CN113642763A - Budget constraint-based high-end equipment development resource allocation and optimal scheduling method - Google Patents

Budget constraint-based high-end equipment development resource allocation and optimal scheduling method Download PDF

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CN113642763A
CN113642763A CN202110743571.4A CN202110743571A CN113642763A CN 113642763 A CN113642763 A CN 113642763A CN 202110743571 A CN202110743571 A CN 202110743571A CN 113642763 A CN113642763 A CN 113642763A
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裴军
李占印
杨善林
周娅
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Abstract

The invention provides a budget constraint-based resource allocation and optimal scheduling method for high-end equipment development, and relates to the technical field of research and development task scheduling and equipment assembly scheduling. The technical scheme of the invention is that input parameters of a variable neighborhood search algorithm are set based on high-end equipment research and development task data and equipment data; then setting execution parameters; initializing an initial solution set of the algorithm and solving for an initial solution X in the initial solution setLShaking operation is carried out to obtain a new solution X ', then local search is carried out on the new solution X' in the selectable neighborhood structure set to obtain an optimal solution X ', and whether the optimal solution X' is superior to the initial solution X or not is comparedLContinuously iterating and finally outputting the global optimal solution XbestAnd according to the global optimal solution XbestAnd carrying out research, development and manufacturing work on the corresponding research, development and manufacturing scheme. The present technologyWhen budget constraint is considered, the approximate optimal solution and the corresponding equilibrium resource configuration strategy scheme can be rapidly and accurately obtained, and the resource utilization rate and the research, development and manufacturing optimization efficiency of enterprises are improved.

Description

Budget constraint-based high-end equipment development resource allocation and optimal scheduling method
Technical Field
The invention relates to the technical field of research and development task scheduling and equipment assembly scheduling, in particular to a budget constraint-based high-end equipment development resource allocation and optimal scheduling method.
Background
High-end equipment can be assembled in small batches after being developed due to the characteristics of complex structure, diversified requirements, customized customers and the like. The development stage of one type of high-end equipment comprises a plurality of development tasks, wherein the development tasks have a constraint relationship between a tight front part and a tight rear part, all the development tasks form a development network diagram, and the manufacturing stage is to assemble parts determined by the development and design in an assembly plant after the development of the high-end equipment is completed. In actual situations, a plurality of types of high-end equipment are often developed and assembled at the same time, and when resources such as research and development personnel and assembly lines cannot be planned according to delivery date constraints, fixed budgets are required to be invested to increase the number of the research and development personnel and the assembly lines so as to face the possible urgent needs in the future.
At present, aiming at the optimization scheduling problem of two stages of research, development and manufacturing of high-end equipment, a precise algorithm, a heuristic method or an artificial intelligence algorithm is mostly adopted for solving. When the condition of budget constraint needs to be considered, the complexity of the problem is greatly increased, so that the prior related art cannot solve the problem, or an optimal solution is solved in a short time, namely, two objectives of solution time and solution speed cannot be considered at the same time, and the production work of two stages of research and development and manufacturing of high-end equipment is influenced.
Therefore, the optimal solution cannot be rapidly and accurately solved by the existing two-stage optimization scheduling technology of high-end equipment research and development-manufacturing when budget constraint is considered.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of the prior art, the invention provides a resource allocation and optimal scheduling method developed by high-end equipment based on budget constraint, and solves the problem that the prior art can not quickly and accurately solve the optimal solution when the budget constraint is considered.
(II) technical scheme
In order to achieve the purpose, the invention is realized by the following technical scheme:
the invention provides a budget constraint-based high-end equipment development resource allocation and optimal scheduling method, which comprises the following steps:
s1, setting input parameters of a variable neighborhood search algorithm based on research and development task data, research and development personnel data, equipment data and assembly line data; the input parameters include:
current available budget B; the number m of research and development projects in the research and development stage; the type number m of high-end equipment in the manufacturing stage; the total number of all development tasks n1 for all development projects in the development phase; total number n2 of all kinds of high-end equipment requiring mass assembly at the manufacturing stage; initial number of developers a in the development phase0The unit cost of the developer can be increased to B1; number of initial assembly lines in the manufacturing stage b0(ii) a The assembly line cost can be increased by B2；
S2, setting operation parameters of a variable neighborhood searching algorithm; the operating parameters specifically include:
maximum number of iterations Iter of the algorithmmax(ii) a Number N of initial solutions in initial solution set0(ii) a Minimum number of Neighborhood Structures (NS) in selectable neighborhood structure setmin(ii) a A number of Neighborhood Structures (NS) in the current set of selectable neighborhood structures; k of the kth neighborhood structure is 0; the L of the lth initial solution is 0, and the initial fitness value of the neighborhood structure is α;
s3, coding the research and development task data and the equipment data based on a variable neighborhood search algorithm to obtain an initial solution set X; then, each solution in the initial solution set X is decoded, and C corresponding to each initial solution is obtainedmaxA value; wherein, CmaxThe value represents the total development-assembly time span;
s4, performing initial solution X in the initial solution set X based on variable neighborhood search algorithmLCarrying out Shaking operation to obtain a new solution X';
s5, carrying out local search on the new solution X 'based on the current optional neighborhood structure set to obtain a local optimal solution X';
s6, comparing the initial solution XLCorresponding to CmaxC whose value corresponds to the local optimal solution X ″maxThe size of the value, if X' corresponds to CmaxValue less than XLCorresponding to CmaxThe value, K is made 0 and X "is assigned to XLCalculating the fitness of the neighborhood structure in the selectable neighborhood structure set; if not, let K be K +1, and execute S7;
s7, judging whether K is less than or equal to (NS) or not, and if so, turning to S5; if not, let L be L +1, and go to S8;
s8, judging that L is less than or equal to N0If yes, making L equal to L +1, and going to S4; otherwise, sorting and updating the neighborhood structure again based on the fitness of the optional neighborhood structure in the optional neighborhood structure set, and then turning to S9;
s9, judging whether the current iteration number Iter is larger than the maximum iteration number ItermaxIf yes, go to S10; if not, let Iter be Iter +1, K be 0, and L be 0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting the global optimal solution Xbest。
Preferably, the encoding the development task data and the equipment data based on the variable neighborhood search algorithm to obtain the initial solution set X in S3 includes:
s31, defining variables a, b, a1Where a represents the number of finally available developers, b represents the number of finally available assembly lines, a1Represents the maximum developer that can be added under budget B;
s32, defining a new initial solution X0Assigning the values of a and b to the initial solution X0At positions n1+ n2+1 and n1+ n2+2, the codes of the development stage and the manufacturing stage are re-randomly generated according to a and b, and all the initial solutions X are solved0Adding the solution into an initial solution set X;
s33, judging whether the number of the initial solutions in the initial solution set X is larger than the number N of the initial solutions in the initial solution set0If not, returning to S31 to continue generating the initial solution, otherwise, outputting the initial solution set X.
