CN113642763B - High-end equipment development resource allocation and optimal scheduling method based on budget constraint - Google Patents

High-end equipment development resource allocation and optimal scheduling method based on budget constraint Download PDF

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CN113642763B
CN113642763B CN202110743571.4A CN202110743571A CN113642763B CN 113642763 B CN113642763 B CN 113642763B CN 202110743571 A CN202110743571 A CN 202110743571A CN 113642763 B CN113642763 B CN 113642763B
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裴军
李占印
杨善林
周娅
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Hefei University of Technology
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Abstract

The invention provides a high-end equipment development resource allocation and optimization scheduling method based on budget constraint, and relates to the technical fields of development task scheduling and equipment assembly scheduling. The technical scheme of the invention is that firstly, input parameters of a variable neighborhood search algorithm are set based on high-end equipment research and development task data and equipment data; setting execution parameters; initializing an initial solution set of an algorithm and performing initial solution X on the initial solution set L Performing a Shaking operation to obtain a new solution X ', performing local search on the new solution X ' in the selectable neighborhood structure set to obtain an optimal solution X ", and comparing whether the optimal solution X ' is superior to the initial solution X L And continuously iterating to finally output a global optimal solution X best And according to the global optimal solution X best Corresponding research and development and manufacturing schemes perform research and manufacturing work. When budget constraint is considered, the technical scheme can rapidly and accurately obtain the approximate optimal solution and the corresponding balanced resource allocation strategy scheme, so that the resource utilization rate of enterprises and the optimization efficiency of research, development and manufacturing are improved.

Description

High-end equipment development resource allocation and optimal scheduling method based on budget constraint
Technical Field
The invention relates to the technical field of research and development task scheduling and equipment assembly scheduling, in particular to a high-end equipment research and development resource allocation and optimization scheduling method based on budget constraint.
Background
Because of the characteristics of complex structure, diversified demands, custom-made and the like, the high-end equipment can be assembled in small batches after being researched and developed. The development stage of one type of high-end equipment comprises a plurality of development tasks, the development tasks have a close-front-close-back constraint relationship, all the development tasks form a development network diagram, and the manufacturing stage is to assemble parts determined by the development design in an assembly plant after the high-end equipment completes development. In practical situations, there are often multiple types of high-end equipment to be developed and assembled simultaneously, and when the resources such as the developer and the assembly line cannot complete the plan according to the delivery date constraint, a fixed budget is required to be input to increase the number of the developer and the assembly line so as to face the emergency demands possibly existing in the future.
Currently, aiming at the problem of optimizing and scheduling in two stages of research and development-manufacturing of high-end equipment, a precise algorithm, a heuristic method or an artificial intelligence algorithm is adopted for solving. When the condition of budget constraint is needed to be considered, the complexity of the problem is greatly increased, so that the prior related technology cannot solve, or an optimal solution can be solved in a short time, namely, the two targets of solving time and solving speed cannot be considered at the same time, thereby influencing the production work of two stages of research and development-manufacturing of high-end equipment.
It can be seen that the existing high-end equipment development-manufacturing two-stage optimal scheduling technology cannot quickly and accurately calculate the optimal solution when considering budget constraints.
Disclosure of Invention
(one) solving the technical problems
Aiming at the defects of the prior art, the invention provides a resource allocation and optimal scheduling method for developing high-end equipment based on budget constraint, which solves the problem that the prior art cannot quickly and accurately calculate the optimal solution when considering the budget constraint.
(II) technical scheme
In order to achieve the above purpose, the invention is realized by the following technical scheme:
the invention provides a high-end equipment development resource allocation and optimization scheduling method based on budget constraint, 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:
the currently available budget B; the number m of development projects in the development stage; the number of types m of high-end equipment in the manufacturing stage; all in the research and development stageThe total number n1 of all the development tasks of the development project; the total number n2 of all kinds of high-end equipment required to be assembled in batches in the manufacturing stage; initial developer quantity a in development stage 0 The unit cost of the research personnel can be increased to be B1; initial assembly line quantity b in manufacturing stage 0 The method comprises the steps of carrying out a first treatment on the surface of the The added cost of the assembly line is B 2 ；
S2, setting operation parameters of a variable neighborhood search algorithm; the operation parameters specifically include:
maximum iteration number Iter of algorithm max The method comprises the steps of carrying out a first treatment on the surface of the Number of initial solutions N in initial solution set 0 The method comprises the steps of carrying out a first treatment on the surface of the Minimum Number (NS) of neighbor structures in a set of selectable neighbor structures min The method comprises the steps of carrying out a first treatment on the surface of the The number of Neighbor Structures (NS) in the set of currently selectable neighbor structures; k=0 for the kth neighborhood structure; l=0 of the L-th initial solution, the initial fitness value α of the neighborhood structure;
s3, encoding 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 decoding each solution in the initial solution set X, and obtaining C corresponding to each initial solution max A value; wherein C is max Values represent development-assembly total time span;
s4, carrying out initial solution X in initial solution set X based on variable neighborhood search algorithm L Performing a Shaking operation to obtain a new solution X';
s5, carrying out local search on the new solution X 'based on the current selectable neighborhood structure set to obtain a local optimal solution X';
s6, comparing the initial solution X L Corresponding C max C with value corresponding to the locally optimal solution X' max The magnitude of the value C corresponding to X' max A value less than X L Corresponding C max Let k=0 and assign X "to X L Calculating the adaptability of the neighborhood structure in the selectable neighborhood structure set; if not, let k=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=l+1 and turn S8;
s8, judging that L is less than or equal to N 0 If so, let l=l+1 and go to S4; otherwise, based on the set of optional neighborhood structuresThe adaptability of the optional neighborhood structure in the step (a) is used for sequencing and updating the neighborhood structure again, and then S9 is carried out;
s9, judging whether the current iteration number Iter is larger than the maximum iteration number Iter max If the number is greater than S10; if not, let Iter=Iter+1, K=0, L=0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting a global optimal solution X best 。
Preferably, the encoding the development task data and the equipment data based on the variable neighborhood search algorithm in S3 to obtain an initial solution set X includes:
s31, defining variables a, b, a 1 Wherein a represents the number of ultimately available developers, b represents the number of ultimately available assembly lines, a 1 Representing the maximum developer that can be increased under budget B;
s32, defining new initial solution X 0 Assigning values of a and b to initial solutions X 0 In the positions n1+n2+1 and n1+n2+2, the code of the development phase and the production phase is randomly generated again according to a, b, and all the initial solutions X are obtained 0 Adding 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 set 0 If not, returning to S31 to continue generating the initial solution, otherwise, outputting the initial solution set X.
