CN104217293A - Effective method for solving multi-target resource-constrained project scheduling - Google Patents

Abstract

The invention discloses an effective method for solving multi-target resource-constrained project scheduling. The method comprises the following steps: (1) establishing a multi-target resource-constrained project scheduling mathematical model based on duration-cost optimization; (2) generating an initial feasible scheduling sequence; (3) evaluating the scheduling sequence; (4) updating the scheduling sequence; (5) configuring non-dominated disaggregation operation; (6) maintaining an external archive set; and (7) performing updating iteration till an optimal solution set is output. According to the method disclosed by the invention, each intelligent body corresponds to a linked list sequence in a scheduling problem, the scheduling sequence of a task linked list and a corresponding execution mode sequence are coded respectively, decoding operation is performed by adopting a serial method, and evolution and update are performed among the linked list sequences through competition, intersection and self-learning; and a project scheduling plan is adjusted, so that comprehensive optimal duration and cost are realized within a control period on the premise of satisfying conditions such as timing constraint and resource constraint.

Description

A kind of effective ways that solve multiple goal Resource-constrained Project Scheduling Problem

Technical field

The invention belongs to system call and control technology field, relate to a kind of effective ways that solve multiple goal Resource-constrained Project Scheduling Problem.

Background technology

Resource constrained project scheduling problem is widely used in the scheduling fields such as construction work, communications and transportation, software development, production, electric system, its difficult point is to meet under the prerequisite of temporal constraint and resource constraint, according to the task of certain regular reasonable arrangement project, and in the implementation of project, include multiple patterns, require between multiple conflicting targets, to weigh in cost resource optimal utilization, find the optimal balance point between each target, be met one group of optimal solution set of project demand.Therefore consider the research of the multiple goal Resource-constrained Project Scheduling Problem of project duration and project cost, not only have important theory significance, and be the most real selection of scheduling problem, therefore formulating rational operation plan is the emphasis of studying at present.

Multi-Agent evolutionary Algorithm is as a branch of intelligent optimization algorithm, it is the angle from multiagent system, individuality in evolution algorithm is used as to an intelligent body that has local sensing, competition cooperation and self-learning capability, reaches and optimize overall object by the interaction between intelligent body self and intelligent body.Due to independence, distributivity, harmony and self organization ability, learning ability and the inferential capability of multiple agent, make it in the time of solving practical problems, there is stronger reliability and higher solution efficiency, but multi-Agent evolutionary Algorithm is used for greatly single goal aspect at present.

Summary of the invention

The object of this invention is to provide a kind of effective ways that solve multiple goal Resource-constrained Project Scheduling Problem, solved existing dispatching method and in scheduling, between the limit for a project and the cost, be difficult to regulate, be difficult for obtaining the problem of optimum efficiency.

The technical solution adopted in the present invention is: a kind of effective ways that solve multiple goal Resource-constrained Project Scheduling Problem, implement according to following steps:

Step 1, the multiple goal Resource-constrained Project Scheduling Problem mathematical model of foundation based on time-cost trade-off

Suppose that the work number in project is J, the temporal constraint before and after having between each work j, has j=1, and 2 ..., J, note Q _jthe j set before of and then working, H _jit is the j set afterwards of and then working; Set maximum iteration time H, iterations initial value h=1, work 1 is unique work of early start, work J is the unique work completing the latest; In project, renewable resources species number is K, and unrenewable resource species number is N, k=1, and 2 ... K, n=1,2 ... N, k kind renewable resources in the aggregate supply in each stage is , n kind unrenewable resource total amount is ; Each work has various modes available, and work j need select M _jone of the pattern of kind operates, and can not interrupt or change in operational process; When work j moves under m kind pattern, m=1,2 ... M _j, the demand of k kind renewable resources is , the demand of n kind unrenewable resource is , be d working time _jm, the work resource sum used moving can not exceed the aggregate supply of resource, above each value round numbers,

Model of creation is as follows accordingly:

$\begin{array}{cc}\min & f_J=\underset{t={\mathrm{ED}}_J}{\overset{{\mathrm{LD}}_J}{\mathrm{\Σ}}}t\·x_{J1T};\end{array}---\left(1\right)$

One of formula (1) is target, and this target is the expression formula that minimizes Project duration, [ED in formula _j, LD _j] for work J the earliest with Late Finish section; T represents t stage, x _j1Tthe completion status in T stage that is work j under the first pattern, if complete x _j1T=1, otherwise x _j1T=0;

$\begin{array}{cc}\min & c_J=\underset{j=1}{\overset{J}{\mathrm{\Σ}}}\underset{m=1}{\overset{M_j}{\mathrm{\Σ}}}{c}_{\mathrm{jm}};\end{array}---\left(2\right)$