Preferably, said CmaxThe values are:
Figure BDA0003142138960000041
Figure BDA0003142138960000042
Figure BDA0003142138960000043
Figure BDA0003142138960000044
wherein, CmaxRepresents the total time span from development to assembly;
Figure BDA0003142138960000045
represents the minimum value of the earliest start-up time of all high-end equipment on the ith assembly line;
Figure BDA0003142138960000046
representing the actual completion time of the research and development project i;
pirepresents the time required for the h-th assembly of the ith high-end equipment;
Figure BDA0003142138960000047
denotes the ith type of h-th high-end equipment EihWaiting time on assembly line l;
Figure BDA0003142138960000048
denotes the ith type of h-th high-end equipment EihActual start-up time on assembly line l;
Figure BDA0003142138960000049
denotes the nth high-end equipment E of the u-th typeuvThe actual completion time on the assembly line l.
Preferably, in S4, the initial solution X in the initial solution set X is determined based on a variable neighborhood search algorithmLPerforming a Shaking operation to obtain a new solution X' includes:
s41, obtaining the L-th initial solution X in the initial solution set XLThe variables I, J ═ 1 are defined;
s42, randomly generating integers in the range of the interval [1, n1], and assigning the integers to variables I and J;
s43, judging the initial solution XLWhether two research and development tasks corresponding to the I and J positions meet the conditions is judged: one task belongs to a critical path set task and the other task belongs to a non-critical path set task, if the condition is not met, returning to the step S42; otherwise, executing S44;
s44 exchange initial solution XLThe I and J elements in the solution are obtained to obtain an initial solution XLNew solution X after the first exchange1Is recorded as the first new solution X1；
S45, randomly generating integers in the range of the interval [ n1+1, n1+ n2], and assigning the integers to variables I and J;
s46 exchanging new solution X1The I and J elements in the solution are subjected to secondary exchange to obtain a new solution X2Record as the second new solution X2；
S47, comparing the structure N based on the disturbance neighborhood1The second new solution X is obtained2With the current initial solution XLIf the second new solution X2Corresponding CmaxValue less than or equal to the initial solution XLCorresponding CmaxValue, then output the second new solution X2(ii) a Otherwise, returning to S42;
s48, solving the second new solution X2And is assigned to X'.
Preferably, the step of locally searching the new solution X' based on the current optional neighborhood structure set to obtain the locally optimal solution X ″ in S5 includes:
s51: setting the initial neighborhood structure K as 0, setting the initial search frequency G as 0 and setting the maximum search frequency G of a single neighborhood structure;
s52: and selecting the K-th neighborhood structure in the selectable neighborhood structure set to operate X ' to obtain X ', and reselecting the selectable neighborhood structure in the selectable neighborhood structure set to continue operating X ' when G is greater than or equal to G.
Preferably, the selectable neighborhood structure in S52 includes:
neighborhood structure 1: defining variables i and j, randomly generating two integers in an interval, assigning the integers to two research and development tasks corresponding to the i, j and the ith and jth positions, wherein the two research and development tasks belong to a non-critical path set, and exchanging the serial numbers of research and development personnel corresponding to the ith and jth positions of a solution; randomly generating an integer in the interval range, assigning the integer to a variable i, j, and exchanging assembly line numbers corresponding to the ith and j positions of the solution;
neighborhood structure 2: defining variables i and j, randomly generating an integer in an interval range, assigning the integer to i, searching a position j which meets the condition and belongs to the key path set at the right side of the position i, inserting the number of a research and development staff corresponding to the position j-1 into the position i +1, and moving the number of the research and development staff corresponding to the position i +1 to the position j-2 to a position in the right direction; randomly generating an integer in the interval range and assigning the integer to i, randomly generating an integer in the interval range and assigning the integer to j, inserting the assembly line number corresponding to the position j-1 into the position i +1, and moving the assembly line number corresponding to the position i +1 to the position j-2 to the right by one position;
neighborhood structure 3: defining variables i and j, randomly generating an integer in an interval range, assigning the integer to i, searching a position j which meets the condition and belongs to the key path set at the right side of the position i, inserting the number of a research and development staff corresponding to the position i +1 into the position j-1, and moving the number of the research and development staff corresponding to the position i +2 to the position j-1 to a position left; randomly generating an integer in the interval range and assigning the integer to i, randomly generating an integer in the interval range and assigning the integer to j, inserting the assembly line number corresponding to the position i +1 into the position j-1, and moving the assembly line number corresponding to the position i +2 to the position j-1 to the left by one position;
neighborhood structure 4: defining variables i and j, randomly generating an integer in an interval range, assigning the integer to i, searching a position j which meets the condition and belongs to the key path set at the right side of the position i, searching the position j of which the task corresponding to the position belongs to the key path set, and performing reverse order processing on the numbers of all research and development personnel corresponding to the position i +1 to the position j-1; randomly generating integers in the interval range, assigning the integers to a variable i, j and meeting conditions, and performing reverse order processing on all assembly line numbers corresponding to the position i +1 to the position j-1;
neighborhood structure 5: defining variables i, j and k, assigning the element value of the ith position to k, randomly generating a research and development personnel number in an interval range and assigning the number to a variable j, randomly generating an integer in the interval range and assigning the integer to a variable i, and changing the value of the element of the ith position into the value of the variable j; and assigning the value of the element at the ith position to k, randomly generating an assembly line number in the interval range and assigning the assembly line number to a variable j, randomly generating an integer in the interval range and assigning the integer to a variable i, and changing the value of the element at the ith position into the value of the variable j.
Preferably, in S8, the reordering and updating the neighborhood structures based on the fitness of the selectable neighborhood structures in the selectable neighborhood structure set includes:
s81, moving the neighborhood structure with the minimum fitness alpha in the current optional neighborhood structure set N to an optional neighborhood structure set N'; if the fitness degrees alpha of a plurality of neighborhood structures are the same and are all the minimum, randomly selecting one neighborhood structure from the plurality of neighborhood structures and moving the selected neighborhood structure into an alternative neighborhood structure set N';
s82, judging the number of neighborhood structures in the current optional neighborhood structure set N, if the number is less than the minimum Number (NS) of neighborhood structures in the optional neighborhood structure setminRandomly selecting a plurality of neighborhood structures from the alternative neighborhood structure set N' and adding the neighborhood structures into the current optional neighborhood structure set N;
s84, the neighborhood structure is reordered and updated according to the fitness alpha of the neighborhood structure in the current optional neighborhood structure set N.