Preferably, the C max The values are:
Figure BDA0003142138960000041
Figure BDA0003142138960000042
Figure BDA0003142138960000043
Figure BDA0003142138960000044
wherein C is max Representing the total time span from development to assembly;
Figure BDA0003142138960000045
a minimum value representing the earliest start-up time of all high-end equipment on the first equipment line;
Figure BDA0003142138960000046
representing the actual completion time of the development project i;
p i representing the time required for the h-th assembly of the i-th high-end equipment;
Figure BDA0003142138960000047
represents an ith high-end equipment E of an ith type ih Waiting time on assembly line l;
Figure BDA0003142138960000048
represents an ith high-end equipment E of an ith type ih Actual start time on assembly line l;
Figure BDA0003142138960000049
the v-th high-end equipment E representing the u-th type uv The actual finishing time on the assembly line l.
Preferably, the S4 is based on a variable neighborhood search algorithm for an initial solution X in the initial solution set X L Performing the Shaking operation to obtain a new solution X' includes:
s41, obtaining the L-th initial solution X in the initial solution set X L Defining the variables I, j=1;
s42, randomly generating integers in the range of the interval [1, n1], and assigning the integers to variables I and J;
s43, judging initial solution X L Whether two research and development tasks corresponding to the I, J positions meet the condition: one of the tasks belongs to a critical path set task and the other task belongs to a non-critical path set task, and if the condition is not satisfied, returning to S42; otherwise, executing S44;
s44, exchange initial solution X L The I, J th element of the solution X is obtained L New solution X after first exchange 1 Recorded as a first new solution X 1 ；
S45, randomly generating integers in the range of the interval [ n1+1, n1+n2], and assigning the integers to variables I and J;
s46, exchange new solution X 1 The I, J th element of the new solution X after the second exchange is obtained 2 Recorded as the second new solution X 2 ；
S47, comparing N based on disturbance neighborhood structure 1 The obtained second new solution X 2 From the current initial solution X L If the second new solution X 2 C corresponding to max The value is less than or equal to the initial solution X L C corresponding to max The value is then output a second new solution X 2 The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to S42;
s48, solving the second new solution X 2 Assigned to X'.
Preferably, in the step S5, performing the local search on the new solution X' based on the current selectable neighborhood structure set to obtain a local optimal solution x″ includes:
s51: let the initial neighborhood structure k=0, the initial search times g=0, the maximum search times G of the single neighborhood structure;
S52: and selecting the Kth neighborhood structure in the selectable neighborhood structure set to operate X ', obtaining X ", and when G is more than or equal to G, reselecting the selectable neighborhood structure in the selectable neighborhood structure set to continue operating X'.
Preferably, the optional neighborhood structure in S52 includes:
neighborhood structure 1: defining variables i and j, randomly generating two integers in an interval, assigning the two integers to the research and development tasks corresponding to i, j, i and j positions, wherein the two research and development tasks belong to a non-critical path set, and the i, j positions of the exchange solution correspond to the research and development personnel numbers; randomly generating integers in the interval range, assigning the integers to the variables i and 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 a range of the interval, assigning the integer to i, searching the right side of the i for a position j meeting the condition and belonging to the critical path set, inserting the number of the research personnel corresponding to the position j-1 into the position i+1, and moving the number of the research personnel corresponding to the positions i+1 to the position j-2 to the right by one position; randomly generating an integer in a range and assigning the integer to i, randomly generating an integer in the 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 a range of the interval, assigning the integer to i, searching the right side of the position i for a position j meeting the condition and belonging to the critical path set, inserting the number of the research personnel corresponding to the position i+1 into the position j-1, and moving the number of the research personnel corresponding to the position i+2 to the position j-1 to the left by one position; randomly generating an integer in a range and assigning the integer to i, randomly generating an integer in the 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 a range of the interval, assigning the integer to i, searching the right side of the i for a position j meeting a condition and having a task corresponding to the position belonging to the critical path set, and carrying out reverse processing on all the numbers of the research personnel corresponding to the positions i+1 to j-1; randomly generating integers in the interval range, assigning the integers to the variables i and j, meeting the conditions, and carrying out reverse order processing on all assembly line numbers corresponding to the positions 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 developer number in an interval range and assigning the developer number to the variable j, randomly generating an integer in the interval range and assigning the integer to the variable i, and changing the value of the element of the ith position into the value of the variable j; and (3) assigning the element value of the first position to k, randomly generating an assembly line number in an 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 of the first position into the value of the variable j.
Preferably, in S8, the reordering and updating the neighborhood structure based on the fitness of the optional neighborhood structure in the optional neighborhood structure set includes:
s81, moving a 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 alpha of a plurality of neighborhood structures is the same and is the minimum, randomly selecting one neighborhood structure from the plurality of neighborhood structures and moving the neighborhood structure to an alternative neighborhood structure set N';
s82, judging the number of neighborhood structures in the current selectable neighborhood structure set N, if the number is smaller than the minimum Number (NS) of the neighborhood structures in the selectable neighborhood structure set min Randomly selecting a plurality of neighborhood structures from the candidate neighborhood structure set N', and adding the neighborhood structures into the current candidate neighborhood structure set N;
S84, reordering and updating the neighborhood structure according to the adaptability alpha of the neighborhood structure in the current selectable neighborhood structure set N.
