algorithms and backward algorithm, this make the break time in the same process between adjacent process not as variable into Row solves, and can minimize the sum of break time automatically while acquiring shortest limit time.Elloumi and Fortmps (2010) the corresponding shortest limit time of search is provided most for the Resource-Constrained Projects scheduling problem (MRCPSP) under Multi -processing mode The genetic algorithm of excellent scheme.Firstly, making MRCPSP by original by converting a target to be optimized for non-renewable resources constraint The single-object problem come is converted into a biobjective scheduling problem；And then it is completed by cluster algorithm to side to be evaluated The distribution of case fitness value.Significantly change although the method for solving before the method comparison that Long and Elloumi are taken has Into, but still have the decision variable of redundancy during their model solution.

Summary of the invention

It is identified project the technology of shortest limit time the object of the present invention is to provide a kind of using potential anti-critical process, it should Technology can identify all potential anti-critical processes in advance, and subsequent calculating also only need to be around potential anti-critical process exhibition It opens, so that eliminating those not is a large amount of processes of potential anti-critical process.It completes finally by genetic algorithm to entire project The optimizing of shortest limit time.

To achieve the goals above, technical solution key step proposed by the present invention includes:

Step 1: to the process A of project_iIt is divided, the process for meeting potential anti-critical process decision condition is put into latent In anti-critical process set X, the process for being unsatisfactory for potential anti-critical process decision condition is put into anti-critical process non-potential In set Y；

Wherein, A_iFor i-th of process of project, i=1,2 ..., M；

M is the quantity of project process；

Step 2: the execution pattern of all process steps in potential anti-critical process set X being encoded, generates initial kind Group, Population Size N_P, most fast execution pattern is then used to all process steps in anti-critical process set Y non-potential；

Step 3: calculating the corresponding chief engineer's time value of individual in population using dispatching algorithm, convert the inverse of total construction period to a The fitness value of body；Then at the beginning of adjusting non-key process using adjustment algorithm, to minimize the sum of break time And the number that interruption occurs；

Step 4: using roulette selection parent, and filial generation, son are generated by single point crossing operator and single-point mutation operator The number in generation is N_P；

Step 5: merging parent and filial generation by fitness value, form new population, new Population Size is still N_P；If at this time Reach maximum genetic algebra, then stop calculating and exports optimal solution；Otherwise, return step 3.

The potential anti-critical process decision condition are as follows:

If (a) process A_iThe continuity that do not work requires, then process A_iExist with precedence activities and starts-terminate SF or knot Beam-end FF type dominance relation constraint, and exist with successor activities and start-terminate SF or beginning-beginning SS type dominance relation Constraint；

If (b) process A_iThere is no beginning-end SF or end-end FF type dominance relation to constrain with precedence activities, Or there is no beginning-end SF or beginning-beginning SS type dominance relation to constrain with successor activities, and process A_iMeet work company Continuous property requirement.

It includes following sub-step that the use dispatching algorithm, which calculates the corresponding chief engineer's time value of individual in population:

Sub-step A1: sub- process a is calculated_i,jDuration D_i,j；Wherein, a_i,jFor process A_iIn j-th of sub- process, j=1, 2 ... N, N are the quantity of process；

Sub-step A2: sub- process a is calculated_i,jAt the beginning of S_i,jWith end time F_i,j, specifically:

(a) as process A_iWith its precedence activities A_hMeet dominance relation SS_h,i=β_h,iWhen:

In process A_iIt does not require in 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；

In process A_iIt is required that in the successional situation of work, F_i,j=S_i,j+D_i,j,

(b) as process A_iWith its precedence activities A_hMeet dominance relation SF_h,i=β_h,iWhen:

In process A_iIt does not require in 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；

In process A_iIt is required that in the continuous situation of work, F_i,j=S_i,j+D_i,j,

(c) as process A_iWith its precedence activities A_hMeet dominance relation FS_h,i=β_h,iWhen:

In process A_iIt does not require in 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；

(d) as process A_iWith its precedence activities A_hMeet dominance relation FF_h,i=β_h,iWhen:

In process A_iIt does not require in 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；

Wherein, β_h,iFor process A_iWith its precedence activities A_hCrucial constraint；

SS_h,iRepresent process A_iWith its precedence activities A_hBetween for beginning-beginning SS type dominance relation constraint；

SF_h,iRepresent process A_iWith its precedence activities A_hBetween for beginning-end SF type dominance relation constraint；

FS_h,iRepresent process A_iWith its precedence activities A_hBetween for end-beginning FS type dominance relation constraint；

FF_h,iRepresent process A_iWith its precedence activities A_hBetween for end-end FF type dominance relation constraint；

Sub-step A3: according to formulaCalculate total construction period.