Formula (2) is target two, and this target is the expression formula that minimizes project cost, M in formula _jwhat represent is the execution pattern number of work j; c _jmthe cost of work j under mode m; J is all working number of project;

$\begin{array}{cc}s.t.& \underset{m=1}{\overset{M_j}{\mathrm{\Σ}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\Σ}}}{x}_{\mathrm{jmt}}=1,j=\mathrm{1,2},...,J;\end{array}---\left(3\right)$

Formula (3) represents that each work can only realize once in one mode, x in formula _jmtwhat represent is the state that work j carried out in the m kind pattern t stage; [ED _j, LD _j] represent be work j the earliest with Late Finish section;

$\underset{m=1}{\overset{M_j}{\mathrm{\Σ}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\Σ}}}t\·x_{\mathrm{imt}}\≤\underset{m=1}{\overset{M_j}{\mathrm{\Σ}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\Σ}}}t\·x_{\mathrm{jmt}}-d_{\mathrm{jm}},j=\mathrm{1,2},...,J,i\∈Q_j;---\left(4\right)$

Formula (4) represents the tight front restriction relation of project, x _imtand x _jmtit is respectively work i and the work j executing state in the m kind pattern t stage; d _jmit is the execution time of work j under m kind pattern;

$\underset{j=1}{\overset{J}{\mathrm{\Σ}}}\underset{m=1}{\overset{M_j}{\mathrm{\Σ}}}{r}_{\mathrm{jmk}}^{\mathrm{\ρ}}\underset{q=\max \{t,{\mathrm{ED}}_j\}}{\overset{\min \{t+d_{\mathrm{jm}}-1,{\mathrm{LD}}_j\}}{\mathrm{\Σ}}}\≤R_k^{\mathrm{\ρ}},k=\mathrm{1,2},...,K,t=\mathrm{1,2},...\stackrel{\‾}{D};---\left(5\right)$

Formula (5) is inequality constrain, has ensured that the renewable resources amount of each work use is no more than the aggregate supply in this stage, be the demand of k kind renewable resources, be k kind renewable resources in the aggregate supply in each stage, for the duration upper limit;

$\underset{j=1}{\overset{J}{\mathrm{\Σ}}}\underset{m=1}{\overset{M_j}{\mathrm{\Σ}}}{r}_{\mathrm{jmn}}^v\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LF}}_j}{\mathrm{\Σ}}}{x}_{\mathrm{jmt}}\≤R_n^v,n=\mathrm{1,2},...N;---\left(6\right)$

Formula (6) is to ensure that the unrenewable resource amount that all working uses can not exceed the total quantity delivered of whole project, be the demand of n kind unrenewable resource, it is n kind unrenewable resource total amount;

x _jmt＝{0,1},j＝1,2,...,J,m＝1,2,...,M _j,t＝ED _j,...,LD _j； (7)

Formula (7) is the span of correlated variables in model, x _jmtthe completion status of expression work j under m kind pattern, has x if complete _jmt=1, otherwise x _jmt=0;

Step 2, produce initial feasible schedule sequence

Each work in project is made up of two parts, that is:

$\left[\begin{array}{c}{S}_i\\ M_i\end{array}\right]=\left[\begin{array}{c}{j}_1,j_2,...,j_J\\ m_1,m_2,...,m_J\end{array}\right],---\left(8\right)$

Wherein, S _i=j ₁, j ₂... j _j, S _ibeing the scheduling sequence that meets temporal constraint in i Task-list, is the execution sequence table of each work in project; M _i=m ₁, m ₂..., m _j, M _ibe the corresponding mode sequences of each task in this Task-list, the mode sequences in project is one to one with scheduling sequence, generates at random in the process of implementation the corresponding pattern M of S, and ensures that the pattern count generating is not more than the assemble mode number of this work,

Determined the preceding activity collection p of work j by temporal constraint _jwith tight rear working set s _j, use adjacency matrix G=[g _ij] _{j × J}represent the tight front tight rear relation of workplace, wherein as i ∈ P _jtime, g _i,j=1, otherwise g _i,j=0;

Initialization project scheduling sequence S and executed work sequence number s ₁=1, making Job is blank vector, k=1, the s of retrieve stored adjacency matrix _hoK, search in-degree and be 1 working set, add in Job sequence, from Job, delete a work sequence number u with highest priority, and this sequence number u is assigned to s _h+1, element a in adjacency matrix simultaneously _iu(i=s _h+1) subtract 1, make k=k+1, if k<J continues to calculate, otherwise output S;

Step 3, to scheduling sequence evaluate

The scheduling sequence S and the mode sequences M that generate according to project, carry out decode operation by serial scheme, makes T _stthe start time of expression project, T _i=t _i1, t _i2..., t _ij..., t _iJand C _i=c _i1, c _i2..., c _ij..., c _iJstart time and the cost of corresponding work in i the chained list that represents respectively to obtain through coding, judgement is operated under its execution pattern whether have resource contention, finds the t on earliest finish time of this chained list _iJ=max{t _ij+ d _jmand corresponding cost c _iJ=∑ c _jm;

Step 4, to scheduling sequence upgrade

Adopt multi-Agent evolutionary Algorithm to upgrade scheduling sequence, by with its neighborhood in work competition, intersect, three kinds of modes of operation of self study complete renewal;

Step 5, construct the operation of non-domination disaggregation;

Step 6, outside filing collection is safeguarded;

Step 7, renewal iterations h=h+1, if h < is J, continue repeating step 2 to step 6, otherwise output Pareto optimal solution set.