Preferably, the method outputs the globally optimal solution X in S10 best Comprising the following steps: set TA k And EA (ethylene oxide) l Wherein TA k Representing a set of tasks formed by the development tasks assigned by the kth developer, EA l Representing that the high-end equipment assigned to the first equipment line is formed into an equipment set EA l 。
(III) beneficial effects
The invention provides a high-end equipment development resource allocation and optimal scheduling method based on budget constraint. Compared with the prior art, the method has the following beneficial effects:
1. the invention firstlySetting 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; setting execution parameters of a variable neighborhood search algorithm; initializing an initial solution set of an algorithm and performing initial solution X on the initial solution set L Performing a Shaking operation to obtain a new solution X ', performing local search on the new solution X ' in the selectable neighborhood structure set to obtain an optimal solution X ", and comparing whether the optimal solution X ' is superior to the initial solution X L And continuously iterating to finally output a global optimal solution X best And according to the global optimal solution X best Corresponding research and development and manufacturing schemes perform research and manufacturing work. When the high-end equipment enterprises consider budget constraint conditions to carry out dynamic configuration and collaborative optimization scheduling of high-end equipment development resources, the technical scheme can rapidly and accurately obtain an approximate optimal solution and a corresponding balanced resource configuration strategy scheme, and meanwhile, the two targets of solving time and solving speed are considered, so that the resources in the development stage and the manufacturing stage can be effectively subjected to collaborative optimization scheduling, and the resource utilization rate and the research-development-manufacturing collaborative efficiency of the high-end equipment enterprises are improved to the greatest extent;
2. According to the invention, the initial solution is subjected to the Shaking operation, the current initial solution is jumped to another point in the feasible region according to a certain rule, so that the situation that local optimum is trapped in the current feasible region is avoided, and the global searching capability of an algorithm is improved;
3. the method and the device calculate the adaptability of the neighborhood structure, then re-screen and order and update the neighborhood structure according to the adaptability of the neighborhood structure, so that the more effective neighborhood structure can be maintained, and meanwhile, the neighborhood structure with poor effect is removed, so that the speed and accuracy in solving the optimal solution are increased.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for developing resource allocation and optimizing scheduling of high-end equipment based on budget constraint according to an embodiment of the invention;
FIG. 2 is a diagram of encoding according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
According to the method for optimizing and scheduling the development resources of the high-end equipment based on the budget constraint, the problem that the optimal solution cannot be rapidly and accurately solved when the budget constraint is considered in the prior art is solved, the two aims of solving time and solving speed are simultaneously achieved when the optimizing and scheduling problem of the high-end equipment in two stages of development and manufacturing is solved, and production efficiency is improved.
The technical scheme in the embodiment of the application aims to solve the technical problems, and the overall thought is as follows:
in order to make an optimal high-end equipment research and development-manufacturing two-stage optimization scheduling scheme under the condition of considering a certain budget constraint, the technical scheme designs a variable neighborhood search algorithm, and the current initial solution is jumped to another point in a feasible region range according to a certain rule by carrying out a training operation on the initial solution obtained by coding, so that the problem of local optimization in the current feasible region range is avoided; in addition, the adaptability of the neighborhood structure is calculated, and then the neighborhood structure is subjected to rescreening, sorting and updating according to the adaptability of the neighborhood structure, so that the more effective neighborhood structure can be maintained, and meanwhile, the neighborhood structure with poor effect is removed, so that the speed and accuracy in solving the optimal solution are increased.
In order to better understand the above technical solutions, the following detailed description will refer to the accompanying drawings and specific embodiments.
The two stages of research and development and manufacturing of high-end equipment are set, the current available budget is B, and the allocation of the budget in the research and development stages and the manufacturing stage directly determines the number of finally available research and development personnel in the research and development stage and the number of finally available assembly lines in the manufacturing stage.
It should be noted that, in the manufacturing stage, one type of high-end equipment corresponds to one project network diagram in the development stage, and the finishing time of a project in the development stage is the earliest start-up time of the high-end equipment corresponding to the type of the project.
The invention provides a high-end equipment development resource allocation and optimization scheduling method based on budget constraint, which 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:
the currently available budget B; the number m of development projects in the development stage; the number of types m of high-end equipment in the manufacturing stage; the total number n1 of all the research and development tasks of all the research and development projects in the research and development stage; the total number n2 of all kinds of high-end equipment required to be assembled in batches in the manufacturing stage; initial developer quantity a in development stage 0 The unit cost of the research personnel can be increased to be B1; initial assembly line quantity b in manufacturing stage 0 The method comprises the steps of carrying out a first treatment on the surface of the The added cost of the assembly line is B 2 ；
S2, setting operation parameters of a variable neighborhood search algorithm; the operation parameters specifically include:
maximum iteration number Iter of algorithm max The method comprises the steps of carrying out a first treatment on the surface of the Number of initial solutions N in initial solution set 0 The method comprises the steps of carrying out a first treatment on the surface of the Minimum Number (NS) of neighbor structures in a set of selectable neighbor structures min The method comprises the steps of carrying out a first treatment on the surface of the The number of Neighbor Structures (NS) in the set of currently selectable neighbor structures; k=0 for the kth neighborhood structure; l=0 of the L-th initial solution, the initial fitness value α of the neighborhood structure;
s3, encoding the research and development task data and the equipment data based on a variable neighborhood search algorithm to obtain an initial solutionA set X; then decoding each solution in the initial solution set X, and obtaining C corresponding to each initial solution max A value; wherein C is max Values represent development-assembly total time span;
s4, carrying out initial solution X in initial solution set X based on variable neighborhood search algorithm L Performing a Shaking operation to obtain a new solution X';
s5, carrying out local search on the new solution X 'based on the current selectable neighborhood structure set to obtain a local optimal solution X';
s6, comparing the initial solution X L Corresponding C max C with value corresponding to the locally optimal solution X' max The magnitude of the value C corresponding to X' max A value less than X L Corresponding C max Let k=0 and assign X "to X L Calculating the adaptability of the neighborhood structure in the selectable neighborhood structure set; if not, let k=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=l+1 and turn S8;
s8, judging that L is less than or equal to N 0 If so, let l=l+1 and go to S4; otherwise, sequencing and updating the neighborhood structure again based on the adaptability of the selectable neighborhood structure in the selectable neighborhood structure set, and turning to S9;
s9, judging whether the current iteration number Iter is larger than the maximum iteration number Iter max If the number is greater than S10; if not, let Iter=Iter+1, K=0, L=0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting a global optimal solution X best 。
It can be seen that the technical scheme of the invention firstly sets the input parameters of the variable neighborhood search algorithm based on the research and development task data of the high-end equipment research and development stage and the equipment data of the manufacturing stage; setting execution parameters of a variable neighborhood search algorithm; initializing an initial solution set of an algorithm and performing initial solution X on the initial solution set L Performing a Shaking operation to obtain a new solution X ', performing local search on the new solution X ' in the selectable neighborhood structure set to obtain an optimal solution X ", and comparing whether the optimal solution X ' is superior to the initial solution X L And continuously iterating to finally output a global optimal solution X best And according to the global optimal solution X best Corresponding research and development and manufacturing schemes perform research and manufacturing work. According to the technical scheme, when the high-end equipment enterprises consider budget constraint conditions to carry out dynamic configuration and collaborative optimization scheduling of high-end equipment development resources, the approximately optimal solution and the corresponding balanced resource configuration strategy scheme can be rapidly and accurately obtained, meanwhile, the two targets of solving time and solving speed are considered, and the resources in the development stage and the manufacturing stage can be effectively subjected to collaborative optimization scheduling, so that the resource utilization rate of the high-end equipment enterprises and the efficiency of research, development and manufacturing collaborative are improved to the greatest extent.