Preference is given toThat is, the global optimal solution X is output in S10bestThe method comprises the following steps: set TAkAnd EAlWherein, TAkRepresenting a set of tasks, EA, formed from the development tasks assigned by the kth developerlRepresenting the formation of high-end equipment assigned by the l assembly line into an equipment set EAl。
(III) advantageous effects
The invention provides a budget constraint-based resource allocation and optimal scheduling method for high-end equipment development. Compared with the prior art, the method has the following beneficial effects:
1. firstly, setting input parameters of a variable neighborhood search algorithm based on research and development task data of a high-end equipment research and development stage and equipment data of a manufacturing stage; then setting execution parameters of a variable neighborhood search algorithm; initializing an initial solution set of the algorithm and solving for an initial solution X in the initial solution setLShaking operation is carried out to obtain a new solution X ', then local search is carried out on the new solution X' in the selectable neighborhood structure set to obtain an optimal solution X ', and whether the optimal solution X' is superior to the initial solution X or not is comparedLContinuously iterating and finally outputting the global optimal solution XbestAnd according to the global optimal solution XbestAnd carrying out research, development and manufacturing work on the corresponding research, development and manufacturing scheme. According to the technical scheme, when a high-end equipment enterprise considers budget constraint conditions to perform high-end equipment development resource dynamic configuration and collaborative optimization scheduling, an approximate optimal solution and a corresponding balanced resource configuration strategy scheme can be rapidly and accurately obtained, two objectives of solution time and solution speed are considered, and collaborative optimization scheduling can be effectively performed on resources in a research and development stage and a manufacturing stage, so that the resource utilization rate and research and development-manufacturing collaborative efficiency of the high-end equipment enterprise are improved to the maximum extent;
2. according to the method, the initial solution is Shaking operated, and the current initial solution is jumped to another point in the feasible region range according to a certain rule, so that the situation that the local optimum is trapped in the current feasible region range is avoided, and the global search capability of the algorithm is improved;
3. according to the method, the fitness of the neighborhood structure is calculated, then the neighborhood structure is re-screened and sorted and updated according to the fitness of the neighborhood structure, so that the more effective neighborhood structure can be reserved, the neighborhood structure with a poor effect is eliminated, and the speed and the accuracy in solving the optimal solution are increased.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart of a method for allocating and optimally scheduling high-end equipment development resources based on budget constraints according to an embodiment of the present invention;
FIG. 2 is a diagram of encoding according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described, and it is obvious that the described embodiments are a part of the embodiments of the present invention, but not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
By providing the budget constraint-based resource allocation and optimal scheduling method for high-end equipment development, the embodiment of the application solves the problem that the optimal solution cannot be rapidly and accurately solved in consideration of budget constraint in the prior art, achieves the purpose of simultaneously considering both the solving time and the solving speed in solving the optimal scheduling problem in the two stages of high-end equipment development and manufacturing, and improves the production efficiency.
In order to solve the technical problems, the general idea of the embodiment of the application is as follows:
in order to make an optimal high-end equipment research and development-manufacturing two-stage optimal scheduling scheme under the condition of considering certain budget constraint, the technical scheme designs a variable neighborhood search algorithm, and the current initial solution is jumped to another point of a feasible domain range according to a certain rule by carrying out Shaking operation on the initial solution obtained by encoding, so that the situation that the current feasible domain range is trapped into partial optimization is avoided; in addition, by calculating the fitness of the neighborhood structure, and then re-screening and sequencing the neighborhood structure according to the fitness of the neighborhood structure, a more effective neighborhood structure can be reserved, and meanwhile, the neighborhood structure with a poor effect is eliminated, so that the speed and the accuracy in solving the optimal solution are increased.
In order to better understand the technical solution, the technical solution will be described in detail with reference to the drawings and the specific embodiments.
Setting the two stages of development-manufacturing of high-end equipment, the currently available budget is B, and the allocation of the budget in the development stage and the manufacturing stage directly determines the number of finally available developers in the development stage and the number of finally available assembly lines in the manufacturing stage.
It should be noted that a high-end equipment of one type in the manufacturing stage corresponds to a project network diagram in the development stage, and the completion time of a project in the development stage is the earliest start-up time of the high-end equipment of the corresponding type.
The invention provides a budget constraint-based high-end equipment development resource allocation and optimal scheduling method, and the method comprises the following steps of:
s1, setting input parameters of a variable neighborhood search algorithm based on research and development task data, research and development personnel data, equipment data and assembly line data; the input parameters include:
current available budget B; the number m of research and development projects in the research and development stage; the type number m of high-end equipment in the manufacturing stage; the total number of all development tasks n1 for all development projects in the development phase; total number n2 of all kinds of high-end equipment requiring mass assembly at the manufacturing stage; initial number of developers a in the development phase0The unit cost of the developer can be increased to B1; number of initial assembly lines in the manufacturing stage b0(ii) a The assembly line cost can be increased by B2；
S2, setting operation parameters of a variable neighborhood searching algorithm; the operating parameters specifically include:
maximum number of iterations Iter of the algorithmmax(ii) a Number N of initial solutions in initial solution set0(ii) a Minimum number of Neighborhood Structures (NS) in selectable neighborhood structure setmin(ii) a A number of Neighborhood Structures (NS) in the current set of selectable neighborhood structures; k of the kth neighborhood structure is 0; the L of the lth initial solution is 0, and the initial fitness value of the neighborhood structure is α;
s3, coding the research and development task data and the equipment data based on a variable neighborhood search algorithm to obtain an initial solution set X; then, each solution in the initial solution set X is decoded, and C corresponding to each initial solution is obtainedmaxA value; wherein, CmaxThe value represents the total development-assembly time span;
s4, performing initial solution X in the initial solution set X based on variable neighborhood search algorithmLCarrying out Shaking operation to obtain a new solution X';
s5, carrying out local search on the new solution X 'based on the current optional neighborhood structure set to obtain a local optimal solution X';
s6, comparing the initial solution XLCorresponding to CmaxC whose value corresponds to the local optimal solution X ″maxThe size of the value, if X' corresponds to CmaxValue less than XLCorresponding to CmaxThe value, K is made 0 and X "is assigned to XLCalculating the fitness of the neighborhood structure in the selectable neighborhood structure set; if not, let K be K +1, and execute S7;
s7, judging whether K is less than or equal to (NS) or not, and if so, turning to S5; if not, let L be L +1, and go to S8;
s8, judging that L is less than or equal to N0If yes, making L equal to L +1, and going to S4; otherwise, sorting and updating the neighborhood structure again based on the fitness of the optional neighborhood structure in the optional neighborhood structure set, and then turning to S9;
s9, judging whether the current iteration number Iter is larger than the maximum iteration number ItermaxIf yes, go to S10; if not, let Iter be Iter +1, K be 0, and L be 0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting the global optimal solution Xbest。
According to the technical scheme, firstly, input parameters of a variable neighborhood search algorithm are set based on research and development task data of a high-end equipment research and development stage and equipment data of a manufacturing stage; then setting execution parameters of a variable neighborhood search algorithm; initializing an initial solution set of the algorithm and solving for an initial solution X in the initial solution setLShaking operation is carried out to obtain a new solution X ', then local search is carried out on the new solution X' in the selectable neighborhood structure set to obtain an optimal solution X ', and whether the optimal solution X' is superior to the initial solution X or not is comparedLContinuously iterating and finally outputting the global optimal solution XbestAnd according to the global optimal solution XbestAnd carrying out research, development and manufacturing work on the corresponding research, development and manufacturing scheme. According to the technical scheme, when a high-end equipment enterprise considers budget constraint conditions to perform high-end equipment development resource dynamic configuration and collaborative optimization scheduling, an approximate optimal solution and a corresponding balanced resource configuration strategy scheme can be rapidly and accurately obtained, two objectives of solution time and solution speed are considered, and collaborative optimization scheduling can be effectively performed on resources in a research and development stage and a manufacturing stage, so that the resource utilization rate and research and development-manufacturing collaborative efficiency of the high-end equipment enterprise are improved to the maximum extent.