The invention has the beneficial effects as follows, utilize the data analysis to the resource-constrained project problem collecting, in conjunction with multi-Agent evolutionary Algorithm, realize solving resource constrained project scheduling problem.A chained list sequence in the corresponding scheduling problem of each intelligent body in algorithm, scheduling sequence to Task-list and execution pattern sequence are corresponding thereto encoded respectively, adopt serial approach to carry out decode operation, between each chained list sequence, realize and evolve and upgrade by operations such as competition, intersection, self studies.By the operation plan of adjusted iterm, under the condition that meets temporal constraint and resource constraint etc., the feasible schedule of the each work of reasonable arrangement day part, for the operation and control of dispatching system provides multiple feasible program, decision maker can therefrom determine final scheme according to different requirements, makes duration and cost in this control cycle reach comprehensive optimum.

The advantage of the inventive method specifically comprises:

1) J is counted in the work that pre-determines out project, renewable resources species number K, unrenewable resource species number N, sequential relationship between each work, the required number of resources of each work, and be provided with temporal constraint and resource constraint according to these preset values, the iteration for the first time of Shi Ge working group vector meets above-mentioned constraint condition, then from the iteration for the first time of each working group vector, carry out loop iteration h-1 time, it is iterative vectorized as global optimum that the final target function value of determining T the period of sening as an envoy to reaches optimum working group's vector, therefore the inventive method takes into full account that Liao Ge working group is in the different resource requirement of day part, the randomness of feasible schedule sequence, on this basis, realize continuing to optimize of project duration by h-1 vectorial iteration, finally obtain the optimal value of working group at day part project duration.

2) there is good global convergence performance and speed of convergence faster, use it for and solve project duration and project cost multiple goal resource constrained project scheduling problem, can effectively realize the scheduling real-time of project.

3) relation between allocate resource use amount and work schedule sufficiently and reasonably, is conducive to find fast optimal solution set.

4) optimum that can automatically obtain working group is allocated scheme, does not need people's participation in optimizing process, and this is conducive to reduce the impact of human factor on optimal speed, optimization quality, improves the gentle optimization quality of Automated water.

Embodiment

Below in conjunction with embodiment, the present invention is described in detail.

The target of the resource constrained project scheduling problem of time-cost trade-off to be solved by this invention is, under the prerequisite that meets work schedule constraint and resource constraint, generate feasible scheduling sequence and mode sequences, the duration of identifying project and corresponding cost, make project duration the shortest, integrated cost minimum.

The present invention solves the effective ways of multiple goal Resource-constrained Project Scheduling Problem, specifically implements according to following steps:

Step 1, the multiple goal Resource-constrained Project Scheduling Problem mathematical model of foundation based on time-cost trade-off

Suppose that the work number in project is J, the temporal constraint before and after having between each work j, has j=1, and 2 ..., J, note Q _jthe j set before of and then working, H _jit is the j set afterwards of and then working; Set maximum iteration time H (H is integer), iterations initial value h=1, work 1 is unique work of early start, work J is the unique work completing the latest, be dummy activity, consumption of natural resource not in the process of implementation, also holding time not; In project, renewable resources species number is K, and unrenewable resource species number is N, k=1, and 2 ... K, n=1,2 ... N, k kind renewable resources in the aggregate supply in each stage is , n kind unrenewable resource total amount is ; Each work has various modes available, and work j need select M _jone of the pattern of kind operates, and can not interrupt or change in operational process; When work j moves under m kind pattern, m=1,2 ... M _j, the demand of k kind renewable resources is , the demand of n kind unrenewable resource is , be d working time _jm, the work resource sum used moving can not exceed the aggregate supply of resource, above each value round numbers.