The implementation of one embodiment of the present invention will be described in detail below in conjunction with an explanation of specific steps of 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:
the currently available budget B; the number m of development projects in the development stage; the number of types m of high-end equipment in the manufacturing stage; the total number n1 of all the research and development tasks of all the research and development projects in the research and development stage; the total number n2 of all kinds of high-end equipment required to be assembled in batches in the manufacturing stage; initial developer quantity a in development stage 0 The unit cost of the research personnel can be increased to be B1; initial assembly line quantity b in manufacturing stage 0 The method comprises the steps of carrying out a first treatment on the surface of the The added cost of the assembly line is B 2 。
Based on the research and development task data and the research and development personnel data of the high-end equipment research and development stage, the equipment data and the assembly line data of the manufacturing stage are set, and the input parameters of the variable neighborhood search algorithm are set. The method comprises the following steps: and acquiring research and development task data and research and development personnel data of the high-end equipment in a research and development stage, equipment data and assembly line data in a manufacturing stage, and setting input parameters of a variable neighborhood search algorithm. The input parameters of the variable neighborhood search algorithm include:
the number m of development projects in the development stage; the total number n1 of all the research and development tasks of all the research and development projects in the research and development stage; single sheetAll research and development task sets of individual projects
Figure BDA0003142138960000131
Wherein T is ij Jth development task representing ith project, < ->
Figure BDA0003142138960000132
Representing the number of development tasks contained in the ith project; initial developer quantity a in development stage 0 And maximum developer number a 1 Initial developer set->
Figure BDA0003142138960000133
Incremental developer set
Figure BDA0003142138960000134
P k Represents the kth developer, wherein k is more than or equal to 1 and less than or equal to a 1 When k > a 0 When the unit cost of the research personnel is increased to be B1;
The number m of types of high-end equipment in the manufacturing stage (since each development project corresponds to one type of high-end equipment, the number m of types of high-end equipment in the manufacturing stage and the number m of development projects in the development stage are both m); total number n2 of batch assembly of all kinds of high-end equipment in the manufacturing stage; all mass production of single type high-end equipment is integrated into
Figure BDA0003142138960000137
Wherein E is ih An h equipment representing an i-th high-end equipment,/->
Figure BDA0003142138960000138
Indicating the number of i-th high-end equipment to be assembled; initial assembly line quantity b in manufacturing stage 0 And maximum assembly line number b 1 Initial assembly line set
Figure BDA0003142138960000135
Addable assembly line set->
Figure BDA0003142138960000136
M l Represents the first assembly line, wherein 1.ltoreq.l.ltoreq.b 1 When l > b 0 When the assembly line cost can be increased is B 2 。
S2, setting operation parameters of a variable neighborhood search algorithm; the operation parameters specifically include:
maximum iteration number Iter of algorithm max ；
Number of initial solutions N in initial solution set 0 ；
Minimum Number (NS) of neighbor structures in a set of selectable neighbor structures min ；
The number of Neighbor Structures (NS) in the set of currently selectable neighbor structures;
k=0 for the kth neighborhood structure;
l=0 for the L-th initial solution;
an initial fitness value α of the neighborhood structure, where α= { α 1 ,α 2 ,...,α NS0 ,}＝{0,0,...,0}；
S3, encoding 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 decoding each solution in the initial solution set X, and obtaining C corresponding to each initial solution max A value; wherein C is max The values represent the development-assembly total time span.
1) And encoding 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 development stage and the manufacturing stage is based on the number of developers and the number of assembly lines, so in the process of generating the initial solution, firstly, budget needs to be allocated to the development stage and the manufacturing stage to determine the final number of developers and the number of assembly lines; second, a random initial solution is generated based on the outcome of the budget allocation.
According to the total number n1 of research and development tasks in the research and development stage and the total number n2 of batch assembly of all kinds of high-end equipment, the research and development stage of the high-end equipment is based on a variable neighborhood search algorithmEncoding the mission data and the equipment data at the manufacturing stage to produce a data stream comprising N 0 Initial solution set X of initial solutions. Referring to FIG. 2, each initial solution X in the initial solution set X 0 The system comprises three parts, wherein each code in the first part corresponds to a research and development personnel assigned by a research and development task, and the position corresponds to the earliest starting time sequence in a multi-project research and development network diagram; each code in the second part corresponds to an assembly line assigned by high-end equipment, and the position of each code corresponds to the earliest finishing sequence of the research and development network diagram; the third partial code represents the maximum number of developers and the maximum number of assembly lines that are ultimately available, the initial solution X that is generated 0 Can be expressed as:
Figure BDA0003142138960000141
wherein x is ij Representing personnel assigned by the j-th development task of the i-th project; y is ih An assembly line assigned by an h equipment representing an i high-end equipment; a, b represent the number of final developers and assembly lines, respectively. Specifically, the generating an initial solution set X process includes:
s31, defining variables a, b, a 1 . Wherein a represents the number of ultimately available developers, b represents the number of ultimately available assembly lines, a 1 Representing the largest developer that can increase under budget B.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003142138960000151
representing no more than +.>
Figure BDA0003142138960000152
Is the largest integer of (2); slave section (a) 0 ,a 0 +a 1 ]Is assigned to variable a, according to the formula +.>
Figure BDA0003142138960000153
Calculating the number of final assembly lines available, +.>
Figure BDA0003142138960000154
Representing nothingIs greater than->
Figure BDA0003142138960000155
Is the largest integer of (a).
S32, defining new initial solution X 0 Assigning values of a and b to initial solutions X 0 In the positions n1+n2+1 and n1+n2+2, the code of the development phase and the production phase is randomly generated again according to a, b, and all the initial solutions X are obtained 0 Added 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 set 0 If not, returning to S31 to continue generating the initial solution, otherwise, outputting the initial solution set X.
