CN111553610B

CN111553610B - Scheduling method and system based on learning-forgetting effect

Info

Publication number: CN111553610B
Application number: CN202010375639.3A
Authority: CN
Inventors: 郑继光
Original assignee: Suning Cloud Computing Co Ltd
Current assignee: Suning Cloud Computing Co Ltd
Priority date: 2020-05-07
Filing date: 2020-05-07
Publication date: 2023-04-07
Anticipated expiration: 2040-05-07
Also published as: CN111553610A

Abstract

The embodiment of the invention discloses a scheduling method and a scheduling system based on a learning-forgetting effect, wherein when the learning efficiency and the learning-forgetting efficiency of developers are comprehensively considered, the cost and the progress of a project are in a moderate state, the cost and progress optimization result is more accurate, the scheduling corresponding to the cost and the progress is more scientific, and the requirement of the actual project is better met. Constructing a scheduling model according to the NSGA-II algorithm, tasks and personnel information; constructing a learning effect scheduling model according to the scheduling model and the learning effect; constructing a learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect; and acquiring scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model.

Description

Scheduling method and system based on learning-forgetting effect

Technical Field

The invention relates to the field of software project management, in particular to a scheduling method and system based on learning-forgetting effect.

Background

In the field, the abilities of various development languages mastered by developers invested in a software project are generally only considered to be fixed, that is, the changes of the skill level of the development languages mastered by the developers are never considered in the scheduling process, and the obtained progress and cost optimization results are often biased. In order to meet the requirements of actual software development projects, when a developer in a project is scheduled, the change of the skill level of the developer is considered, namely when the developer continuously uses a development language for development, the skill level of the developer is continuously increased until a peak value is reached; when a developer does not use a development language continuously, the skill level of the developer can be continuously reduced until a minimum value is reached; the developer's skill level will increase when part of the time a development language is used and will decrease when part of the time the development language is not used.

Disclosure of Invention

The embodiment of the invention provides a scheduling method and a scheduling system based on a learning-forgetting effect, when the learning efficiency and the learning-forgetting efficiency of a developer are comprehensively considered, the cost and the progress of a project are in a moderate state, the cost and progress optimization result is more accurate, the scheduling corresponding to the cost and the progress is more scientific, and the requirements of the actual project are better met.

In order to achieve the above purpose, the embodiment of the invention adopts the following technical scheme:

in a first aspect, an embodiment of the present invention provides a scheduling method based on a learning-forgetting effect, which constructs a scheduling model according to an NSGA-II algorithm, tasks, and personnel information; constructing a learning effect scheduling model according to the scheduling model and the learning effect; constructing a learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect; and acquiring scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model.

With reference to the first aspect, in a first possible implementation manner of the first aspect, the constructing a scheduling model according to the NSGA-II algorithm, the task, and the person information includes: a double-layer coding algorithm is adopted, the first layer of codes are sequential codes, the second layer of codes are task assignment codes, and a scheduling model is constructed; the task comprises a task construction period; the personnel information includes: personnel cost, initial skill value of personnel, and personnel skill use time.

With reference to the first possible implementation manner of the first aspect, in a second possible implementation manner of the first aspect, the constructing a learning effect scheduling model according to the scheduling model and the learning effect includes:

acquiring a learning operator according to the learning effect, the sequence code and the task assignment code; constructing a learning effect scheduling model according to the learning operator and the scheduling model; the method for constructing the learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect comprises the following steps: acquiring a forgetting operator according to the learning forgetting effect, the sequence codes and the task assignment codes; and constructing a learning forgetting effect scheduling model according to the forgetting operator and the scheduling model.

With reference to the first aspect, in a third possible implementation manner of the first aspect, the obtaining scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model includes: acquiring a learning effect task construction period, learning effect personnel cost and a learning effect personnel working time balance value according to the learning effect scheduling model; and acquiring a learning forgetting effect task construction period, learning forgetting effect personnel cost and a learning forgetting effect personnel working time balance value according to the learning forgetting effect scheduling model.