Model of creation is as follows accordingly:

$\begin{array}{cc}\min & f_J=\underset{t={\mathrm{ED}}_J}{\overset{{\mathrm{LD}}_J}{\mathrm{\&Sigma;}}}t\&CenterDot;x_{J1T};\end{array}---\left(1\right)$

One of formula (1) is target, and this target is the expression formula that minimizes Project duration, [ED in formula _j, LD _j] for work J the earliest with Late Finish section; T represents t stage, x _j1Tthe completion status in T stage that is work j under the first pattern, if complete x _j1T=1, otherwise x _j1T=0;

$\begin{array}{cc}\min & c_J=\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{c}_{\mathrm{jm}};\end{array}---\left(2\right)$

Formula (2) is target two, and this target is the expression formula that minimizes project cost, M in formula _jwhat represent is the execution pattern number of work j; c _jmthe cost of work j under mode m; J is all working number of project;

$\begin{array}{cc}s.t.& \underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\&Sigma;}}}{x}_{\mathrm{jmt}}=1,j=\mathrm{1,2},...,J;\end{array}---\left(3\right)$

Formula (3) represents that each work can only realize once in one mode, x in formula _jmtwhat represent is the state that work j carries out in the time of the m kind pattern t stage; [ED _j, LD _j] represent be work j the earliest with Late Finish section;

$\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\&Sigma;}}}t\&CenterDot;x_{\mathrm{imt}}\&le;\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\&Sigma;}}}t\&CenterDot;x_{\mathrm{jmt}}-d_{\mathrm{jm}},j=\mathrm{1,2},...,J,i\&Element;Q_j;---\left(4\right)$

Formula (4) represents the tight front restriction relation of project, before tight, restriction relation refers to and between work in every, exists ordinal relation, other are operated in this work and can not start before completing, the deadline of work is the summation of its start time and execution time, and the work after this work all must be after this end-of-job and met under the condition of resource constraint and could start execution; x _imtand x _jmtrespectively work i and the executing state of work j in the time of the m kind pattern t stage; d _jmit is the execution time of work j under m kind pattern;

$\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{r}_{\mathrm{jmk}}^{\mathrm{\&rho;}}\underset{q=\max \{t,{\mathrm{ED}}_j\}}{\overset{\min \{t+d_{\mathrm{jm}}-1,{\mathrm{LD}}_j\}}{\mathrm{\&Sigma;}}}\&le;R_k^{\mathrm{\&rho;}},k=\mathrm{1,2},...,K,t=\mathrm{1,2},...\stackrel{\&OverBar;}{D};---\left(5\right)$

Formula (5) is inequality constrain, has ensured that the renewable resources amount of each work use is no more than the aggregate supply in this stage; In formula be the demand of k kind renewable resources, be k kind renewable resources in the aggregate supply in each stage, for the duration upper limit;

$\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{r}_{\mathrm{jmn}}^v\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LF}}_j}{\mathrm{\&Sigma;}}}{x}_{\mathrm{jmt}}\&le;R_n^v,n=\mathrm{1,2},...N;---\left(6\right)$

Formula (6) is to ensure that the unrenewable resource amount that all working uses can not exceed the total quantity delivered of whole project, be the demand of n kind unrenewable resource, it is n kind unrenewable resource total amount;

x _jmt＝{0,1},j＝1,2,...,J,m＝1,2,...,M _j,t＝ED _j,...,LD _j； (7)

Formula (7) is the span of correlated variables in model, x _jmtthe completion status of expression work j under m kind pattern, has x if complete _jmt=1, otherwise x _jmt=0;

Step 2, produce initial feasible schedule sequence (i.e. coding)

Each work in project is made up of two parts, that is:

$\left[\begin{array}{c}{S}_i\\ M_i\end{array}\right]=\left[\begin{array}{c}{j}_1,j_2,...,j_J\\ m_1,m_2,...,m_J\end{array}\right],---\left(8\right)$

Wherein, S _i=j ₁, j ₂... j _j, S _ibeing the scheduling sequence that meets temporal constraint in i Task-list, is the execution sequence table of each work in project; M _i=m ₁, m ₂..., m _j, M _ibe the corresponding mode sequences of each task in this Task-list, the mode sequences in project is one to one with scheduling sequence, generates at random in the process of implementation the corresponding pattern M of S, and ensures that the pattern count generating is not more than the assemble mode number of this work,

Determined the preceding activity collection p of work j by temporal constraint _jwith tight rear working set s _j, use adjacency matrix G=[g _ij] _{j × J}represent the tight front tight rear relation of workplace, wherein as i ∈ P _jtime, g _i,j=1, otherwise g _i,j=0;

Initialization project scheduling sequence S and executed work sequence number s ₁=1, making Job is blank vector, k=1, the s of retrieve stored adjacency matrix _hoK, search in-degree and be 1 working set, add in Job sequence, from Job, delete a work sequence number u with highest priority, and this sequence number u is assigned to s _h+1, element a in adjacency matrix simultaneously _iu(i=s _h+1) subtract 1, make k=k+1, if k<J continues to calculate, otherwise output S;