The sum of described minimum break time includes following sub-step:

Sub-step B1: enabling i=M, M is the quantity of project process；

Sub-step B2: if process A_iIt is not require the successional process of work, then executes sub-step B3；Otherwise, i=is enabled I-1 executes sub-step B6；

Sub-step B3: enabling j=N-1, N is the quantity of sub- process；

Sub-step B4: as process A_iWith its successor activities A_tMeet dominance relation SS_i,t=β_i,tWhen, enable 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 process A_iWith its successor activities A_tMeet dominance relation SF_i,t=β_i,tWhen, enable 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 process A_iWith its successor activities A_tMeet FS_i,t=β_i,tWhen, enable F_i,j=min (S_t,j-β_i,t,S_i,j+1), S_i,j= F_i,j-D_i,j；

As process A_iWith its successor activities A_tMeet FF_i,t=β_i,tWhen, enable 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 process A_iWith successor activities A_tCrucial constraint；

SS_i,tRepresent process A_iWith its successor activities A_tBetween for beginning-beginning SS type dominance relation constraint；

SF_i,tRepresent process A_iWith its successor activities A_tBetween for beginning-end SF type dominance relation constraint；

FS_i,tRepresent process A_iWith its successor activities A_tBetween for end-beginning FS type dominance relation constraint；

FF_i,tRepresent process A_iWith its successor activities A_tBetween for end-end FF type dominance relation constraint；

Sub-step B5: enabling j=j-1, if j >=1, returns to sub-step B4；If j < 1, sub-step B6 is executed；

Sub-step B6: if i >=1, sub-step B2 is returned to；If i < 1 terminates.

The number for minimizing interruption appearance includes following sub-step:

Sub-step C1: i=1 is enabled；

Sub-step C2: if process A_iIt is not require the successional process of work, then executes sub-step C3；Otherwise, i=is enabled I-1 executes sub-step C6；

Sub-step C3: j=2 is enabled；

Sub-step C4: as process A_iWith its precedence activities A_hMeet dominance relation SS_h,i=β_h,iWhen, enable S_i,j=max (S_h,j+ β_h,i,F_i,j-1), F_i,j=S_i,j+D_i,j；

As process A_iWith its precedence activities A_hMeet dominance relation SF_h,i=β_h,iWhen, enable 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 process A_iWith its precedence activities A_hMeet dominance relation FS_h,i=β_h,iWhen, enable S_i,j=max (F_h,j+β_h,i, F_i,j-1), F_i,j=S_i,j+D_i,j；

As process A_iWith its precedence activities A_hMeet dominance relation FF_h,i=β_h,iWhen, enable 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；

Sub-step C5: enabling j=j+1, if j≤N, returns to sub-step C4；If j > N, sub-step C6 is executed；

Sub-step C6: if i≤M, sub-step C2 is returned to；If i > M terminates.

The beneficial effects of the present invention are: firstly, by the elasticity theory of all types of critical processes, only by potential anti-pass The execution pattern of key process is as variable, and other process is not re-used as variable, greatly reduces the variable of process execution pattern Number, potential anti-critical process is fewer, then this algorithm is just more obvious the simplification of solution procedure；Second, by adjusting algorithm, certainly At the beginning of dynamic determining each process, to automatically determine the break time between each process, become break time also no longer Variable reduces variable number compared with existing algorithm, and the unit number of project is more, simplifies effect and is more obvious.

Detailed description of the invention

Fig. 1 is Project duration schematic diagram；

Fig. 2 is the process corresponding relationship in RSM in process and GPRs network；

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

Fig. 4 is process A_iWork continuity schematic diagram is not required；

Fig. 5 is process A_iIt is required that 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 is (b) methods and results curve graph provided by the invention.