With reference to the third possible implementation manner of the first aspect, in a fourth possible implementation manner of the first aspect, a learning effect skill value is obtained according to the learning effect scheduling model, the initial skill value of the person, and the learning effect formula; acquiring a learning effect task construction period according to the learning effect skill value and the task construction period; acquiring the cost of the learning effect personnel according to the learning effect skill value and the personnel cost; and acquiring a working time balance value of the learning effect personnel according to the learning effect skill value and the personnel skill using time.

With reference to the third possible implementation manner of the first aspect, in a fifth possible implementation manner of the first aspect, a learning forgetting effect skill value is obtained according to the learning effect scheduling model, the initial skill value of the person, and the learning forgetting effect formula; acquiring a learning forgetting effect task construction period according to the learning forgetting effect skill value and the task construction period; acquiring the cost of the learning forgetting effect personnel according to the learning forgetting effect skill value and the personnel cost; and acquiring a work time balance value of the learning forgetting effect personnel according to the learning forgetting effect skill value and the personnel skill use time.

In a second aspect, an embodiment of the present invention provides a scheduling system based on a learning-forgetting effect, including:

the scheduling model building module is used for building a scheduling model according to the NSGA-II algorithm, tasks and personnel information;

the learning effect scheduling model building module is used for building a learning effect scheduling model according to the scheduling model and the learning effect;

the learning forgetting effect scheduling model building module is used for building a learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect;

and the scheduling information acquisition module is used for acquiring scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model.

With reference to the second aspect, in a first possible implementation manner of the second aspect, the scheduling model building module includes:

the double-layer coding module is used for adopting a double-layer coding algorithm, wherein the first layer of coding is sequential coding, and the second layer of coding is task assignment coding, so that a scheduling model is constructed; the task comprises a task construction period; the personnel information includes: personnel cost, initial skill value of personnel, and personnel skill use time.

With reference to the first possible implementation manner of the second aspect, in a second possible implementation manner of the second aspect, the learning effect scheduling model building module includes:

the learning operator obtaining sub-module is used for obtaining a learning operator according to the learning effect, the sequence code and the task assignment code;

the learning effect scheduling model constructing submodule is used for constructing a learning effect scheduling model according to the learning operator and the scheduling model;

the learning forgetting effect scheduling model building module comprises:

the forgetting operator obtaining sub-module is used for obtaining a forgetting operator according to the learning forgetting effect, the sequence codes and the task assignment codes;

and the learning forgetting effect scheduling model constructing submodule is used for constructing a learning forgetting effect scheduling model according to the forgetting operator and the scheduling model.

With reference to the second aspect, in a third possible implementation manner of the second aspect, the scheduling information obtaining module includes:

the learning effect value acquisition submodule is used for acquiring a learning effect task period, a learning effect personnel cost and a learning effect personnel working time balance value according to the learning effect scheduling model;

and the learning forgetting effect value acquisition submodule is used for acquiring a learning forgetting effect task construction period, the learning forgetting effect personnel cost and the learning forgetting effect personnel working time balance value according to the learning forgetting effect scheduling model.

With reference to the third possible implementation manner of the second aspect, in a fourth possible implementation manner of the second aspect, the learning effect value obtaining sub-module includes:

the learning effect skill value acquisition unit is used for acquiring a learning effect skill value according to the learning effect scheduling model, the personnel initial skill value and the learning effect formula;

the learning effect task construction period obtaining unit is used for obtaining a learning effect task construction period according to the learning effect skill value and the task construction period;

the learning effect personnel cost obtaining unit is used for obtaining the learning effect personnel cost according to the learning effect skill value and the personnel cost;

and the learning effect worker working time balance value acquisition unit is used for acquiring a learning effect worker working time balance value according to the learning effect skill value and the worker skill using time.

With reference to the third possible implementation manner of the second aspect, in a fifth possible implementation manner of the second aspect, the learning forgetting effect value obtaining sub-module includes:

the learning forgetting effect skill value acquisition unit is used for acquiring a learning forgetting effect skill value according to the learning effect scheduling model, the personnel initial skill value and the learning forgetting effect formula;

the learning forgetting effect task construction period obtaining unit is used for obtaining a learning forgetting effect task construction period according to the learning forgetting effect skill value and the task construction period;

the learning forgetting effect personnel cost obtaining unit is used for obtaining the learning forgetting effect personnel cost according to the learning forgetting effect skill value and the personnel cost;

and acquiring the working time balance value of the learning forgetting effect worker according to the learning forgetting effect skill value and the worker skill using time.