The following describes the implementation of one embodiment of the present invention in detail with reference to the explanation of specific steps S1-S10.
S1, setting input parameters of a variable neighborhood search algorithm based on research and development task data, research and development personnel data, equipment data and assembly line data; the input parameters include:
current available budget B; the number m of research and development projects in the research and development stage; the type number m of high-end equipment in the manufacturing stage; the total number of all development tasks n1 for all development projects in the development phase; total number n2 of all kinds of high-end equipment requiring mass assembly at the manufacturing stage; initial number of developers a in the development phase0The unit cost of the developer can be increased to B1; number of initial assembly lines in the manufacturing stage b0(ii) a The assembly line cost can be increased by B2。
And setting input parameters of a variable neighborhood search algorithm based on research and development task data and research and development personnel data of a high-end equipment research and development stage, and equipment data and assembly line data of a manufacturing stage. The method specifically comprises the following steps: the method comprises the steps of acquiring research and development task data and research and development personnel data of a high-end equipment research and development stage, equipment data and assembly line data of a manufacturing stage and setting input parameters of a variable neighborhood search algorithm in a manual input mode. Input parameters of the variable neighborhood search algorithm include:
the number m of research and development projects in the research and development stage; the total number of all development tasks n1 for all development projects in the development phase; all sets of development tasks for a single project
Figure BDA0003142138960000131
Wherein, TijRepresents the jth development task of the ith project,
Figure BDA0003142138960000132
representing the number of research and development tasks contained in the ith project; initial number of developers a in the development phase0And maximum number of developers a1Initial set of developers
Figure BDA0003142138960000133
Increasable set of research and development personnel
Figure BDA0003142138960000134
PkDenotes the kth developer, where 1. ltoreq. k. ltoreq.a1When k > a0Then, the unit cost of the developer can be increased to B1;
the number m of types of high-end equipment in the manufacturing stage (since each research and development project corresponds to one type of high-end equipment, the number of types of high-end equipment in the manufacturing stage and the number of research and development projects in the research and development stage are both m); total number n2 of all kinds of high-end equipment mass assembly at the manufacturing stage; all mass production sets for a single type of high-end equipment are
Figure BDA0003142138960000137
Wherein E isihThe h-th equipment representing the ith high-end equipment,
Figure BDA0003142138960000138
represents the number of high-end equipment of the ith category to be assembled; number of initial assembly lines in the manufacturing stage b0And maximum number of assembly lines b1Set of initial assembly lines
Figure BDA0003142138960000135
Increasable assembly line set
Figure BDA0003142138960000136
MlDenotes the first assembly line, where l is more than or equal to 1 and less than or equal to b1When l > b0The assembly line cost which can be increased is B2。
S2, setting operation parameters of a variable neighborhood searching algorithm; the operating parameters specifically include:
maximum number of iterations Iter of the algorithmmax；
Number N of initial solutions in initial solution set0；
Minimum number of Neighborhood Structures (NS) in selectable neighborhood structure setmin；
A number of Neighborhood Structures (NS) in the current set of selectable neighborhood structures;
k of the kth neighborhood structure is 0;
l of the lth initial solution is 0;
initial fitness value α of the neighborhood structure, where α ═ α1,α2,...,αNS0,}＝{0,0,...,0}；
S3, coding the research and development task data and the equipment data based on a variable neighborhood search algorithm to obtain an initial solution set X; then, each solution in the initial solution set X is decoded, and C corresponding to each initial solution is obtainedmaxA value; wherein, CmaxThe values represent the total development-assembly time span.
1) And coding the research and development task data and the equipment data based on a variable neighborhood search algorithm to obtain an initial solution set X.
In the process of generating the initial solution, the assignment of the research and development stage and the manufacturing stage is based on the number of research and development personnel and the number of assembly lines, so in the process of generating the initial solution, firstly, budgets are required to be allocated to the research and development stage and the manufacturing stage, and the final research and development personnel number and the final assembly line number are determined; second, a random initial solution is generated based on the results of the budget allocation.
Encoding the task data of the development stage and the equipment data of the manufacturing stage of the high-end equipment based on a variable neighborhood search algorithm according to the total number N1 of development tasks of the development stage and the total number N2 of batch assembly of all kinds of high-end equipment, and generating a product containing N0An initial solution set X of initial solutions. Referring to FIG. 2, each initial solution X in the initial solution set X0The first part comprises three parts, each bit code corresponds to a research and development personnel assigned by a research and development task, and the position of each bit code corresponds to the earliest starting time sequence of the research and development personnel in the multi-project research and development network diagram; each bit code in the second part corresponds to an assembly line assigned by high-end equipment, and the position of each bit code corresponds to the earliest completed sequence of the developed network diagram; the third part of code represents the maximum number of developers and maximum assembly line finally available, and the generated initial solution X0Can be expressed as:
Figure BDA0003142138960000141
wherein xijRepresenting the assigned personnel of the jth development task of the ith project; y isihAn assembly line assigned by an h-th equipment representing an i-th high-end equipment; a, b represent the number of final developers and assembly lines, respectively. Specifically, the process of generating the initial solution set X includes:
s31, defining variables a, b, a1. Where a represents the number of developers ultimately available, b represents the number of assembly lines ultimately available, a1Representing the largest developer that can be added under budget B.
Wherein the content of the first and second substances,
Figure BDA0003142138960000151
means not more than
Figure BDA0003142138960000152
The largest integer of (a); slave interval (a)0,a0+a1]Randomly generating an integer, assigning the integer to a variable a, and calculating according to a formula
Figure BDA0003142138960000153
The number of final available assembly lines is calculated,
Figure BDA0003142138960000154
means not more than
Figure BDA0003142138960000155
Is the largest integer of (a).
S32, defining a new initial solution X0Assigning the values of a and b to the initial solution X0At positions n1+ n2+1 and n1+ n2+2, the codes of the development stage and the manufacturing stage are re-randomly generated according to a and b, and all the initial solutions X are solved0Added to the initial solution set X.
S33, judging whether the number of the initial solutions in the initial solution set X is larger than the number N of the initial solutions in the initial solution set0If not, returning to S31 to continue generating the initial solution, otherwise, outputting the initial solution set X.
2) Then, each solution in the initial solution set X is decoded, and C corresponding to each initial solution is obtainedmaxA value; wherein, CmaxThe values represent the total development-assembly time span.
The decoding process is to calculate the assignment scheme represented by the solution according to the constraint in the actual scene. Based on this assignment scheme, all developers complete the development project for all kinds of high-end equipment and all assembly lines complete the time required for all kinds of high-end equipment. In practical situations, there is a constraint that, in a research and development stage, any research and development personnel cannot simultaneously perform research and development of two research and development tasks, and after all the immediately preceding research and development tasks of a certain research and development task are completed, the research and development task can be performed. In the assembly phase, either assembly line cannot simultaneously perform the assembly of two high-end equipment.