2) Then decoding each solution in the initial solution set X, and obtaining C corresponding to each initial solution max A value; wherein C is max The values represent the development-assembly total time span.
The decoding process is to calculate the assignment scheme represented by the solution according to the constraint in the actual scenario. Based on this assignment scheme, all developers complete the development projects 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, during the development stage, any developer cannot develop two development tasks at the same time, and after all the immediately preceding development tasks of a certain development task are completed, the development task can only be performed. During the assembly phase, neither assembly line can perform assembly of two high-end equipments at the same time.
The parameters are defined in this example as follows:
d ij the development time of the jth development task of the ith project is represented; a is that ij Representing a development task T ij For all immediately preceding tasks of (C), only when set A ij All the research and development tasks are completed, and the research and development task T ij Can only go on to develop task T ij Assigned to developer k;
Figure BDA0003142138960000167
and->
Figure BDA0003142138960000166
Respectively representing actual start time and finishing time; c (C) i 1 Representing the actual completion time of item i; p is p i Representing the time required for the h-th assembly of the i-th high-end equipment; the same assembly time is required for the high-end installation of the same type, the earliest start-up time >
Figure BDA0003142138960000168
The actual finishing time for its corresponding development project +.>
Figure BDA0003142138960000169
And->
Figure BDA00031421389600001610
Respectively represent high-end equipment E ih Start time and finish time on assembly line l; c (C) l 2 Indicating the time the assembly line completed all assembly tasks.
During the development phase, all the development task sets of the ith project
Figure BDA00031421389600001611
Each research and development task T ij Is set to be A ij Set A ij With 0 or several immediately preceding development tasks, provided T ir As the immediately preceding set A ij The constraint relation exists in the r-th immediately before development task:
Figure BDA0003142138960000161
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003142138960000162
representing a development task T ij Is the earliest start time of (2)>
Figure BDA0003142138960000163
Representing a development task T ir Is the earliest start-up time of (c). In item i, according to d ij And A ij Can get research and development task T ij The earliest start time of all development tasks can be obtained. If develop task T ij There is a constraint relationship:
Figure BDA0003142138960000164
then indicate development task T ir At the position of
Figure BDA0003142138960000165
At the beginning of the development task, there is a time interval
Figure BDA0003142138960000171
Research and development task T ir In section->
Figure BDA0003142138960000172
At the beginning, develop task T ij Is->
Figure BDA0003142138960000173
Unchanged, thus research and development task T ir There is the latest start-up time:
Figure BDA0003142138960000174
similarly, research and development task T ij There is also the latest start-up time
Figure BDA0003142138960000175
I.e., each development task of development project i has an earliest start time and a latest start time.
In development project i, there are multiple paths from the first development task to the last development task, and when all development tasks on a path have a relationship:
Figure BDA0003142138960000176
when the path is the critical path of the research and development project, the sum of the research and development time of all the research and development tasks on the critical path is the maximum finishing time of the project i. Defining critical path set CP i Representing a set formed by sequencing all research and development tasks on a certain critical path in the project i from small to large according to the earliest start time, T io Representing a set CP i The (o) th element of the set of non-critical paths NP is defined i Representing a set formed by other development tasks except all development tasks on a critical path in the project i, T iq Representing a collection NP i The q-th element of (b). The following relationships exist at the same time: CP (control program) i ∪NP i ＝T i I.e. the union of the critical path set and the non-critical path set is the research and development task set T of item i i 。
Inputting the solution to the target value C obtained in the decoding process max ，C max Representing the total time span from development to assembly.
Defining a local variable i1=0, and j1=0;
SS1: forming the research and development tasks assigned by the kth research and development personnel into a task set TA k ；
SS2: let k=k+1, judge whether to meet k > a, if yes, go to step SS3, otherwise go to step SS1;
SS3: traversing the development stage codes from left to right in the solution and judging the ith 1 code, if the task T ij Immediately preceding task set A ij If the signal is empty, turning to step SS4, otherwise turning to step SS5;
SS4: research and development task T ij Person x assigned thereto ij The position in the task set is j1 st, then its actual start time
Figure BDA0003142138960000181
Actual completion time of the j1-1 development task in the task set;
SS5: research and development task T ij Person x assigned thereto ij The position in the task set is j1 st, then its actual start time
Figure BDA0003142138960000182
The actual completion time of the j1-1 development task in the task set is the immediately preceding task set A ij Maximum value of actual finishing time of the development task; />
SS6: research and development task T ij Is the actual time of completion of (a)
Figure BDA0003142138960000183
For its actual start-up time->
Figure BDA0003142138960000184
And development time d ij And (3) summing;
SS7: let i1=i1+1, and judge whether i1 > n1 is true, if yes, go to step SS8, otherwise go to step SS3;
SS8: the actual completion time of the last development task of a single project is the actual completion time of the project, thereby knowing the actual completion time of project i
Figure BDA0003142138960000185
At the same time the actual finishing time of item i is also the earliest start-up time of high-end equipment of category i>
Figure BDA0003142138960000186
SS9: forming the high-end equipment assigned by the first equipment line into an equipment set EA l ；
SS10: sequencing all high-end equipment on an assembly line from small to large according to the earliest start time;
SS11: assembly line assembly EA l Actual start-up time of high-end equipment at j1 th position in the process
Figure BDA0003142138960000187
For its earliest start time->
Figure BDA0003142138960000188
And the j1-1 th positionMaximum of the actual finishing time of the high-end equipment. Its actual time of completion
Figure BDA0003142138960000189
For its actual start-up time->
Figure BDA00031421389600001810
With assembly time p i And (3) summing. At the same time the actual finishing time of the assembly line l +.>
Figure BDA00031421389600001811
Actual finishing time of high-end equipment not less than j1 st position +.>
Figure BDA00031421389600001812
SS12: let l=l+1, determine whether l > b is satisfied, if so, go to step SS13, otherwise go to step SS9.