According to the scheduling method and system based on the learning-forgetting effect, when the learning effect and the learning-forgetting effect of the developer are comprehensively considered, the cost and the progress of the project are in a moderate state, the cost and progress optimization result is more accurate, the scheduling corresponding to the cost and the progress is more scientific, and the requirement of the actual project is better met. Compared with the prior art, in the implementation of the invention, a scheduling model is constructed according to the NSGA-II algorithm, tasks and personnel, and the software project is completed with lower cost and shorter time by using the Non-dominated Sorting genetic algorithm (NSGA-II) with elite strategy, so that the scheduling result is more accurate. And constructing a learning effect scheduling model according to the scheduling model and the learning effect, considering the learning effect of the skill type employees, and recording and analyzing the condition that the final skill value of the skill type employees participating in the project is increased compared with the initial skill value by the learning effect scheduling model. And constructing a learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect, considering the learning forgetting effect of the skill type employees, and recording and analyzing the final skill value of the skill type employees participating in the project by the learning forgetting effect scheduling model after the final skill value of the skill type employees is changed to a certain extent compared with the initial skill value. And acquiring scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model, wherein in a software project, each task needs to meet the constraints of software developers and the skills thereof and the time sequence constraints among the tasks, and the skill performance of the software developers is often one-specific and multifunctional and can specifically express and master various development languages. In the actual software project scheduling process, the skill level of a software developer is also continuously changed, and the rule of 'using for entering and exiting' is met. On the premise of meeting the rule, the learning effect and the learning forgetting effect of developers are comprehensively considered, the multi-skill staff are reasonably scheduled in the software project, the cost and the progress are in a moderate state, the cost and the progress optimization result is more accurate, the shift arrangement corresponding to the cost and the progress is more scientific, and the requirement of the actual project is met.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

FIG. 1 is a flow chart of a method of an embodiment of the present invention;

FIG. 2 is a flow chart of an embodiment of the present invention;

FIG. 3 is a three-level architecture diagram of a project scheduling problem with multiple development language skills and human resource constraints according to an embodiment of the present invention;

FIG. 4 is a network diagram of project task nodes according to an embodiment of the present invention;

FIG. 5 is a graph illustrating an iteration of a learning effect period according to an embodiment of the present invention;

FIG. 6 is a graph of an iteration of a learning effect cost for an embodiment of the present invention;

FIG. 7 is a graph of a learning effect pareto frontier for an embodiment of the present invention;

FIG. 8 is an iterative graph illustrating the learning forgetting effect period according to an embodiment of the present invention;

FIG. 9 is a graph of an iterative cost curve for learning forgetting effect according to an embodiment of the present invention;

FIG. 10 is a pareto frontier graph of learning forgetting effect according to an embodiment of the present invention;

fig. 11 is a block diagram of a system configuration according to an embodiment of the present invention.

Detailed Description

In order to make the technical solutions of the present invention better understood, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, those skilled in the art can obtain the embodiments without any inventive step in advance, and the embodiments are within the protection scope of the present invention.

It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

The embodiment of the invention provides a scheduling method based on learning-forgetting effect, as shown in fig. 1, comprising:

and S110, constructing a scheduling model according to the NSGA-II algorithm, the tasks and the personnel information.

NSGA-II, elitistonnon-doped Sorting genetic Algorithm, non-dominated Sorting multi-target genetic algorithm with elite strategy.

A double-layer coding algorithm is adopted, the first layer of codes are sequential codes, the second layer of codes are task assignment codes, and a scheduling model is constructed;

the tasks comprise task construction period, task quantity and task execution priority;

the personnel information includes: personnel cost, initial skill value of personnel, and personnel skill use time, etc.

And S120, constructing a learning effect scheduling model according to the scheduling model and the learning effect.

Acquiring a learning operator according to the learning effect, the sequence code and the task assignment code; and constructing a learning effect scheduling model according to the learning operator and the scheduling model.

S130, constructing a learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect.

Acquiring a forgetting operator according to the learning forgetting effect, the sequence codes and the task assignment codes; and constructing a learning forgetting effect scheduling model according to the forgetting operator and the scheduling model.

And S140, acquiring scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model.