The parameters are defined in this example as follows:
dijrepresenting the development time of the jth development task of the ith project; a. theijRepresenting a research and development task TijAll immediately preceding tasks of (2) are set, only set AijAll the research and development tasks are completed, and the research and development task TijCould go on, research and development task TijAssigned to a developer k;
Figure BDA0003142138960000167
and
Figure BDA0003142138960000166
respectively representing actual start time and completion time; ci 1Represents the actual completion time of item i; p is a radical ofiRepresents the time required for the h-th assembly of the ith high-end equipment; the same assembly time is required for high-end equipment of the same type, with the earliest start-up time
Figure BDA0003142138960000168
Actual completion time for its corresponding development project
Figure BDA0003142138960000169
And
Figure BDA00031421389600001610
respectively, high-end equipment EihStart-up time and completion time on assembly line l; cl 2Indicating the time for the assembly line to complete all assembly tasks.
In the research and development stage, all research and development tasks of the ith project are set
Figure BDA00031421389600001611
Each research and development task TijIs AijSet A ofijWith 0 or several research and development tasks immediately before, assuming TirIs set A immediately beforeijThe r-th immediate research and development task in (1), then there is a constraint relationship:
Figure BDA0003142138960000161
wherein the content of the first and second substances,
Figure BDA0003142138960000162
representing a research and development task TijThe earliest time of start-up of the plant,
Figure BDA0003142138960000163
representing a research and development task TirThe earliest start-up time. In the ith item, according to dijAnd AijCan obtain the research and development task TijThe earliest start-up time of all the research and development tasks can be obtained. If the research and development task TijThere is a constraint relationship:
Figure BDA0003142138960000164
then indicating a development task TirIn that
Figure BDA0003142138960000165
There is a time interval from the beginning to the end of the research and development task
Figure BDA0003142138960000171
Research and development task TirIn the interval
Figure BDA0003142138960000172
At the beginning of the study, research and development task TijIs/are as follows
Figure BDA0003142138960000173
Unchanged, therefore, the development task TirThere is the latest start-up time:
Figure BDA0003142138960000174
in the same way, research and development task TijThere is also the latest time of operation
Figure BDA0003142138960000175
Namely, the earliest start time and the latest start time exist in each research and development task of the research and development project i.
In a research and development project i, a plurality of paths exist from a first research and development task to a last research and development task, and when all the research and development tasks on a certain path have a relationship:
Figure BDA0003142138960000176
and then, the path is a critical path of the research and development project, and the sum of the research and development time of all the research and development tasks on the critical path is the maximum completion time of the project i. Defining a set of critical paths CPiRepresenting a set formed by sequencing all the research and development tasks on a certain critical path in the project i from small to large according to the earliest starting time, TioRepresentation set CPiThe o-th element in (1), defining a non-critical path set NPiRepresenting a set formed by other research and development tasks except all the research and development tasks on the critical path in the project i, TiqRepresentation set NPiThe qth element in (1). The following relationships coexist: CP (CP)i∪NPi＝TiI.e. a set of research and development tasks T which are a union of a critical path set and a non-critical path set and are project ii。
Inputting the solution to the decoding process to obtain the target value Cmax，CmaxRepresenting the total time span from development to assembly.
Defining local variables i 1-0, j 1-0;
SS 1: the research and development tasks assigned by the kth research and development personnel form a task set TAk；
SS 2: making k equal to k +1, judging whether k is more than a, if so, turning to the step SS3, otherwise, turning to the step SS 1;
SS 3: traversing the codes in the research and development stage in the solution from left to right and judging the i1 th codes, if the task T isijSet of immediately preceding tasks of AijIf the result is null, the step SS4 is carried out, otherwise, the step SS5 is carried out;
SS 4: grinding machineTask sending TijAt his assigned person xijIs j1 th, then its actual operating time
Figure BDA0003142138960000181
The actual completion time of the j1-1 th development task in the task set;
SS 5: research and development task TijAt his assigned person xijIs j1 th, then its actual operating time
Figure BDA0003142138960000182
The actual completion time of the j1-1 th development task in the task set, which is the task set A immediately beforeijMaximum value of actual completion time of the research and development task;
SS 6: research and development task TijActual time of completion
Figure BDA0003142138960000183
For its actual working time
Figure BDA0003142138960000184
And its development time dijSumming;
SS 7: making i1 be i1+1, judging whether i1 > n1 is true, if true, turning to a step SS8, and if not, turning to a step SS 3;
SS 8: the actual completion time of the last research and development task of a single project is the actual completion time of the project, so that the actual completion time of the project i can be known
Figure BDA0003142138960000185
Meanwhile, the actual completion time of the project i is the earliest start time of high-end equipment of the type i
Figure BDA0003142138960000186
SS 9: forming the high-end equipment assigned by the l assembly line into an equipment set EAl；
SS 10: sequencing all high-end equipment on an assembly line l from small to large according to the earliest start time of the high-end equipment;
SS 11: assembly line l equipment assembly EAlActual start-up time of high-end equipment at the j1 th position in the middle
Figure BDA0003142138960000187
For the earliest time of operation
Figure BDA0003142138960000188
Maximum value of actual completion time of the high-end equipment corresponding to the j1-1 th position. Actual time of completion thereof
Figure BDA0003142138960000189
For its actual working time
Figure BDA00031421389600001810
And assembly time piAnd (4) summing. Actual completion time of simultaneous assembly line l
Figure BDA00031421389600001811
Actual completion time of high-end equipment not less than j1 th position
Figure BDA00031421389600001812
SS 12: and (4) judging whether l is greater than b or not by changing l to l +1, if so, switching to the step SS13, and otherwise, switching to the step SS 9.
SS 13: according to formula Cmax≥max
Figure BDA00031421389600001910
The target value C can be obtainedmaxOutput CmaxOutput set TAkAnd EAlThe set is the assignment scheme corresponding to the initial solution. In particular, the method comprises the following steps of,
Figure BDA0003142138960000191
Figure BDA0003142138960000192
Figure BDA0003142138960000193
Figure BDA0003142138960000194
wherein, CmaxRepresents the total time span from development to assembly;
Figure BDA0003142138960000195
represents the minimum value of the earliest start time of all high-end equipment on the ith assembly line, namely the actual start time of the assembly line l;
Figure BDA0003142138960000196
representing the actual completion time of the research and development project i;
pirepresents the time required for the h-th assembly of the ith high-end equipment;
Figure BDA0003142138960000197
denotes the ith type of h-th high-end equipment EihWaiting time on assembly line l;
Figure BDA0003142138960000198
denotes the ith type of h-th high-end equipment EihActual start-up time on assembly line l;
Figure BDA0003142138960000199
denotes the nth high-end equipment E of the u-th typeuvThe actual completion time on the assembly line l.
S4 radicalInitial solution X in initial solution set X by variable neighborhood search algorithmLAnd carrying out Shaking operation to obtain a new solution X'.