Specific embodiment

With reference to the accompanying drawing, it elaborates to preferred embodiment.It is emphasized that following the description is only exemplary , the range and its application being not intended to be limiting of the invention.

Embodiment 1

Below with reference to example, invention is further explained.Embodiment 1 is illustrated the principle of the present invention.

Assuming that a repeated project is made of M process, each process will repeat in N number of unit.Process A_i (i=1 ..., M) possess ΩⁱExecution pattern is planted, wherein the working efficiency of kth kind execution pattern isIt is assumed that process A_i(i= 1 ..., M) it requires to keep the constraint of resource constancy, then as process A_iAfter selecting a kind of execution pattern, it must just be held with this Row mode works until the process terminates.With a_i,jIndicate process A_iSub- process in j-th of unit, Q_i,jIndicate corresponding Workload, then sub- process a_i,jDuration D_i,jIt can be obtained by formula (1).

For 0-1 variable,Indicate process A_iKth kind execution pattern has been selected, has otherwise meaned not to be selected.For Meet the constant requirement of resource,It must satisfy formula (2).

Respectively with C_SS、C_SF、C_FSAnd C_FFIndicate the process set for meeting corresponding dominance relation constraint, for example, if (i, j, β_i,j)∈C_SS, then it represents that process A_iAs process A_jPrecedence activities, with A_jThere are time-constrain SS_i,j=β_i,j.Enable S_i,jAnd F_i,j Respectively indicate process a_i,jAt the beginning of and the end time, then repeated project shortest limit time problem can be described as with work Sequence A_iExecution patternWith process a_i,jTime started S_i,jFor the following planning problem P of variable:

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)

Wherein, formula (3) is the objective function of planning problem P, that is, minimizes repeated Project duration.In formula (4), set All process steps are required to keep work continuity constraint in W, and essence is in sub- process a_i,jAnd a_i,j+1Between apply minimum simultaneously Time-constrain FS=0 and maximum time constrain FS=0, i.e., sub- process a_i,jAfter 0 day, sub- process a_i,j+1It could start, simultaneously Sub- process a_i,jAfter at most 0 day, sub- process a_i,j+1It must start.In formula (5), setMiddle all process steps do not require work Make continuity constraint, that is, is equivalent to sub- process a_i,jAnd a_i,j+1Between only exist minimum time constraint FS=0.Formula (6) is to formula (9) Guarantee that all processes meet given dominance relation, β_i,tFor corresponding to process A_iAnd A_tBetween dominance relation amount of restraint, this It invents discussed dominance relation constraint and belongs to minimum time constraint.Formula (10) requires under the premise of acquiring most short total construction period, So that sub- process a_i,jWith sub- processBetween break time summation it is minimum, ES_i,jIndicate work Sequence a_i,jEarliest start time.

In critical path method (CPM) network, the length of critical path determines the total construction period of project, includes on critical path The crucial constraint of two critical processes of critical process and connection.Similar, in repeated schedule item (RSM), project chief engineer Phase is determined by the length of critical path, includes the crucial constraint of two critical processes of critical process and connection on critical path. Critical path is indicated with Pc, then R={ R_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_FFIndicate the set that all dominance relations constrain.Then Project duration_TpIt may be expressed as:

Crucial constraint beta_i,tIt is by engineering project defined itself, not by process a_i,jProcess patterns affect.If work Sequence a_i,jIt is positive critical process, then D_i,jTake positive sign；, whereas if process a_i,jIt is anti-critical process, then D_i,jTake negative sign.For point Critical process, D_i,jTake 0.Such as shown in Fig. 1, the dominance relation between process isWithAnd process A₁、A₃And A₄It is required that work continuity, heavy black line indicates critical path in Fig. 1, then chief engineer Phase T_PIt can indicate are as follows:

By formula (11) it is found that the total construction period of project is determined by the amount of restraint of critical process duration and crucial constraint, for same For one project, the amount of restraint of key constraint, which is equal to, determines value, therefore only needs to pay close attention to the variation of critical process duration to total construction period Influence.