And acquiring a study effect task construction period, study effect personnel cost and a study effect personnel working time balance value according to the study effect scheduling model.

Acquiring learning effect skill values according to the learning effect scheduling model, the personnel initial skill values and the learning effect formula;

acquiring a learning effect task construction period according to the learning effect skill value and the task construction period;

acquiring the cost of the learning effect personnel according to the learning effect skill value and the personnel cost;

and acquiring a working time balance value of the learning effect personnel according to the learning effect skill value and the personnel skill using time.

Acquiring a learning forgetting effect task construction period, learning forgetting effect personnel cost and a learning forgetting effect personnel working time balance value according to the learning forgetting effect scheduling model;

acquiring learning forgetting effect skill values according to the learning effect scheduling model, the personnel initial skill values and the learning forgetting effect formula;

acquiring a learning forgetting effect task construction period according to the learning forgetting effect skill value and the task construction period;

acquiring the cost of the learning forgetting effect personnel according to the learning forgetting effect skill value and the personnel cost;

and acquiring a work time balance value of the learning forgetting effect personnel according to the learning forgetting effect skill value and the personnel skill use time.

The embodiment of the invention provides a scheduling method based on learning-forgetting effect, as shown in fig. 2, comprising:

reading task data, setting algorithm parameters, initializing chromosomes, calculating the extremely poor construction period, cost and employee time, and then performing rapid non-dominated sorting.

And selecting individuals by using a binary tournament method for the population P, obtaining a new population Q through chromosome variation and chromosome crossing, then combining the population R, and then performing chromosome decoding.

And then, performing coding layering operation, including task sequence and personnel assignment, calculating the extremely poor construction period, cost and employee time, calculating constraint conditions, performing rapid non-dominated sorting, obtaining a new generation population P through a displacement and elite retention strategy, judging whether the algorithm is finished in an iterative mode, re-performing chromosome decoding if the algorithm is not finished in the iterative mode, and outputting a Pareto (Pareto) front edge solution set result if the algorithm is finished in the iterative mode.

(1) Encoding and initializing the population.

NSGA-II introduces a rapid non-dominated sorting, thereby reducing the complexity of the algorithm; the NSGA-II introduces an elite strategy into the algorithm, which enlarges the sampling space; the NSGA-II can uniformly expand individuals in the quasi-pareto domain to the whole pareto domain, and ensures the diversity of the population.

NSGA-II is based on genetic algorithm, so the design form of encoding and population initialization is the same as genetic algorithm. Coding is the representation of the solution in question in chromosomal form, thereby enabling efficient genetic manipulation. According to the completeness, soundness and non-redundancy principles of the codes and the configuration characteristics of the employees in various development languages mastered in the software project, the embodiment adopts the algorithm design principle of double-layer coding, wherein the first layer of codes are sequential codes, and the second layer of codes are task assignment codes for tasks needing to master the tasks of the employees in various development languages.

And double-layer coding is adopted in the scheme, the first layer is used for sequencing tasks, the second layer is used for sequencing personnel, and the problem of personnel scheduling in a project is solved by adopting the double-layer coding.

For example, if the number of tasks is n and the number of resources is m, the first layer coding length is n, and a non-repeated ordering of integers from 1 to n represents the priority of task execution, and the tasks are firstly randomly generated and then converted according to the immediate constraint. The second level codes are integers of length L = n × m, and the gene positions are integers of [ lb (i), ub (i) ], indicating the type of choice. If n =5,m =2, and the total number of workers is 5, then one legal chromosome can be represented as [5,4,2,1,3;3,2, 11,5,3,2,4], the first layer of coding is the access sequence of the nodes, 5,4,2,1,3, which means that task 5 is arranged first, then task 4 is arranged, then task 2 is arranged, and so on, the second layer of coding is that task needs to master the codes assigned by employees in various development languages: 3,2,3,2,1 and 1,5,3,2,4, with 3 at position 1 indicating that the 3 rd person possessing development language skill 1 is assigned to provide development language skill 1 to task 1,2 at position 2 indicating that the 2 nd person possessing development language skill 2 is assigned to provide development language skill 2 to task 1,3 at position 3 indicating that the 3 rd person possessing development language skill 1 is assigned to provide development language skill 1 to task 2,2 at position 4 indicating that the 2 nd person possessing development language skill 2 is assigned to provide development language skill 2 to task 2, and so on.