The purpose of performing Shaking operation on the initial solution is to jump the current initial solution to another point in the feasible region range according to a certain rule, so that the partial optimization is prevented from being trapped in the current feasible region range, and the global searching capability of the algorithm is improved.
When Shaking operation is carried out, setting a disturbance neighborhood structure N of a variable neighborhood search algorithm Shaking operation1For the Lth initial solution X in the initial solution set XLAnd carrying out Shaking operation to obtain a new solution X'. The specific perturbation operation is as follows:
s41, obtaining the L-th initial solution X in the initial solution set XLThe variables I, J ═ 1 are defined,
s42, randomly generating integers in the range of the interval [1, n1], and assigning the integers to variables I and J;
s43, judging the initial solution XLWhether two research and development tasks corresponding to the I and J positions meet the conditions is judged: one task belongs to a critical path set task and the other task belongs to a non-critical path set task, if the condition is not met, returning to the step S42; otherwise, executing S44;
s44 exchange initial solution XLThe I and J elements in the solution are obtained to obtain an initial solution XLNew solution X after the first exchange1Is recorded as the first new solution X1；
S45, randomly generating integers in the range of the interval [ n1+1, n1+ n2], and assigning the integers to variables I and J;
s46 exchanging new solution X1The I and J elements in the solution are subjected to secondary exchange to obtain a new solution X2Record as the second new solution X2；
S47, comparing the structure N based on the disturbance neighborhood1The second new solution X is obtained2With the current initial solution XLIf the second new solution X2Corresponding CmaxValue less than or equal to the initial solution XLCorresponding CmaxValue, then output the second new solution X2(ii) a Otherwise, returning to S42;
s48, solving the second new solution X2And is assigned to X'.
S5, carrying out local search on the new solution X 'based on the current optional neighborhood structure set to obtain a local optimal solution X'.
Performing local search on the solution X 'in the Kth neighborhood structure in the current optional neighborhood structure set to obtain X'; the method comprises the following specific steps:
s51: setting the initial neighborhood structure K as 0, setting the initial search frequency G as 0 and setting the maximum search frequency G of a single neighborhood structure;
s52: and selecting the K-th neighborhood structure in the selectable neighborhood structure set to operate X ' to obtain X ', and reselecting the selectable neighborhood structure in the selectable neighborhood structure set to continue operating X ' when G is greater than or equal to G.
Specifically, in step S52, the selectable neighborhood structure includes the following five types:
neighborhood structure 1: defining variables i and j, randomly generating two integers in an interval, assigning the integers to two research and development tasks corresponding to the i, j and the ith and jth positions, wherein the two research and development tasks belong to a non-critical path set, and exchanging the serial numbers of research and development personnel corresponding to the ith and jth positions of a solution; randomly generating an integer in the interval range, assigning the integer to a variable i, j, and exchanging assembly line numbers corresponding to the ith and j positions of the solution;
neighborhood structure 2: defining variables i and j, randomly generating an integer in an interval range, assigning the integer to i, searching a position j which meets the condition and belongs to the key path set at the right side of the position i, inserting the number of a research and development staff corresponding to the position j-1 into the position i +1, and moving the number of the research and development staff corresponding to the position i +1 to the position j-2 to a position in the right direction; randomly generating an integer in the interval range and assigning the integer to i, randomly generating an integer in the interval range and assigning the integer to j, inserting the assembly line number corresponding to the position j-1 into the position i +1, and moving the assembly line number corresponding to the position i +1 to the position j-2 to the right by one position;
neighborhood structure 3: defining variables i and j, randomly generating an integer in an interval range, assigning the integer to i, searching a position j which meets the condition and belongs to the key path set at the right side of the position i, inserting the number of a research and development staff corresponding to the position i +1 into the position j-1, and moving the number of the research and development staff corresponding to the position i +2 to the position j-1 to a position left; randomly generating an integer in the interval range and assigning the integer to i, randomly generating an integer in the interval range and assigning the integer to j, inserting the assembly line number corresponding to the position i +1 into the position j-1, and moving the assembly line number corresponding to the position i +2 to the position j-1 to the left by one position;
neighborhood structure 4: defining variables i and j, randomly generating an integer in an interval range, assigning the integer to i, searching a position j which meets the condition and belongs to the key path set at the right side of the position i, searching the position j of which the task corresponding to the position belongs to the key path set, and performing reverse order processing on the numbers of all research and development personnel corresponding to the position i +1 to the position j-1; randomly generating integers in the interval range, assigning the integers to a variable i, j and meeting conditions, and performing reverse order processing on all assembly line numbers corresponding to the position i +1 to the position j-1;
neighborhood structure 5: defining variables i, j and k, assigning the element value of the ith position to k, randomly generating a research and development personnel number in an interval range and assigning the number to a variable j, randomly generating an integer in the interval range and assigning the integer to a variable i, and changing the value of the element of the ith position into the value of the variable j; and assigning the value of the element at the ith position to k, randomly generating an assembly line number in the interval range and assigning the assembly line number to a variable j, randomly generating an integer in the interval range and assigning the integer to a variable i, and changing the value of the element at the ith position into the value of the variable j.
S6, comparing the initial solution XLCorresponding to CmaxC whose value corresponds to the local optimal solution X ″maxThe size of the value, if X' corresponds to CmaxValue less than XLCorresponding to CmaxThe value, K is made 0 and X "is assigned to XLCalculating the fitness of the neighborhood structure in the selectable neighborhood structure set; if not, let K be K +1, and execute S7.
When calculating the adaptability of the neighborhood structure in the optional neighborhood structure set, calculating the adaptability of the neighborhood structure in the optional neighborhood structure set according to a formula
Figure BDA0003142138960000221
Calculating the fitness value of the neighborhood structure, and calculating to obtain the fitness alpha of the neighborhood structure with the latest solution X ═ alpha + delta alpha; where α represents the fitness value of the neighborhood structure.
S7, judging whether K is less than or equal to (NS) or not, and if so, turning to S5; if not, let L be L +1, and go to S8.
S8, judging that L is less than or equal to N0If yes, making L equal to L +1, and going to S4; otherwise, the neighborhood structures are sorted and updated again based on the fitness of the optional neighborhood structures in the optional neighborhood structure set, and then the process goes to S9.
The number and the sequence of the neighborhood structures of the variable neighborhood searching algorithm are kept unchanged in the whole iteration process, and only when a solution better than the current optimal solution is found in a certain neighborhood structure, the first neighborhood structure is jumped back again to perform local searching again. In order to retain a more effective neighborhood structure and simultaneously reject a neighborhood structure with a poor effect, the fitness is added into a variable neighborhood search algorithm, and the neighborhood structure is re-screened and sorted according to the self fitness. Specifically, when the neighborhood structure is sorted and updated, the method comprises the following steps:
s81, moving the neighborhood structure with the minimum fitness alpha in the current optional neighborhood structure set N to the optional neighborhood structure set N'. If the fitness degrees alpha of a plurality of neighborhood structures are the same and are all the minimum, one neighborhood structure is randomly selected from the plurality of neighborhood structures and moved to the alternative neighborhood structure set N'.