In order to acquire shortest limit time, under the conditions of existing resource, considered first by all process steps all in accordance with possible most fast Execution pattern arrangement, and all process steps start in earliest start time, thus obtain an initial schedule scheme, it is clear that this is One feasible solution of former problem.In initial schedule scheme, since all critical processes have all been most fast execution patterns, because This can not make total construction period shorter by improving its working efficiency.If anti-critical process is not present on critical path at this time, then The total construction period acquired at this time is most short total construction period, if there are anti-critical processes on critical path, by formula (11) it is found that passing through Slower execution pattern is selected to extend the duration of positive critical process, point critical process or non-key process, will not all be made total Duration is reduced, and the duration of anti-critical process, can just be such that total construction period shortens only in extension initial scheme.The work of the anti-critical process After phase is extended, new anti-critical process may be generated, needs to carry out a new wheel optimization at this time, until there is no anti-crucial Process or until further cannot shortening total construction period by extending the duration of anti-critical process.In this change procedure, quilt What is adjusted is the process that those are possible to generate anti-critical process always, that is, meets necessary condition existing for anti-critical process, this Invention is defined as potential anti-critical process.It is noted that the solution obtained by the above process be not be optimal solution because it Meet under the premise of shortest limit time there is no minimizing the sum of break time, for this purpose, the present invention is by Long and Ohsato (2009) The forwards algorithms and backward algorithm designed under end-beginning FS dominance relation constraint are generalized to whole four kinds of dominance relations about Beam starts-starts SS, beginning-end SF, end-beginning FS and end-end FF, with reach minimize break time it The purpose of sum.

In conclusion the general thought for solving project shortest limit time problem is to find out potential anti-key all in project Process using its execution pattern as variable, and then uses most fast execution pattern to other processes, the calculation designed through the invention Method quickly acquires the optimal execution mode of each process and the optimal time started of process, so that corresponding total construction period and break time The sum of minimum.

In RSM, process A_i(i=1 ..., M) is decision condition (or the process A of potential anti-critical process_iIt is middle to exist instead The necessary condition of critical process) are as follows:

Condition (1) if, process A_iThe continuity that do not work requires, then process A_iThere are SF or FF type is preferential with precedence activities Relation constraint, and there are the constraints of SF or SS type dominance relation with successor activities.

Condition (2) if, process A_iThere is no the constraints of SF or FF type dominance relation with precedence activities, or do not deposit with successor activities It is constrained in SF or SS type dominance relation, then process 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 with ordinary priority relationship (GPRs) network corresponding, i.e., converted RSM to Network.The method for transformation of RSM and network model is that any one RSM scheduling scheme can be converted into GPRs network, and Critical path, critical process in RSM and the critical path in GPRs, critical process correspond.Any process a in RSM_i,j A process in corresponding GPRs network is indicated, as shown in Figure 2 with two real arrows contrary, that flexible strategy are opposite.Wherein, D_i,jIndicate process a_i,jDuration.The left end of arrow with positive flexible strategy value is process a_i,jStarting point, right end be process a_i,j End point.If there are minimum time constraints for two processes, obligatory point and another work in a process are connected with arrow Restrained point in sequence, and arrow is directed toward restrained point, and the flexible strategy of arrow are the amount of restraint of minimum time constraint；If two works There are maximum time constraints for sequence, equally use arrow connection constraints point and restrained point, but arrow directing constraint point at this time, arrow Flexible strategy are the opposite number of amount of restraint.Process A is separately connected with two virtual source nodes (s) and sink nodes (w)_iMiddle all process steps Starting point and process A_MThe end point of middle all process steps, in this way, RSM is with regard to equivalent conversion GPRs network.Such as Fig. 1 middle term Purpose RSM figure is converted into after GPRs network as shown in figure 3, black thick line indicates critical path.Critical path in Fig. 1 is corresponding Critical path in Fig. 3, critical process correspond the critical process in Fig. 3.

In GPRs network, process a_i,jNecessary condition as anti-critical process is there are one from source point (s) to remittance The route (elementary path) of point (w), so that process a_i,jNegative flexible strategy arrow be located on the route.

Critical path is the longest route for connecting source point (s) and meeting point (w), and the characteristics of anti-critical process is that the duration is longer Total construction period is shorter, i.e., the negative flexible strategy arrow of anti-critical process is located on critical path.So, any one process is wanted to become anti- The necessary condition of critical process is: the negative flexible strategy arrow of the process will be located on a route from source point (s) to meeting point (w).