Step 3, to scheduling sequence evaluate

The target of resource constrained project scheduling problem is the duration-cost minimization of project, and the scheduling sequence S and the mode sequences M that generate according to project, carry out decode operation by serial scheme,

Make T _stthe start time of expression project, T _i=t _i1, t _i2..., t _ij..., t _iJand C _i=c _i1, c _i2..., c _ij..., c _iJstart time and the cost of corresponding work in i the chained list that represents respectively to obtain through coding, judgement is operated under its execution pattern whether have resource contention, finds the t on earliest finish time of this chained list _iJ=max{t _ij+ d _jmand corresponding cost c _iJ=∑ c _jm;

Step 4, to scheduling sequence upgrade

Start to adopt multi-Agent evolutionary Algorithm to upgrade scheduling sequence from step 4, by with its neighborhood in work competition, intersect, three kinds of modes of operation of self study complete renewal,

4.1) contention operation

Suppose i chained list { S _i, M _icorresponding duration-cost is { t _i, c _i, duration-cost optimum in its neighborhood is if, and (this symbol is not is less than, is a kind of symbol that represents precedence relationship), this chained list continues survival in grid, otherwise is removed grid, and with the new chained list of generation S ' _i, M ' _ireplace P ₀∈ (0,1) is occupation probability, and detailed process is:

Step1: initialization S ' _i, M ' _i, by { S _i, M _ibe assigned to S ' _i, M ' _i, make k=1;

Step2: produce at random u ∈ (0,1), if u≤P ₀, turn Step4, otherwise make k=k+1;

Step3: if k < is J, turn Step2, otherwise turn Step6;

Step4: a random integer r who is not equal to k, the exchange j of selecting between (1, J) _rand j _kobtain S ' _iif, S ' _imeet tight front relation constraint, turn Step5, otherwise recover, make k=k+1, turn Step3;

Step5: the pattern of a certain work j of randomly changing, obtains M ' _i, check whether this pattern dispatching sequence meets resource constraint, if meet, turn Step6, otherwise recover;

Step6: upgrade chained list, calculate corresponding duration-cost, obtain new sequence;

4.2) interlace operation

Suppose i chained list sequence { S _i, M _icarry out interlace operation with the chained list in its neighborhood, and 1≤i≤Popsize, that participate in intersecting is { S ^f, M ^fand { S ^m, M ^m, after intersecting, generate respectively { S ^d, M ^dand { S ^s, M ^s, two integer r of random generation between (1, J) ₁and r ₂, specific operation process is:

4.2.1) scheduling sequence is intersected

If point of crossing is r ₁, S ^dfront r ₁individual sequence k=1,2 ..., r ₁derive from S ^m, rear J-r ₁individual sequence k=r ₁+ 1 ..., J derives from S ^f, and S ^din existing sequence no longer consider, maintain all the other sequences at S ^fin relative position constant, S ^sgeneration in contrast;

4.2.2) mode sequences is intersected

If point of crossing is r ₂, M ^dfront r ₂individual sequence k=1,2 ..., r ₂derive from M ^m, rear J-r ₂individual sequence k=r ₂+ 1 ..., J derives from M ^f, M ^sgeneration in contrast;

4.3) self study operation

Self study operation is used for realizing Local Search operation, increases the diversity of population,, under the restriction that meets temporal constraint, some work in chained list is carried out to the displacement of position, and the change of pattern, according to probability P _s1carry out task scheduling sequence self study operation, according to probability P _s2carry out mission mode sequence self study operation, detailed process is:

Step1 produces w ∈ (0,1) at random, if w < is P _s1, turn Step2, the scheduling sequence in chained list is carried out to self study operation; If w < is P _s2, turn Step3, the mode sequences in chained list is carried out to self study operation; Otherwise, turn Step4;

Step2 is the random a certain position V that generates scheduling sequence S between (1, J), finds all tight front nodal point of this position at the rearmost position u dispatching in sequence ₁, and all tight posterior nodal points in scheduling the front position u in sequence ₂, between front position and rearmost position, position u of random choose, is inserted into u place v, is newly dispatched sequence S ';

The pattern of Step3 randomly changing task j, obtains M', checks the work under this pattern whether to meet the constraint of resource, if meet, turns Step4, otherwise regenerates a group mode;

Step4 upgrades chained list sequence, calculates corresponding duration-cost;

Step 5, construct the operation of non-domination disaggregation

Prior art generally adopts NSGA-II[14] in non-dominated Sorting constructing tactics Pareto disaggregation, but this strategy is easily lost the individuality of not arranging mutually.