The generation of the initialized individual mainly comprises the following 5 steps:

step1: firstly, initializing relevant parameters, specifically comprising the number m of tasks, the number s of development language skills and the development language skill Set required by the task d _d Task d requires the minimum time to develop language skills j

Set of employees for mastering development language skills j _j Chromosome personal = [ (]) ]]Population size popsize.

Step2: determining iteration steps according to the size of the population popsize.

Step3: the development language number cycles from 1 to s, cycling from 1 to m according to the task number.

Step4: checking whether task d requires development language skills j, if

If the task d is more than 0, the task d is considered to need the development language skill j, and the Set of the employees who master the development language skill j is selected _j Selecting a staff member with the number i, and assigning the value of i to the gene position personal = ub [ i ] of the current individual]If +>

Less than 0, then the next loop can be skipped.

Step5: in this way, personnel are scheduled up to the development language skills of all projects.

In a software development project scheduling model based on learning effect of research personnel, a double-layer coding algorithm design flow mainly comprises the following five steps:

step1: initializing the priority order of tasks, the type of skills required in the tasks and the shortest time of the skills, the type of skills mastered by the staff and the initial skill value, the average skill wage of the staff and the time of using the skills by the staff, learning operators and other variables.

Step2: and (4) performing iteration according to the serial number of the task, wherein if the task has no immediately preceding task, the starting time of the task is 0, otherwise, if the task has the immediately preceding task, the starting time of the task is the latest completion time of all the immediately preceding tasks.

Step3: the task scheduling method includes the steps that when the tasks are iterated according to numbers, skills needed by each task are determined, a staff with corresponding skills is selected from a staff skill matrix, the staff numbers of the skills are determined, each staff can only use one skill to participate in the same task punishment value, and the task completion time is the latest completion time of the skills needed by the tasks.

Step4: if the employee i uses the skill j to participate in the task d, firstly calculating the skill value of the employee i when the employee i uses the skill j to participate in the task d, then calculating the construction period of the task d, and calculating the skill value of the skill j of the employee i after the task is finished according to a learning effect formula; and if the employee i does not use the project d, the skill value of the skill j of the employee i is kept unchanged, and the initial value is taken.

Step5: the method comprises the steps of constructing a staff skill use time table to calculate the use time of each skill of each staff, calculating the final skill value of each skill of the staff at the end of a project by using a learning effect formula, calculating the accumulated use time of the staff according to the staff skill use time table, and finally calculating the project construction period, the cost and the balance value of the working time of the staff respectively.

In a software development project scheduling model based on learning forgetting effect of research personnel, a double-layer coding algorithm design flow mainly comprises the following six steps:

step1: initializing the priority of tasks, the type of skills required in the tasks and the shortest time of the skills, the skill type and initial skill value mastered by the staff, the average skill wage of the staff, the time of using the skills by the staff, learning operators, forgetting operators and other variables.

Step2: and performing iteration according to the serial number of the task, wherein if the task does not have an immediately preceding task, the starting time of the task is 0, otherwise, if the task has an immediately preceding task, the starting time of the task is the latest completion time of all immediately preceding tasks.

Step3: the task processing method includes the steps that when tasks are iterated according to numbers, skills needed by each task are determined, a corresponding skill employee is selected from an employee skill matrix, the employee number of the skill is determined, each employee can only use one skill to participate in the same task punishment value, and the completion time of the tasks is the latest completion time of the skills needed by the tasks.

Step4: if the employee i uses the skill j to participate in the task d, firstly calculating the skill value of the skill j used by the employee i when the employee i participates in the task d, then calculating the construction period of the task d, calculating the skill value of the skill j of the employee i after the task is finished according to a learning effect formula, and taking the moment as the last using moment of the skill j of the employee i.

Step5: if the employee i uses the skill j to participate in the project d and then uses the skill j to participate in the task d ', the forgetting effect of the employee is considered when the task d ' starts, the difference between the task starting time and the final using time of the skill is calculated, and the actual skill of the employee when the task d ' starts is calculated; if the skill j of the employee i is not used until the task d ', the skill value at the start of the task d ' is calculated by calculating the time difference between the start of the project and the start of d ' only considering the forgetting effect.