First card condition (1) is set up.In RSM, the constraint of any process is both from two aspects: 1) adjacent in the same process The minimum and maximum time-constrain generated due to there are the requirement of work continuity between process, or because being wanted there is no work continuity The minimum time constraint asked and generated.2) when the minimum generated between two processes with dominance relation constraint in same unit Between constrain；In the corresponding GPRs network of RSM, it is assumed that process A_iIn process a_i,jFor anti-critical process, then should in GPRs The negative flexible strategy arrow one of process is positioned on critical path.Again due to process A_iWork continuity is not required, then process a_i,jWith a_i,j+1Minimum time constraint FS=0 is only existed between (j=1 ..., N-1), but these constraints can not make process a_i,jIt is negative Flexible strategy arrow is located on any route (elementary path) from source point (s) to meeting point (w), as shown in Figure 4.Therefore, process a_i,jIt can only make its negative power by the minimum time constraint generated between two processes with dominance relation constraint in same unit Number arrow is located on critical path, this allows for process A_iCentainly by with its precedence activities A_kDominance relation effect of contraction its knot Beam spot, and by with its successor activities A_iDominance relation effect of contraction its starting point, i.e., with precedence activities A_kThere are SF or FF type is excellent First relation constraint, with successor activities A_iThere are the constraints of SF or SS type dominance relation.

Condition (2) establishment is demonstrate,proved again.Assuming that process A_iIn process a_i,jFor anti-critical process, then in GPRs network The negative flexible strategy arrow one of the process is positioned on critical path.Process A again_iSF or FF type dominance relation is not present with precedence activities Constraint, or there is no the constraints of SF or SS type dominance relation with successor activities, then process A_iWith precedence activities A_kWith successor activities A_t Dominance relation constrained type can be divided into three classes: 1) with precedence activities A_kThere are the constraints of FS or SS type dominance relation, and with next work Sequence A_tThere are the constraints of FS or FF type dominance relation；2) with precedence activities A_kThere are the constraints of FS or SS type dominance relation, and with next work Sequence A_tThere are the constraints of SF or SS type dominance relation；3) with precedence activities A_kThere are the constraints of SF or FF type dominance relation, and with next work Sequence A_tThere are the constraints of FS or FF type dominance relation.But these three types of situations can not make process a_i,jNegative flexible strategy arrow be located at On any route (elementary path) from source point to meeting point, wherein the first kind is as shown in Figure 5.Therefore, process a_i,jIt can only be according to Constraint is located at its negative flexible strategy arrow on critical path between adjacent process in the same process, then process A_iIn adjacent process Between require there are maximum time constrain FS=0, it is meant that process A_iMeet the requirement of work continuity.

The decision condition of above-mentioned potential anti-critical process is set up as a result,.

According to above-mentioned analysis it is found that being included the following steps: using the identify project method of shortest limit time of anti-critical process

Step 1: to the process A of project_iIt is divided, the process for meeting potential anti-critical process decision condition is put into latent In anti-critical process set X, the process for being unsatisfactory for potential anti-critical process decision condition is put into anti-critical process non-potential In set Y.

Step 2: the execution pattern of all process steps in potential anti-critical process set X being encoded, generates initial kind Group, Population Size N_P, most fast execution pattern is then used to all process steps in anti-critical process set Y non-potential.

Step 3: calculating the corresponding chief engineer's time value of individual in population using dispatching algorithm, convert the inverse of total construction period to a The fitness value of body；Then at the beginning of adjusting non-key process using adjustment algorithm, to minimize the sum of break time And the number that interruption occurs.

In above-mentioned steps 3, calculating the corresponding chief engineer's time value of individual in population using dispatching algorithm includes following sub-step:

Sub-step A1: calculation process a_i,jDuration D_i,j；Wherein, a_i,jFor process A_iIn j-th of process, j=1, 2 ... N, N are the quantity of process.

Sub-step A2: calculation process a_i,jAt the beginning of S_i,jWith end time F_i,j, specifically:

In process A_iIt does not require in 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。

In process A_iIt does not require in 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。

In process A_iIt does not require in 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。

In process A_iIt does not require in 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。

Wherein, β_h,iFor process A_iWith its precedence activities A_hCrucial constraint.