The present invention adopts following methods to form Pareto disaggregation, and concrete steps are:

5.1) all individual sequence numbers are initialized as to rank (a)=1;

5.2) to any individual a, b,

If , rank (b)=rank (b)+1;

If , rank (a)=rank (a)+1; If both do not arrange mutually, individual a, the sequence number of b is constant;

5.3) individuality that is 1 by sequence number is put into non-domination solution and is concentrated, and forms contemporary Pareto disaggregation;

Step 6, outside filing collection is safeguarded

Utilize extraction, analysis to relevant information in resource scheduling system, in conjunction with multiple goal multi-Agent evolutionary Algorithm, realize the optimization of scheduling sequence; Because target is that project duration and project cost are simultaneously optimum, therefore the non-bad feasible schedule solution that relatively duration and cost obtain being each time stored in to outside filing concentrates, outside the renewal of outside filing collection except the non-domination scheduling in population, also combine existing crowding distance method and make the outside filing obtaining collect more even, detailed process is:

The active power of the non-domination feasible schedule in population is put into outside filing one by one to be concentrated, if the active power that the active power of this feasible schedule is filed concentrated feasible schedule by outside is arranged, the active power of this feasible schedule is deleted from filing to concentrate, otherwise the active power of this feasible schedule adds filing collection; Be less than max cap. if file the active power number of concentrated feasible schedule, do not carry out deletion action, otherwise the crowding distance that calculates the active power of the concentrated all feasible schedule of current filing, the active power of deleting that feasible schedule of crowding distance minimum makes to file concentrated feasible schedule and remains on the number that is less than or equal to max cap.;

Step 7, renewal iterations h=h+1, if h < is J, continue repeating step 2 to step 6, otherwise output Pareto optimal solution set.

The inventive method is for the multiple goal multi-mode resource constrained project scheduling problem of duration-cost, a kind of new multiple goal multi-Agent evolutionary Algorithm has been proposed, utilize intelligent body Distributed and parallel structure and neighbour structure, not only effectively avoid algorithm to enter precocity, also maintain the diversity of population, realized the Resource-constrained Project Scheduling Problem taking the shortest and cost minimization of duration as target.

Claims (4)

1. solve effective ways for multiple goal Resource-constrained Project Scheduling Problem, its feature is, implements according to following steps:

Step 1, the multiple goal Resource-constrained Project Scheduling Problem mathematical model of foundation based on time-cost trade-off

Suppose that the work number in project is J, the temporal constraint before and after having between each work j, has j=1, and 2 ..., J, note Q _jthe j set before of and then working, H _jit is the j set afterwards of and then working; Set maximum iteration time H, iterations initial value h=1, work 1 is unique work of early start, work J is the unique work completing the latest; In project, renewable resources species number is K, and unrenewable resource species number is N, k=1, and 2 ... K, n=1,2 ... N, k kind renewable resources in the aggregate supply in each stage is n kind unrenewable resource total amount is each work has various modes available, and work j need select M _jone of the pattern of kind operates, and can not interrupt or change in operational process; When work j moves under m kind pattern, m=1,2 ... M _j, the demand of k kind renewable resources is the demand of n kind unrenewable resource is be d working time _jm, the work resource sum used moving can not exceed the aggregate supply of resource, above each value round numbers,

Model of creation is as follows accordingly:

$\begin{array}{cc}\min & f_J=\underset{t={\mathrm{ED}}_J}{\overset{{\mathrm{LD}}_J}{\mathrm{\&Sigma;}}}t\&CenterDot;x_{J1T};\end{array}---\left(1\right)$

One of formula (1) is target, and this target is the expression formula that minimizes Project duration, [ED in formula _j, LD _j] for work J the earliest with Late Finish section; T represents t stage, x _j1Tthe completion status in T stage that is work j under the first pattern, if complete x _j1T=1, otherwise x _j1T=0;

$\begin{array}{cc}\min & c_J=\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{c}_{\mathrm{jm}};\end{array}---\left(2\right)$

Formula (2) is target two, and this target is the expression formula that minimizes project cost, M in formula _jwhat represent is the execution pattern number of work j; c _jmthe cost of work j under mode m; J is all working number of project;

$\begin{array}{cc}s.t.& \underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\&Sigma;}}}{x}_{\mathrm{jmt}}=1,j=\mathrm{1,2},...,J;\end{array}---\left(3\right)$

Formula (3) represents that each work can only realize once in one mode, x in formula _jmtwhat represent is the state that work j carries out in the time of the m kind pattern t stage; [ED _j, LD _j] represent be work j the earliest with Late Finish section;

$\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\&Sigma;}}}t\&CenterDot;x_{\mathrm{imt}}\&le;\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LD}}_j}{\mathrm{\&Sigma;}}}t\&CenterDot;x_{\mathrm{jmt}}-d_{\mathrm{jm}},j=\mathrm{1,2},...,J,i\&Element;Q_j;---\left(4\right)$

Formula (4) represents the tight front restriction relation of project, x _imtand x _jmtrespectively work i and the executing state of work j in the time of the m kind pattern t stage; d _jmit is the execution time of work j under m kind pattern;