SS13: according to formula C max ≥max
Figure BDA00031421389600001910
The target value C can be obtained max Output C max Output set TA k With EA l The set is the initial solution corresponding assignment scheme. In particular, the method comprises the steps of,
Figure BDA0003142138960000191
Figure BDA0003142138960000192
Figure BDA0003142138960000193
Figure BDA0003142138960000194
wherein C is max Representing the total time span from development to assembly;
Figure BDA0003142138960000195
the minimum value representing the earliest start time of all high-end equipment on the first assembly line, namely the actual start time of the assembly line;
Figure BDA0003142138960000196
representing the actual completion time of the development project i;
p i representing the time required for the h-th assembly of the i-th high-end equipment;
Figure BDA0003142138960000197
represents an ith high-end equipment E of an ith type ih Waiting time on assembly line l;
Figure BDA0003142138960000198
Represents an ith high-end equipment E of an ith type ih Actual start time on assembly line l;
Figure BDA0003142138960000199
the v-th high-end equipment E representing the u-th type uv The actual finishing time on the assembly line l.
S4, carrying out initial solution X in initial solution set X based on variable neighborhood search algorithm L The Shaking operation is performed to obtain a new solution X'.
The purpose of carrying out the Shaking operation on the initial solution is to jump the current initial solution to another point in the feasible domain range according to a certain rule, so as to avoid the local optimum in the current feasible domain range, thereby improving the global searching capability of the algorithm.
When the Shaking operation is carried out, a disturbance neighborhood structure N of the Shaking operation of the variable neighborhood search algorithm is set 1 For the L-th initial solution X in the initial solution set X L The Shaking operation is performed 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 X L The variables I, j=1,
s42, randomly generating integers in the range of the interval [1, n1], and assigning the integers to variables I and J;
s43, judging initial solution X L Whether two research and development tasks corresponding to the I, J positions meet the condition: one of the tasks belongs to a critical path set task and the other task belongs to a non-critical path set task, and if the condition is not satisfied, returning to S42; otherwise, executing S44;
S44, exchange initial solution X L The I, J th element of the solution X is obtained L New solution X after first exchange 1 Recorded as a first new solution X 1 ；
S45, randomly generating integers in the range of the interval [ n1+1, n1+n2], and assigning the integers to variables I and J;
s46, exchange new solution X 1 The I, J th element of the new solution X after the second exchange is obtained 2 Recorded as the second new solution X 2 ；
S47, comparing N based on disturbance neighborhood structure 1 The obtained second new solution X 2 From the current initial solution X L If the second new solution X 2 C corresponding to max A value less than or equal to the initial solution X L C corresponding to max The value is then output a second new solution X 2 The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to S42;
s48, solving the second new solution X 2 Assigned to X'.
S5, carrying out local search on the new solution X 'based on the current selectable neighborhood structure set to obtain a local optimal solution X'.
Carrying out local search on the solution X 'in the K-th neighborhood structure in the current selectable neighborhood structure set to obtain X'; the method comprises the following specific steps:
s51: let the initial neighborhood structure k=0, the initial search times g=0, the maximum search times G of the single neighborhood structure;
s52: and selecting the Kth neighborhood structure in the selectable neighborhood structure set to operate X ', obtaining X ", and when G is more than or equal to G, reselecting the selectable neighborhood structure in the selectable neighborhood structure set to continue operating X'.
Specifically, in step S52, the optional neighborhood structure includes the following five types:
neighborhood structure 1: defining variables i and j, randomly generating two integers in an interval, assigning the two integers to the research and development tasks corresponding to i, j, i and j positions, wherein the two research and development tasks belong to a non-critical path set, and the i, j positions of the exchange solution correspond to the research and development personnel numbers; randomly generating integers in the interval range, assigning the integers to the variables i and 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 a range of the interval, assigning the integer to i, searching the right side of the i for a position j meeting the condition and belonging to the critical path set, inserting the number of the research personnel corresponding to the position j-1 into the position i+1, and moving the number of the research personnel corresponding to the positions i+1 to the position j-2 to the right by one position; randomly generating an integer in a range and assigning the integer to i, randomly generating an integer in the 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 a range of the interval, assigning the integer to i, searching the right side of the position i for a position j meeting the condition and belonging to the critical path set, inserting the number of the research personnel corresponding to the position i+1 into the position j-1, and moving the number of the research personnel corresponding to the position i+2 to the position j-1 to the left by one position; randomly generating an integer in a range and assigning the integer to i, randomly generating an integer in the 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 a range of the interval, assigning the integer to i, searching the right side of the i for a position j meeting a condition and having a task corresponding to the position belonging to the critical path set, and carrying out reverse processing on all the numbers of the research personnel corresponding to the positions i+1 to j-1; randomly generating integers in the interval range, assigning the integers to the variables i and j, meeting the conditions, and carrying out reverse order processing on all assembly line numbers corresponding to the positions 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 developer number in an interval range and assigning the developer number to the variable j, randomly generating an integer in the interval range and assigning the integer to the variable i, and changing the value of the element of the ith position into the value of the variable j; and (3) assigning the element value of the first position to k, randomly generating an assembly line number in an 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 of the first position into the value of the variable j.
S6, comparing the initial solution X L Corresponding C max C with value corresponding to the locally optimal solution X' max The magnitude of the value C corresponding to X' max A value less than X L Corresponding C max Let k=0 and assign X "to X L Calculating the adaptability of the neighborhood structure in the selectable neighborhood structure set; if not, let k=k+1, and execute S7.
When calculating the adaptability of the neighborhood structure in the selectable neighborhood structure set, the method is based on the formula
Figure BDA0003142138960000221
Calculating the fitness value of the neighborhood structure, and calculating the fitness alpha=alpha+delta alpha of the neighborhood structure of the latest solution X'; 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=l+1 and go to S8.
S8, judging that L is less than or equal to N 0 If so, let l=l+1 and go to S4; otherwise, based on optional neighborThe adaptability of the optional neighborhood structure in the domain structure set reorders and updates the neighborhood structure, and then goes to S9.
Because the number and the sequence of the neighborhood structures of the variable neighborhood search algorithm are kept unchanged in the whole iterative process, only if a solution better than the current optimal solution is found in a certain neighborhood structure, the first neighborhood structure can be skipped back again, and the local search is performed again. In order to keep more effective neighborhood structures and reject neighborhood structures with poor effects, fitness is added in a variable neighborhood search algorithm, and the neighborhood structures are rescreened and ranked according to the fitness of the neighborhood structures. When the neighborhood structure is specifically ordered and updated, the method comprises the following steps:
s81, the neighborhood structure with the minimum fitness alpha in the current optional neighborhood structure set N is moved to an optional neighborhood structure set N'. If the fitness alpha of the plurality of neighborhood structures is the same and is the minimum, randomly selecting one neighborhood structure from the plurality of neighborhood structures and moving the neighborhood structure to the alternative neighborhood structure set N'.