SS_h,iRepresent process A_iWith its precedence activities A_hBetween for beginning-beginning SS type dominance relation constraint.

SF_h,iRepresent process A_iWith its precedence activities A_hBetween for beginning-end SF type dominance relation constraint.

FS_h,iRepresent process A_iWith its precedence activities A_hBetween for end-beginning FS type dominance relation constraint.

FF_h,iRepresent process A_iWith its precedence activities A_hBetween for end-end FF type dominance relation constraint.

Sub-step A3: according to formulaCalculate total construction period.

It include two stages, first rank at the beginning of adjusting non-key process using adjustment algorithm in above-mentioned steps 3 Section is used to minimize the number that interruption occurs for minimizing the sum of break time, second stage.

The target of first stage is to minimize the break time of the scheduling scheme after dispatching algorithm calculates, therefore only right It does not require the successional process of work to be adjusted, is kept for the total construction period of the scheduling scheme constant during adjustment.From last A process A_MStart successively to find forward not requiring the successional process A of work_i, and according to process A_iWith its successor activities A_t's Dominance relation is constrained to process A_iTime parameter be adjusted, its essence is fixed step A_iWork in the last one unit Sequence a_i,N, and allow process A_iIn remaining process start in late start time.Its detailed process includes:

Sub-step B1: enabling i=M, M is the quantity of project process.

Sub-step B2: if process A_iIt is not require the successional process of work, then executes sub-step B3；Otherwise, i=is enabled I-1 executes sub-step B6.

Sub-step B3: enabling j=N-1, N is the quantity of process.

Sub-step B4: as process A_iWith its successor activities A_tMeet dominance relation SS_i,t=β_i,tWhen, enable 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 process A_iWith its successor activities A_tMeet dominance relation SF_i,t=β_i,tWhen, enable 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 process A_iWith its successor activities A_tMeet FS_i,t=β_i,tWhen, enable F_i,j=min (S_t,j-β_i,t,S_i,j+1), S_i,j= F_i,j-D_i,j。

As process A_iWith its successor activities A_tMeet FF_i,t=β_i,tWhen, enable 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 process A_iWith successor activities A_tCrucial constraint.

SS_i,tRepresent process A_iWith its successor activities A_tBetween for beginning-beginning SS type dominance relation constraint.

SF_i,tRepresent process A_iWith its successor activities A_tBetween for beginning-end SF type dominance relation constraint.

FS_i,tRepresent process A_iWith its successor activities A_tBetween for end-beginning FS type dominance relation constraint.

FF_i,tRepresent process A_iWith its successor activities A_tBetween for end-end FF type dominance relation constraint.

Sub-step B5: enabling j=j-1, if j >=1, returns to sub-step B4；If j < 1, sub-step B6 is executed.

Sub-step B6: if i >=1, sub-step B2 is returned to；If i < 1 terminates.

Code is realized are as follows:

Second stage in the first stage on the basis of minimize interruption occur number, scheduling scheme is total during adjustment Duration and break time summation remain unchanged.From first process A₁Start successively to find backward not requiring work successional Process A_i, and according to process A_iWith its precedence activities A_kDominance relation constrain to process A_iTime parameter be adjusted, in fact Matter is fixed step A_iProcess a in first unit_i,1, and allow process A_iIn remaining process start in earliest start time. Specific calculating process is as follows:

Sub-step C1: i=1 is enabled.

Sub-step C2: if process A_iIt is not require the successional process of work, then executes sub-step C3；Otherwise, i=is enabled I-1 executes sub-step C6.

Sub-step C3: j=2 is enabled.

Sub-step C4: as process A_iWith its precedence activities A_hMeet dominance relation SS_h,i=β_h,iWhen, enable S_i,j=max (S_h,j+ β_h,i,F_i,j-1), F_i,j=S_i,j+D_i,j。

As process A_iWith its precedence activities A_hMeet dominance relation SF_h,i=β_h,iWhen, enable 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 process A_iWith its precedence activities A_hMeet dominance relation FS_h,i=β_h,iWhen, enable S_i,j=max (F_h,j+β_h,i, F_i,j-1), F_i,j=S_i,j+D_i,j。

As process A_iWith its precedence activities A_hMeet dominance relation FF_h,i=β_h,iWhen, enable 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。

Sub-step C5: enabling j=j+1, if j≤N, returns to sub-step C4；If j > N, sub-step C6 is executed.