$\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{r}_{\mathrm{jmk}}^{\mathrm{\&rho;}}\underset{q=\max \{t,{\mathrm{ED}}_j\}}{\overset{\min \{t+d_{\mathrm{jm}}-1,{\mathrm{LD}}_j\}}{\mathrm{\&Sigma;}}}\&le;R_k^{\mathrm{\&rho;}},k=\mathrm{1,2},...,K,t=\mathrm{1,2},...\stackrel{\&OverBar;}{D};---\left(5\right)$

Formula (5) is inequality constrain, has ensured that the renewable resources amount of each work use is no more than the aggregate supply in this stage, be the demand of k kind renewable resources, be k kind renewable resources in the aggregate supply in each stage, for the duration upper limit;

$\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{M_j}{\mathrm{\&Sigma;}}}{r}_{\mathrm{jmn}}^v\underset{t={\mathrm{ED}}_j}{\overset{{\mathrm{LF}}_j}{\mathrm{\&Sigma;}}}{x}_{\mathrm{jmt}}\&le;R_n^v,n=\mathrm{1,2},...N;---\left(6\right)$

Formula (6) is to ensure that the unrenewable resource amount that all working uses can not exceed the total quantity delivered of whole project, be the demand of n kind unrenewable resource, it is n kind unrenewable resource total amount;

x _jmt＝{0,1},j＝1,2,...,J,m＝1,2,...,M _j,t＝ED _j,...,LD _j； (7)

Formula (7) is the span of correlated variables in model, x _jmtthe completion status of expression work j under m kind pattern, has x if complete _jmt=1, otherwise x _jmt=0;

Step 2, produce initial feasible schedule sequence

Each work in project is made up of two parts, that is:

$\left[\begin{array}{c}{S}_i\\ M_i\end{array}\right]=\left[\begin{array}{c}{j}_1,j_2,...,j_J\\ m_1,m_2,...,m_J\end{array}\right],---\left(8\right)$

Wherein, S _i=j ₁, j ₂... j _j, S _ibeing the scheduling sequence that meets temporal constraint in i Task-list, is the execution sequence table of each work in project; M _i=m ₁, m ₂..., m _j, M _ibe the corresponding mode sequences of each task in this Task-list, the mode sequences in project is one to one with scheduling sequence, generates at random in the process of implementation the corresponding pattern M of S, and ensures that the pattern count generating is not more than the assemble mode number of this work,

Determined the preceding activity collection p of work j by temporal constraint _jwith tight rear working set s _j, use adjacency matrix G=[g _ij] _{j × J}represent the tight front tight rear relation of workplace, wherein as i ∈ P _jtime, g _i,j=1, otherwise g _i,j=0;

Initialization project scheduling sequence S and executed work sequence number s ₁=1, making Job is blank vector, k=1, the s of retrieve stored adjacency matrix _hoK, search in-degree and be 1 working set, add in Job sequence, from Job, delete a work sequence number u with highest priority, and this sequence number u is assigned to s _h+1, element a in adjacency matrix simultaneously _iu(i=s _h+1) subtract 1, make k=k+1, if k<J continues to calculate, otherwise output S;

Step 3, to scheduling sequence evaluate

The scheduling sequence S and the mode sequences M that generate according to project, carry out decode operation by serial scheme, makes T _stthe start time of expression project, T _i=t _i1, t _i2..., t _ij..., t _iJand C _i=c _i1, c _i2..., c _ij..., c _iJstart time and the cost of corresponding work in i the chained list that represents respectively to obtain through coding, judgement is operated under its execution pattern whether have resource contention, finds the t on earliest finish time of this chained list _iJ=max{t _ij+ d _jmand corresponding cost c _iJ=∑ c _jm;

Step 4, to scheduling sequence upgrade

Adopt multi-Agent evolutionary Algorithm to upgrade scheduling sequence, by with its neighborhood in work competition, intersect, three kinds of modes of operation of self study complete renewal;

Step 5, construct the operation of non-domination disaggregation;

Step 6, outside filing collection is safeguarded;

Step 7, renewal iterations h=h+1, if h < is J, continue repeating step 2 to step 6, otherwise output Pareto optimal solution set.