Step6: the method comprises the steps of constructing a staff skill use time table to calculate the use time of each skill of each staff, calculating the final skill value of each skill of the staff at the end of a project by using a learning forgetting effect formula, calculating the accumulated use time of the staff through the staff skill use time table, and finally calculating the project construction period, the cost and the balance value of the staff working time.

(2) And (5) evaluating the fitness.

When the multi-objective optimization problem is solved, because a plurality of optimization objectives are often contradictory, an appropriate selection mechanism, particularly how to evaluate the individual fitness by adopting an appropriate evaluation mode becomes a key factor for judging whether the evolutionary algorithm is finally converged to the Pareto optimal solution.

Generally, the multi-objective evolutionary algorithm mainly uses three fitness evaluation strategies, namely a combined function method, a method based on a population without introducing a Pareto dominant concept, and a method based on the population with introducing the Pareto dominant concept. The Non-dominated Sorting Genetic Algorithm (NSGA-II) fitness evaluation method with elite strategy adopted in the embodiment adopts a method of introducing Pareto domination concept based on population, and determines parent individuals of the next iteration mainly through Sorting values and crowding degrees.

(3) Genetic operator

Selection is a genetic operation that selects good individuals from parents into the next generation. The selection operator compares the advantages and disadvantages of the individuals according to the fitness of the individuals, the smaller the fitness, the smaller the probability that the individual is selected, and conversely, the larger the fitness, the greater the probability that the individual is selected. Common types of selection operators are: tournament selection, roulette selection, uniform ordering, preserving best choice, etc.

The tournament selection method mainly comprises the following steps:

the method comprises the following steps that firstly, assuming that the population size is n, n individuals are randomly generated to serve as a first generation;

secondly, randomly selecting k (k is smaller than n) individuals from the n individuals, wherein the value of k is small, the efficiency is high, but the value is not too small, and the value is generally n/2 (integer);

thirdly, selecting the largest individual from the k individuals as one of the n next-generation individuals;

and fourthly, repeating the second step and the third step until new n individuals are obtained.

The selection operator adopted in the embodiment is a binary tournament method, and the basic principle is to perform selection according to the ordinal value and the congestion distance, wherein individuals with small ordinal values are selected when the ordinal values are different, and individuals with large congestion distance are selected when the ordinal values are the same, so that the evolution can be performed towards the direction of non-dominant solution and uniform dispersion.

The crossover belongs to one of the core operators of the genetic algorithm.

Crossover produces progeny by mimicking the genetic pattern of the organism by mating and recombining chromosomes to produce new progeny. The new filial generation individuals are the new feasible solution of the problem, so that the algorithm can carry out iterative search in the feasible solution space of the optimization problem through cross operation, and further the global search capability of the algorithm can be improved.

The embodiment of the invention adopts two-point intersection.

The operation steps of the crossover operator in the first layer coding are as follows:

(1) Randomly selecting two chromosomes as male parents;

(2) Generating 2 random natural numbers r1 and r2;

(3) Exchanging gene segments between the two male parent chromosomes r 1-r 2 to obtain two offspring chromosomes, and revising the two obtained offspring chromosomes to prevent the two offspring chromosomes from conflicting.

For example, two paternal chromosomes [1,3,2,5,4] [1,2,4,5,3], r1=2, r2=4 were selected, then the crossover process is: before crossing [1,3,2,5,4] [1,2,4,5,3], after crossing [1,2,4,5,4] [1,3,2,5,3], after repairing [1,2,4,5,3] [1,3,2,5,4], wherein the repairing method is that after crossing, the complementary set of the crossed segments is taken and randomly rearranged to the non-crossed segments.

The operation steps of the crossover operator in the second layer coding are as follows:

(1) Randomly selecting two chromosomes as male parents;

(2) Generating 2 random natural numbers r1 and r2;

(3) And exchanging the gene segments between the two male parent chromosomes r 1-r 2 to obtain two offspring chromosomes.

For example, two selected paternal chromosomes [1,3,2, 1,2] [2,3,1, 2,3], r1=2,r2=4, then [1,3,1,1,1,2] [2,3,3,2,2,3] after the crossover.

Mutation is a genetic operation for forming a new individual by replacing some gene values in the individual with other values, and the local search capability of the genetic algorithm can be effectively improved.