Sub-step C6: if i≤M, sub-step C2 is returned to；If i > M terminates.

Code is accomplished by

Embodiment 2

Below with reference to a specific example, effect of the invention is illustrated.As shown in fig. 6, Fig. 6 gives one Repeated project, includes 11 processes and 5 units, the continuity of process requires, dominance relation constrained type and amount of restraint, can The engineering informations such as the execution pattern of energy are shown in Fig. 6, seek a scheduling scheme and make the total construction period of the project most short, and is corresponding Break time summation is also minimum.

According to algorithm steps, first according to the dominance relation constrained type and work continuity requirement division collection between process Close X and Y.Process A₃、A₇、A₈And A₁₀Since there are the decision condition that work continuity required and met potential anti-critical process, work Sequence A₅Do not require work continuity, but with precedence activities A₄In the presence of terminate-terminate FF type dominance relation constraint, and with next work Sequence A₆In the presence of starting-starting the constraint of SS type dominance relation, so A₅Also meet the decision condition of potential anti-critical process, remaining work Necessary condition is not satisfied in sequence, so set X={ A₃,A₅,A₇,A₈,A₁₀, and set Y={ A₁,A₂,A₄,A₆,A₉,A₁₁}.So Afterwards with process A₃、A₅、A₇、A₈And A₁₀Execution pattern be that variable carries out subsequent calculating.The optimal scheduling that algorithm acquires such as Fig. 7 It is shown, the shortest limit time acquired be 31.4 days, corresponding break time and be 4.4 days.

If the break time between the execution pattern and process of all process steps is known as generality as the algorithm of variable Solution is shown in Fig. 8 then being compared with the result that general solution and method of the invention solve example respectively.It can from Fig. 8 Out, under the premise of genetic algorithm parameter setting is identical, the time needed for method provided by the invention converges to optimal solution Only 0.27s, convergence times were the 10th generation；And the time needed for general solution converges to optimal solution is 10.48s, restrains generation Number was the 395th generation.Fig. 8 shows that method provided by the invention is substantially better than general solution, in large-scale project, with non- The increase of potential anti-critical process and unit number, this superiority will be apparent from.

According to anti-critical process, reversely increased characteristic, repeated project shortest limit time problem be can be regarded as with total construction period The process of Time Optimization is carried out using anti-critical process.The present invention has studied necessary condition existing for anti-critical process, and with this Based on find out potential anti-critical process all in repeated project, using its execution pattern as decision variable, and to other Process then can find out corresponding shortest limit time using most fast execution pattern.In instance analysis, the high efficiency of calculating is able to It embodies.

Method provided by the invention reduces variable number in terms of two.Firstly, by the spy of all types of critical processes Property it is theoretical, only using the execution pattern of potential anti-critical process as variable, and other process is not re-used as variable, greatly reduces The variable number of process execution pattern.The simplification of this process is related with the number of potential anti-critical process.Potential anti-key Process is fewer, then the present invention is just more obvious the simplification of solution procedure.Second, by adjusting algorithm, automatically determine each process Time started makes break time also no longer become variable, with existing algorithm to automatically determine the break time between each process It compares, reduces variable number.The unit number of project is more, and simplification is more obvious.

The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto, In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art, It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of protection of the claims Subject to.

Claims

1. a kind of identified project the method for shortest limit time using potential anti-critical process, it is characterized in that the described method includes:

Step 1: to the process A of project_iIt is divided, the process for meeting potential anti-critical process decision condition is put into potential anti- In critical process set X, the process for being unsatisfactory for potential anti-critical process decision condition is put into anti-critical process set Y non-potential In；

Wherein, A_iFor i-th of process of project, i=1,2 ..., M；

M is the quantity of project process；

Step 2: the execution pattern of all process steps in potential anti-critical process set X being encoded, initial population, kind are generated Group's size is N_P, most fast execution pattern is then used to all process steps in anti-critical process set Y non-potential；

Step 3: calculating the corresponding chief engineer's time value of individual in population using dispatching algorithm, convert individual for the inverse of total construction period Fitness value；Then at the beginning of adjusting non-key process using adjustment algorithm, to minimize the sum of break time and It is interrupted the number occurred；