S82, judging the number of neighborhood structures in the current selectable neighborhood structure set N, if the number is smaller than the minimum Number (NS) of the neighborhood structures in the selectable neighborhood structure set min And randomly selecting a plurality of neighborhood structures from the candidate neighborhood structure set N', and adding the neighborhood structures into the current candidate neighborhood structure set N.
S84, reordering and updating the neighborhood structure according to the adaptability alpha of the neighborhood structure in the current selectable neighborhood structure set N.
S9, judging whether the current iteration number Iter is larger than the maximum iteration number Iter max If the number is greater than S10; if not, let Iter=Iter+1, K=0, L=0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting a global optimal solution X best 。
The output global optimal solution is global optimal initial solution X best Optimal initial solution X best Available set TA k And EA (ethylene oxide) l Wherein TA k Representing a set of tasks formed by the development tasks assigned by the kth developer, EA l Representing that the high-end equipment assigned to the first equipment line is formed into an equipment set EA l Set TA k With EA l I.e., the final assignment scheme, by which the enterprise can perform two stages of development-manufacturing development and equipment work for high-end equipment.
The whole process of the high-end equipment development resource allocation and optimization scheduling method based on 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 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; setting execution parameters of a variable neighborhood search algorithm; initializing an initial solution set of an algorithm and performing initial solution X on the initial solution set L Performing a Shaking operation to obtain a new solution X ', performing local search on the new solution X ' in the selectable neighborhood structure set to obtain an optimal solution X ", and comparing whether the optimal solution X ' is superior to the initial solution X L And continuously iterating to finally output a global optimal solution X best And according to the global optimal solution X best Corresponding research and development and manufacturing schemes perform research and manufacturing work. When the high-end equipment enterprises consider budget constraint conditions to carry out dynamic configuration and collaborative optimization scheduling of high-end equipment development resources, the technical scheme can rapidly and accurately obtain an approximate optimal solution and a corresponding balanced resource configuration strategy scheme, and meanwhile, the two targets of solving time and solving speed are considered, so that the resources in the development stage and the manufacturing stage can be effectively subjected to collaborative optimization scheduling, and the resource utilization rate and the research-development-manufacturing collaborative efficiency of the high-end equipment enterprises are improved to the greatest extent;
According to the technical scheme, the initial solution is subjected to the Shaking operation, the current initial solution is jumped to another point in the feasible region according to a certain rule, so that the situation that local optimization is trapped in the current feasible region is avoided, and the global searching capability of an algorithm is improved;
according to the technical scheme, the adaptability of the neighborhood structure is calculated, then the neighborhood structure is subjected to rescreening and sorting updating according to the adaptability of the neighborhood structure, so that the more effective neighborhood structure can be maintained, and meanwhile, the neighborhood structure with poor effect is removed, so that the speed and accuracy in solving the optimal solution are increased.
It is noted that relational terms such as first and second, and the like are 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. Moreover, 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 one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the 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 scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. The method for developing resource allocation and optimizing scheduling of high-end equipment based on budget constraint 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:
the currently available budget B; the number m of development projects in the development stage; the number of types m of high-end equipment in the manufacturing stage; all of the research and development stagesThe total number n1 of all development tasks of the project; the total number n2 of all kinds of high-end equipment required to be assembled in batches in the manufacturing stage; initial developer quantity a in development stage 0 The unit cost of the research personnel can be increased to be B1; initial assembly line quantity b in manufacturing stage 0 The method comprises the steps of carrying out a first treatment on the surface of the The added cost of the assembly line is B 2 ；
S2, setting operation parameters of a variable neighborhood search algorithm; the operation parameters specifically include:
maximum iteration number Iter of algorithm max The method comprises the steps of carrying out a first treatment on the surface of the Number of initial solutions N in initial solution set 0 The method comprises the steps of carrying out a first treatment on the surface of the Minimum number NS of neighbor structures in a set of selectable neighbor structures min The method comprises the steps of carrying out a first treatment on the surface of the The number NS of neighbor structures in the current set of selectable neighbor structures; k=0 for the kth neighborhood structure; l=0 of the L-th initial solution, the initial fitness value α of the neighborhood structure;
s3, encoding 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 decoding each solution in the initial solution set X, and obtaining C corresponding to each initial solution max A value; wherein C is max Values represent development-assembly total time span;
s4, carrying out initial solution X in initial solution set X based on variable neighborhood search algorithm L Performing a Shaking operation to obtain a new solution X';
s5, carrying out local search on the new solution X 'based on the current selectable neighborhood structure set to obtain a local optimal solution X';
s6, comparing the initial solution X L Corresponding C max C with value corresponding to the locally optimal solution X' max The magnitude of the value C corresponding to X' max A value less than X L Corresponding C max Let k=0 and assign X "to X L Calculating the adaptability of the neighborhood structure in the selectable neighborhood structure set; if not, let k=k+1, and execute S7;
S7, judging whether K is smaller than or equal to NS or not, and if so, turning to S5; if not, let l=l+1 and turn S8;
s8, judging that L is less than or equal to N 0 If so, turning to S4; otherwise, re-pairing based on fitness of the optional neighborhood structure in the optional neighborhood structure setSequencing and updating the neighborhood structure, and then turning to S9;
s9, judging whether the current iteration number Iter is larger than the maximum iteration number Iter max If the number is greater than S10; if not, let Iter=Iter+1, K=0, L=0, and return to step S4;
s10, terminating the algorithm, traversing all solutions in the initial solution set, and outputting a global optimal solution X best 。
2. The method of claim 1, wherein the encoding the development task data and equipment data based on a variant neighborhood search algorithm in S3 to obtain an initial solution set X comprises:
s31, defining variables a, b, a 1 Wherein a represents the number of ultimately available developers, b represents the number of ultimately available assembly lines, a 1 Representing the maximum developer that can be increased under budget B;
s32, defining new initial solution X 0 Assigning values of a and b to initial solutions X 0 In the positions n1+n2+1 and n1+n2+2, the code of the development phase and the production phase is randomly generated again according to a, b, and all the initial solutions X are obtained 0 Adding 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 set 0 If not, returning to S31 to continue generating the initial solution, otherwise, outputting the initial solution set X.