S82, judging the number of neighborhood structures in the current optional neighborhood structure set N, if the number is less than the minimum Number (NS) of neighborhood structures in the optional neighborhood structure setminAnd randomly selecting a plurality of neighborhood structures from the alternative neighborhood structure set N' and adding the neighborhood structures into the current alternative neighborhood structure set N.
S84, the neighborhood structure is reordered and updated according to the fitness alpha of the neighborhood structure in the current optional neighborhood structure set N.
S9, judging whether the current iteration number Iter is larger than the maximum iteration number ItermaxIf yes, go to S10; if not greater thanLet Iter be Iter +1, K be 0, and L be 0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting the global optimal solution Xbest。
The output global optimal solution is the global optimal initial solution XbestOptimal initial solution XbestAvailable set TAkAnd EAlWherein, TAkRepresenting a set of tasks, EA, formed from the development tasks assigned by the kth developerlRepresenting the formation of high-end equipment assigned by the l assembly line into an equipment set EAlSet TAkAnd EAlThat is, the final assignment plan, the enterprise may perform a two-stage development-manufacturing development and equipment job of high-end equipment in accordance with the plan.
Therefore, the whole process of developing the resource allocation and optimizing the scheduling method of the high-end equipment based on the budget constraint is completed.
In summary, compared with the prior art, the method has the following beneficial effects:
the technical scheme of the invention is that input parameters of a variable neighborhood search algorithm are set based on research and development task data of a high-end equipment research and development stage and equipment data of a manufacturing stage; then setting execution parameters of a variable neighborhood search algorithm; initializing an initial solution set of the algorithm and solving for an initial solution X in the initial solution setLShaking operation is carried out to obtain a new solution X ', then local search is carried out on the new solution X' in the selectable neighborhood structure set to obtain an optimal solution X ', and whether the optimal solution X' is superior to the initial solution X or not is comparedLContinuously iterating and finally outputting the global optimal solution XbestAnd according to the global optimal solution XbestAnd carrying out research, development and manufacturing work on the corresponding research, development and manufacturing scheme. According to the technical scheme, when a high-end equipment enterprise considers budget constraint conditions to perform high-end equipment development resource dynamic configuration and collaborative optimization scheduling, an approximate optimal solution and a corresponding balanced resource configuration strategy scheme can be rapidly and accurately obtained, two objectives of solution time and solution speed are considered, and collaborative optimization scheduling can be effectively performed on resources in a research and development stage and a manufacturing stage, so that the maximum degree of improvement is achievedResource utilization and research, development and manufacturing cooperation efficiency of high-end equipment enterprises;
according to the technical scheme, the initial solution is subjected to Shaking operation, the current initial solution is jumped to another point in the feasible region range according to a certain rule, the condition that the local optimum is trapped in the current feasible region range is avoided, and the global search capability of the algorithm is improved;
according to the technical scheme, the fitness of the neighborhood structure is calculated, then the neighborhood structure is re-screened and sorted and updated according to the fitness of the neighborhood structure, the more effective neighborhood structure can be reserved, meanwhile, the neighborhood structure with a poor effect is eliminated, and the speed and the accuracy in solving the optimal solution are increased.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (8)

1. A budget constraint-based high-end equipment development resource allocation and optimal scheduling method is characterized by comprising the following steps:
s1, setting input parameters of a variable neighborhood search algorithm based on research and development task data, research and development personnel data, equipment data and assembly line data; the input parameters include:
current available budget B; the number m of research and development projects in the research and development stage; the type number m of high-end equipment in the manufacturing stage; the total number of all development tasks n1 for all development projects in the development phase; total number n2 of all kinds of high-end equipment requiring mass assembly at the manufacturing stage; initial number of developers a in the development phase0The unit cost of the developer can be increased to B1; number of initial assembly lines in the manufacturing stage b0(ii) a The assembly line cost can be increased by B2；
S2, setting operation parameters of a variable neighborhood searching algorithm; the operating parameters specifically include:
maximum number of iterations Iter of the algorithmmax(ii) a Number N of initial solutions in initial solution set0(ii) a Minimum number of Neighborhood Structures (NS) in selectable neighborhood structure setmin(ii) a A number of Neighborhood Structures (NS) in the current set of selectable neighborhood structures; k of the kth neighborhood structure is 0; the L of the lth initial solution is 0, and the initial fitness value of the neighborhood structure is α;
s3, coding the research and development task data and the equipment data based on a variable neighborhood search algorithm to obtain an initial solution set X; then, each solution in the initial solution set X is decoded, and C corresponding to each initial solution is obtainedmaxA value; wherein, CmaxThe value represents the total development-assembly time span;
s4, performing initial solution X in the initial solution set X based on variable neighborhood search algorithmLCarrying out Shaking operation to obtain a new solution X';
s5, carrying out local search on the new solution X 'based on the current optional neighborhood structure set to obtain a local optimal solution X';
s6, comparing the initial solution XLCorresponding to CmaxC whose value corresponds to the local optimal solution X ″maxThe size of the value, if X' corresponds to CmaxValue less than XLCorresponding to CmaxThe value, K is made 0 and X "is assigned to XLCalculating the fitness of the neighborhood structure in the selectable neighborhood structure set; if not, let K be K +1, and execute S7;
s7, judging whether K is less than or equal to (NS) or not, and if so, turning to S5; if not, let L be L +1, and go to S8;
s8, judging that L is less than or equal to N0If yes, go to S4; otherwise, sorting and updating the neighborhood structure again based on the fitness of the optional neighborhood structure in the optional neighborhood structure set, and then turning to S9;
s9, judging whether the current iteration number Iter is larger than the maximum iteration number ItermaxIf yes, go to S10; if not, let Iter be Iter +1, K be 0, and L be 0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting the global optimal solution Xbest。
2. The method of claim 1, wherein the encoding the development task data and equipment data based on a variable neighborhood search algorithm to obtain an initial solution set X in S3 comprises:
s31, defining variables a, b, a1Where a denotes the number of finally available developers, b denotes the number of finally available assembly lines, a1Represents the maximum developer that can be added under budget B;
s32, defining a new initial solution X0Assigning the values of a and b to the initial solution X0At positions n1+ n2+1 and n1+ n2+2, the codes of the development stage and the manufacturing stage are re-randomly generated according to a and b, and all the initial solutions X are solved0Adding the solution into an initial solution set X;
s33, judging whether the number of the initial solutions in the initial solution set X is larger than the number N of the initial solutions in the initial solution set0If not, returning to S31 to continue generating the initial solution, otherwise, outputting the initial solution set X.