Step 4: roulette selection parent is used, and filial generation is generated by single point crossing operator and single-point mutation operator, filial generation Number is N_P；

Step 5: merging parent and filial generation by fitness value, form new population, new Population Size is still N_P；If reaching at this time Maximum genetic algebra then stops calculating and exports optimal solution；Otherwise, return step 3；

The potential anti-critical process decision condition are as follows:

(1) if process A_iThe continuity that do not work requires, then process A_iExist with precedence activities and starts-terminate SF or end-knot The constraint of beam FF type dominance relation, and exist with successor activities and start-terminate SF or beginning-beginning SS type dominance relation constraint；

(2) if process A_iThere is no beginning-end SF or end-end FF type dominance relation to constrain with precedence activities, Huo Zheyu There is no beginning-end SF or beginning-beginning SS type dominance relation to constrain for successor activities, and process A_iMeet work continuity to want It asks；

It is described to calculate the corresponding chief engineer's time value of individual in population, including following sub-step using dispatching algorithm:

Sub-step A1: sub- process a is calculated_i,jDuration D_i,j；Wherein, a_i,jFor process A_iIn j-th of sub- process, j=1,2, ... N, N are the quantity of sub- process；

In process A_iIt does not require in 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；

In process A_iIt is required that in the successional situation of work,F_i,j=S_i,j+D_i,j,

In process A_iIt does not require in 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；

In process A_iIt is required that in the continuous situation of work,F_i,j=S_i,j+D_i,j,

In process A_iIt does not require in 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；

In process A_iIt does not require in 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；

Sub-step A3: according to formulaCalculate total construction period；

The sum of described minimum break time, including following sub-step:

Sub-step B1: enabling i=M, M is the quantity of project process；

Sub-step B2: if process A_iIt is not require the successional process of work, then executes sub-step B3；Otherwise, i=i-1 is enabled, Execute sub-step B6；

Sub-step B3: enabling j=N-1, N is the quantity of sub- process；

Sub-step B4: as process A_iWith its successor activities A_tMeet dominance relation SS_i,t=β_i,tWhen, enable 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 process A_iWith its successor activities A_tMeet dominance relation SF_i,t=β_i,tWhen, it enables

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 process A_iWith its successor activities A_tMeet FS_i,t=β_i,tWhen, it enables

F_i,j=min (S_t,j-β_i,t,S_i,j+1), S_i,j=F_i,j-D_i,j；

As process A_iWith its successor activities A_tMeet FF_i,t=β_i,tWhen, it enables

F_i,j=min (F_t,j-β_i,t,S_i,j+1), S_i,j=F_i,j-D_i,j；

Sub-step B5: enabling j=j-1, if j >=1, returns to sub-step B4；If j < 1 executes sub-step B6；

Sub-step B6: if i >=1, sub-step B2 is returned to；If i < 1, terminates；

The number for minimizing interruption and occurring, including following sub-step:

Sub-step C1: i=1 is enabled；

Sub-step C2: if process A_iIt is not require the successional process of work, then executes sub-step C3；Otherwise, i=i-1 is enabled, Execute sub-step C6；

Sub-step C3: j=2 is enabled；

Sub-step C4: as process A_iWith its precedence activities A_hMeet dominance relation SS_h,i=β_h,iWhen, it enables

S_i,j=max (S_h,j+β_h,i,F_i,j-1), F_i,j=S_i,j+D_i,j；

As process A_iWith its precedence activities A_hMeet dominance relation SF_h,i=β_h,iWhen, it enables

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 process A_iWith its precedence activities A_hMeet dominance relation FS_h,i=β_h,iWhen, it enables

S_i,j=max (F_h,j+β_h,i,F_i,j-1), F_i,j=S_i,j+D_i,j；

As process A_iWith its precedence activities A_hMeet dominance relation FF_h,i=β_h,iWhen, it enables

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 process A_iWith its precedence activities A_hControl constraints；

Sub-step C5: enabling j=j+1, if j≤N, returns to sub-step C4；If j > N, executes sub-step C6；

Sub-step C6: if i≤M, sub-step C2 is returned to；If i > M, terminates.