2. the effective ways that solve multiple goal Resource-constrained Project Scheduling Problem according to claim 1, its feature is, in described step 4, competition, intersection, three kinds of mode of operation detailed processes of self study are:

4.1) contention operation

Suppose i chained list { S _i, M _icorresponding duration-cost is { t _i, c _i, duration-cost optimum in its neighborhood is if and this chained list continues survival in grid, otherwise is removed grid, and with the new chained list of generation S ' _i, M ' _ireplace P ₀∈ (0,1) is occupation probability, and detailed process is:

Step1: initialization S ' _i, M ' _i, by { S _i, M _ibe assigned to S ' _i, M ' _i, make k=1;

Step2: produce at random u ∈ (0,1), if u≤P ₀, turn Step4, otherwise make k=k+1;

Step3: if k < is J, turn Step2, otherwise turn Step6;

Step4: a random integer r who is not equal to k, the exchange j of selecting between (1, J) _rand j _kobtain S ' _iif, S ' _imeet tight front relation constraint, turn Step5, otherwise recover, make k=k+1, turn Step3;

Step5: the pattern of a certain work j of randomly changing, obtains M ' _i, check whether this pattern dispatching sequence meets resource constraint, if meet, turn Step6, otherwise recover;

Step6: upgrade chained list, calculate corresponding duration-cost, obtain new sequence;

4.2) interlace operation

Suppose i chained list sequence { S _i, M _icarry out interlace operation with the chained list in its neighborhood, and 1≤i≤Popsize, that participate in intersecting is { S ^f, M ^fand { S ^m, M ^m, after intersecting, generate respectively { S ^d, M ^dand { S ^s, M ^s, two integer r of random generation between (1, J) ₁and r ₂, specific operation process is:

4.2.1) scheduling sequence is intersected

If point of crossing is r ₁, S ^dfront r ₁individual sequence k=1,2 ..., r ₁derive from S ^m, rear J-r ₁individual sequence k=r ₁+ 1 ..., J derives from S ^f, and S ^din existing sequence no longer consider, maintain all the other sequences at S ^fin relative position constant, S ^sgeneration in contrast;

4.2.2) mode sequences is intersected

If point of crossing is r ₂, M ^dfront r ₂individual sequence k=1,2 ..., r ₂derive from M ^m, rear J-r ₂individual sequence k=r ₂+ 1 ..., J derives from M ^f, M ^sgeneration in contrast;

4.3) self study operation

Self study operation is used for realizing Local Search operation, increases the diversity of population,, under the restriction that meets temporal constraint, some work in chained list is carried out to the displacement of position, and the change of pattern, according to probability P _s1carry out task scheduling sequence self study operation, according to probability P _s2carry out mission mode sequence self study operation, detailed process is:

Step1 produces w ∈ (0,1) at random, if w < is P _s1, turn Step2, the scheduling sequence in chained list is carried out to self study operation; If w < is P _s2, turn Step3, the mode sequences in chained list is carried out to self study operation; Otherwise, turn Step4;

Step2 is the random a certain position V that generates scheduling sequence S between (1, J), finds all tight front nodal point of this position at the rearmost position u dispatching in sequence ₁, and all tight posterior nodal points in scheduling the front position u in sequence ₂, between front position and rearmost position, position u of random choose, is inserted into u place v, is newly dispatched sequence S ';

The pattern of Step3 randomly changing task j, obtains M', checks the work under this pattern whether to meet the constraint of resource, if meet, turns Step4, otherwise regenerates a group mode;

Step4 upgrades chained list sequence, calculates corresponding duration-cost.

3. the effective ways that solve multiple goal Resource-constrained Project Scheduling Problem according to claim 1, its feature is, in described step 5, adopts following methods to form Pareto disaggregation, concrete steps are:

5.1) all individual sequence numbers are initialized as to rank (a)=1;

5.2) to any individual a, b,

If rank (b)=rank (b)+1;

If rank (a)=rank (a)+1; If both do not arrange mutually, individual a, the sequence number of b is constant;

5.3) individuality that is 1 by sequence number is put into non-domination solution and is concentrated, and forms contemporary Pareto disaggregation.

4. the effective ways that solve multiple goal Resource-constrained Project Scheduling Problem according to claim 1, its feature is, in described step 6, utilizes extraction, analysis to relevant information in resource scheduling system, in conjunction with multiple goal multi-Agent evolutionary Algorithm, realize the optimization of scheduling sequence, because target is that project duration and project cost are simultaneously optimum, therefore the non-bad feasible schedule solution that relatively duration and cost obtain being each time stored in to outside filing concentrates, outside the renewal of outside filing collection except the non-domination scheduling in population, also combining existing crowding distance method makes the outside filing obtaining collect more even, detailed process is: the active power of the non-domination feasible schedule in population is put into outside filing one by one and concentrate, if the active power that the active power of this feasible schedule is filed concentrated feasible schedule by outside is arranged, the active power of this feasible schedule is deleted from filing to concentrate, otherwise the active power of this feasible schedule adds filing collection, be less than max cap. if file the active power number of concentrated feasible schedule, do not carry out deletion action, otherwise the crowding distance that calculates the active power of the concentrated all feasible schedule of current filing, the active power of deleting that feasible schedule of crowding distance minimum makes to file concentrated feasible schedule and remains on the number that is less than or equal to max cap..