3. The method of claim 1, wherein the C max The values are:
Figure FDA0004171121090000031
Figure FDA0004171121090000032
/>
Figure FDA0004171121090000033
Figure FDA0004171121090000034
wherein C is max Representing the total time span from development to assembly;
Figure FDA0004171121090000035
a minimum value representing the earliest start-up time of all high-end equipment on the first equipment line;
Figure FDA0004171121090000036
representing the actual completion time of the development project i;
p i representing the time required for the h-th assembly of the i-th high-end equipment;
Figure FDA0004171121090000037
represents an ith high-end equipment E of an ith type ih Waiting time on assembly line l;
Figure FDA0004171121090000038
represents an ith high-end equipment E of an ith type ih Actual start time on assembly line l;
Figure FDA0004171121090000039
the v-th high-end equipment E representing the u-th type uv The actual finishing time on the assembly line l.
4. The method of claim 1, wherein the S4 is based on variant neighborThe domain search algorithm performs a search on an initial solution X in an initial solution set X L Performing the Shaking operation to obtain a new solution X' includes:
s41, obtaining the L-th initial solution X in the initial solution set X L Defining the variables I, j=1;
s42, randomly generating integers in the range of the interval [1, n1], and assigning the integers to variables I and J;
S43, judging initial solution X L Whether two research and development tasks corresponding to the I, J positions meet the condition: one of the tasks belongs to a critical path set task and the other task belongs to a non-critical path set task, and if the condition is not satisfied, returning to S42; otherwise, executing S44;
s44, exchange initial solution X L The I, J th element of the solution X is obtained L New solution X after first exchange 1 Recorded as a first new solution X 1 ；
S45, randomly generating integers in the range of the interval [ n1+1, n1+n2], and assigning the integers to variables I and J;
s46, exchange new solution X 1 The I, J th element of the new solution X after the second exchange is obtained 2 Recorded as the second new solution X 2 ；
S47, comparing N based on disturbance neighborhood structure 1 The obtained second new solution X 2 From the current initial solution X L If the second new solution X 2 C corresponding to max The value is less than or equal to the initial solution X L C corresponding to max The value is then output a second new solution X 2 The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to S42;
s48, solving the second new solution X 2 Assigned to X'.
5. The method of claim 1, wherein the step of performing a local search for the new solution X' based on the current set of selectable neighborhood structures to obtain a locally optimal solution X "in S5 comprises:
s51: let the initial neighborhood structure k=0, the initial search times g=0, the maximum search times G of the single neighborhood structure;
S52: and selecting the Kth neighborhood structure in the selectable neighborhood structure set to operate X ', obtaining X ", and when G is more than or equal to G, reselecting the selectable neighborhood structure in the selectable neighborhood structure set to continue operating X'.
6. The method of claim 5, wherein the optional neighborhood structure in S52 comprises:
neighborhood structure 1: defining variables i and j, randomly generating two integers in a section [1, n1], assigning the two integers to two research and development tasks corresponding to i, j, i and j positions, belonging to a non-critical path set, and exchanging the numbers of research and development personnel corresponding to the i, j positions of the solution; randomly generating integers in the range of the interval [ 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 variables i and j, randomly generating an integer in the range of a section [1, n1], assigning the integer to i, searching the right side of the position i for a position j meeting the condition j-i not less than 3 and the task corresponding to the position belonging to the critical path set, inserting the number of the research personnel corresponding to the position j-1 into the position i+1, and moving the number of the research personnel corresponding to the positions i+1 to j-2 to the right 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 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 the range of a section [1, n1], assigning the integer to i, searching the right side of the position i for a position j meeting the condition j-i not less than 3 and the task corresponding to the position belonging to the critical path set, inserting the number of the research personnel corresponding to the position i+1 into the position j-1, and moving the number of the research personnel 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 to the left by one position;
neighborhood structure 4: defining variables i and j, randomly generating an integer in the range of a section [1, n1], assigning the integer to i, searching the right side of the i for a position j which meets the condition j-i not less than 3 and the task corresponding to the position belongs to a critical path set, and carrying out reverse sequence processing on all the numbers of the research and development personnel corresponding to the positions i+1 to j-1; randomly generating integers in the range of the interval [ n1+1, n1+n2], assigning the integers to the variables i and j, and carrying out reverse processing on all assembly line numbers corresponding to the positions i+1 to j-1 when the conditions j-i are more than or equal to 3;
Neighborhood structure 5: defining variables i, j and k, assigning element values of the n < 1 > +n < 2 > +1 position to k, randomly generating a research and development personnel number in a range of a section [1, k ] and assigning the research and development personnel number to the variable j, randomly generating an integer in the range of the section [1, n < 1 > -and assigning the integer to the variable i, and changing the value of the element of the i < th > position to the value of the variable j; and (3) assigning the element value of the n < 1+ > n < 2+ > position to k, randomly generating an assembly line number in the range of the interval [1, k ] and assigning the assembly line number to a variable j, randomly generating an integer in the range of the interval [ n < 1+ > 1, n < 1+ > n < 2 > ] and assigning the integer to a variable i, and changing the value of the element of the i < th > position to the value of the variable j.
7. The method of claim 1, wherein the reordering and updating of the neighbor structures based on the fitness of the selectable neighbor structures in the set of selectable neighbor structures in S8 comprises:
s81, moving a 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 alpha of a plurality of neighborhood structures is the same and is the minimum, randomly selecting one neighborhood structure from the plurality of neighborhood structures and moving the neighborhood structure to 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 smaller than the minimum number NS of the neighborhood structures in the optional neighborhood structure set min Randomly selecting a plurality of neighborhood structures from the candidate neighborhood structure set N', and adding the neighborhood structures into the current candidate neighborhood structure set N;
s84, reordering and updating the neighborhood structure according to the adaptability alpha of the neighborhood structure in the current selectable neighborhood structure set N.
8. The method of claim 1, wherein a global optimal solution X is output in S10 best Comprising the following steps: set TA k And EA (ethylene oxide) l Wherein TA k Representing a set of tasks formed by the development tasks assigned by the kth developer, EA l Representing that the high-end equipment assigned to the first equipment line is formed into an equipment set EA l 。
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