3. The method of claim 1, wherein C ismaxThe values are:
Figure FDA0003142138950000031
Figure FDA0003142138950000032
Figure FDA0003142138950000033
Figure FDA0003142138950000034
wherein, CmaxRepresents the total time span from development to assembly;
Figure FDA0003142138950000035
represents the minimum value of the earliest start-up time of all high-end equipment on the ith assembly line;
Figure FDA0003142138950000036
representing the actual completion time of the research and development project i;
pirepresents the time required for the h-th assembly of the ith high-end equipment;
Figure FDA0003142138950000037
denotes the ith type of h-th high-end equipment EihWaiting time on assembly line l;
Figure FDA0003142138950000038
indicates the ith high end of the ith typeEquipment EihActual start-up time on assembly line l;
Figure FDA0003142138950000039
denotes the nth high-end equipment E of the u-th typeuvThe actual completion time on the assembly line l.
4. The method according to claim 1, wherein the initial solution X in the initial solution set X is searched based on a variable neighborhood search algorithm in S4LPerforming a Shaking operation to obtain a new solution X' includes:
s41, obtaining the L-th initial solution X in the initial solution set XLThe variables I, J ═ 1 are defined;
s42, randomly generating integers in the range of the interval [1, n1], and assigning the integers to variables I and J;
s43, judging the initial solution XLWhether two research and development tasks corresponding to the I and J positions meet the conditions is judged: one task belongs to a critical path set task and the other task belongs to a non-critical path set task, if the condition is not met, returning to the step S42; otherwise, executing S44;
s44 exchange initial solution XLThe I and J elements in the solution are obtained to obtain an initial solution XLNew solution X after the first exchange1Is recorded as the first new solution X1；
S45, randomly generating integers in the range of the interval [ n1+1, n1+ n2], and assigning the integers to variables I and J;
s46 exchanging new solution X1The I and J elements in the solution are subjected to secondary exchange to obtain a new solution X2Record as the second new solution X2；
S47, comparing the structure N based on the disturbance neighborhood1The second new solution X is obtained2With the current initial solution XLIf the second new solution X2Corresponding CmaxValue less than or equal to the initial solution XLCorresponding CmaxValue, then output the second new solution X2(ii) a Otherwise, returning to S42;
s48, solving the second new solution X2And is assigned to X'.
5. The method of claim 1, wherein the step of locally searching the new solution X' based on the current optional neighborhood structure set to obtain the locally optimal solution X ″ in S5 includes:
s51: setting the initial neighborhood structure K as 0, setting the initial search frequency G as 0 and setting the maximum search frequency G of a single neighborhood structure;
s52: and selecting the K-th neighborhood structure in the selectable neighborhood structure set to operate X ' to obtain X ', and reselecting the selectable neighborhood structure in the selectable neighborhood structure set to continue operating X ' when G is greater than or equal to G.
6. The method of claim 5, wherein the selectable neighborhood structure in S52 comprises:
neighborhood structure 1: defining variables i and j, randomly generating two integers in an interval [1, n1], assigning values to two research and development tasks corresponding to the ith and j positions of the i, j and exchanging the serial numbers of research and development personnel corresponding to the ith and j positions of the solution, wherein the two research and development tasks belong to a non-critical path set; randomly generating integers in the range of the intervals [ n1+1, n1+ n2], assigning the integers to variables i and j, and exchanging assembly line numbers corresponding to the ith and j positions of the solution;
neighborhood structure 2: defining a variable i, j, randomly generating an integer within the range of the interval [1, n1], assigning the integer to i, searching a position j meeting the condition that j-i is more than or equal to 3 and the task corresponding to the position belongs to the key path set on the right side of the position i, inserting the number of a developer corresponding to the position j-1 into the position i +1, and moving the number of the developer corresponding to the position i +1 to the position j-2 to a position rightward; randomly generating an integer in the range of the interval [ n1+1, n1+ n2-4] and assigning the integer to i, randomly generating an integer in the range of the interval [ i +4, n2] and assigning the integer to j, inserting the assembly line number corresponding to the position j-1 into the position i +1, and moving the assembly line number corresponding to the position i +1 to the position j-2 to the right by one position;
neighborhood structure 3: defining a variable i, j, randomly generating an integer within the range of [1, n1], assigning the integer to i, searching a position j meeting the condition that j-i is more than or equal to 3 and the task corresponding to the position belongs to the key path set on the right side of the position i, inserting the number of a developer corresponding to the position i +1 into the position j-1, and moving the number of the developer corresponding to the position i +2 to the position j-1 to the left by one position; randomly generating an integer in the range of the interval [ n1+1, n1+ n2-4] and assigning the integer to i, randomly generating an integer in the range of the interval [ i +4, n2] and assigning the integer to j, inserting the assembly line number corresponding to the position i +1 into the position j-1, and moving the assembly line number corresponding to the position i +2 to the position j-1 by a position to the left;
neighborhood structure 4: defining a variable i, j, randomly generating an integer within the range of [1, n1], assigning the integer to i, searching a position j meeting the condition that j-i is more than or equal to 3 and the task corresponding to the position belongs to the key path set on the right side of the position i, and performing reverse order processing on the numbers of all research and development personnel corresponding to the position between the position i +1 and the position j-1; randomly generating integers in the range of the intervals [ n1+1, n1+ n2], assigning the integers to a variable i, j and satisfying the condition that j-i is more than or equal to 3, and performing reverse processing on all assembly line numbers corresponding to the positions from i +1 to j-1;
neighborhood structure 5: defining variables i, j and k, assigning the element value of the n1+ n2+1 position to k, randomly generating a research and development personnel number in the range of the interval [1, k ] and assigning the number to a variable j, randomly generating an integer in the range of the interval [1, n1] and assigning the integer to a variable i, and changing the value of the element at the ith position into the value of the variable j; and assigning the value of the element at the n1+ n2+2 position to k, randomly generating an assembly line number within the range of the interval [1, k ] and assigning the assembly line number to a variable j, randomly generating an integer within the range of the interval [ n1+1, n1+ n2] and assigning the integer to a variable i, and changing the value of the element at the ith position into the value of the variable j.
7. The method according to claim 1, wherein the reordering and updating the neighborhood structure based on the fitness of the selectable neighborhood structures in the set of selectable neighborhood structures in S8 comprises:
s81, moving the neighborhood structure with the minimum fitness alpha in the current optional neighborhood structure set N to an optional neighborhood structure set N'; if the fitness degrees alpha of a plurality of neighborhood structures are the same and are all the minimum, randomly selecting one neighborhood structure from the plurality of neighborhood structures and moving the selected neighborhood structure into an alternative neighborhood structure set N';
s82, judging the number of neighborhood structures in the current optional neighborhood structure set N, if the number is less than the minimum Number (NS) of neighborhood structures in the optional neighborhood structure setminRandomly selecting a plurality of neighborhood structures from the alternative neighborhood structure set N' and adding the neighborhood structures into the current optional neighborhood structure set N;
s84, the neighborhood structure is reordered and updated according to the fitness alpha of the neighborhood structure in the current optional neighborhood structure set N.
8. The method of claim 1, wherein said is that a global optimal solution X is output in S10bestThe method comprises the following steps: set TAkAnd EAlWherein, TAkRepresenting a set of tasks, EA, formed from the development tasks assigned by the kth developerlRepresenting the formation of high-end equipment assigned by the l assembly line into an equipment set EAl。
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