According to the characteristics of the coding, the first layer coding design uses two-point reciprocity mutation, and the mutation steps are as follows:

(1) Generating 2 random natural numbers r1 and r2;

(2) The genes at positions r1 and r2 were exchanged.

For example, r1=2, then the variation of the chromosome is [1,3,2,5,4] → [1,5,2,3,4].

The second layer coding design uses single point variation, and comprises the following steps:

(1) Generating a random natural number r1, wherein r1 represents the variation of the gene at the r1 position;

(2) And (3) mutating the r1 gene by adopting a random mutation mode.

For example, r1=3, then the chromosomal variation is [1,3,3,2,1,2] → [1,3,1,2,1,2].

(4) Constraint processing

The difficulty of the non-dominated sorting multi-target genetic algorithm NSGA-II with the elite strategy in solving the constraint problem is that a feasible solution often becomes an infeasible solution after various genetic operations, which violates the inherent constraint, so that certain strategies need to be used when the NSGA-II is used for solving the problem.

Generally, constraints can be considered with a straightforward idea, that is, in the course of evolution, a procedure of detecting whether a new individual violates a constraint can be performed after one iteration. If there is no violation, the valid individual is retained, otherwise, the invalid individual is removed. This approach may work for weak constraint problems, but not for strong constraint problems.

Under strong constraint conditions, the difficulty of finding an effective individual is greatly increased, and the individual is almost converted into an infeasible individual through one-time evolution because of more constraint conditions.

According to the characteristics of the three models established in the embodiment, part of constraint conditions are realized through coding and coding rules, and the other part of constraint conditions are mainly realized through a penalty function method.

The embodiment of the invention provides a scheduling method based on learning-forgetting effect, which comprises the following steps:

learning effects, also known as learning phenomena, are the effects of the accumulated experience through long-term work leaving memory in the mind of the operator, which helps the operator to improve the efficiency of the same or similar operations. The learning curve was originally developed by Wright in 1936 when studying the time of aircraft manufacture, which gradually decreased as aircraft production increased. This patent uses the research and development personnel learning model proposed by foreign scholars Wu and Sun, who indicate that the longer the time that a research and development staff uses a skill, the more the research and development efficiency on that skill will increase, and assuming that staff research and development staff p attends research and development task k, the learning curve formula is:

where n represents the total time period employee p spends on task k;

represents the average efficiency of employee p at the time of initiating the task; />

Represents the average efficiency accumulated after employee p spends n cycles in task k;

b is called a learning factor, r is called a learning percentage, and the smaller the value of r, the larger the value of b, the higher the learning effect.

Along with the study on the learning effect, the study results show that the forgetting effect corresponding to the learning effect also appears in the production activities and has an important influence on the production activities, and the study-forgetting curve of developers studied by foreign scholars Attia and Nembrard is used by the scholars, and the significance of a calculation formula and a symbol is given as follows:

wherein T represents the total time range and the range of values are positive integers; e _ijt Level value representing skill j of employee i after time period t, 0 < E _ijt ≤1；

An initial level value representing skill j at the beginning of time period t for employee i>

t _ij Represents the total time of i using skill j in the time period T, and is more than or equal to 0 and less than or equal to T _ij ≤T。

a _ij A learning factor representing skill j of employee i, the calculation formula is as follows:

a _ij ＝-(ln(l _ij ))/ln2

wherein l _ij The learning rate of the skill j of the employee i is represented, and l is more than or equal to 0 _ij ≤1；l _ij The smaller the value a _ij The larger the value, the greater the learning effect of employee i.

b _ij A forgetting factor representing the skill j of the employee i, the calculation formula is as follows:

b _ij ＝-(ln(1-f _ij ))/ln2

wherein f is _ij F is more than or equal to 0 and represents the forgetting rate of the skill j of the employee i _ij ≤1；f _ij The smaller the value, b _ij The larger the value, the smaller the forgetting effect of employee i.

From the above formula, it can be seen that _ij If =1, the learning-forgetting curve becomes a forgetting curve, and when f is greater than f _ij A learning forgetting curve becomes a learning curve when =0, and when a developer i uses a development language j, the skill level of the development language j increases; when the developer i does not use the development language j, the skill level of the development language j may be reduced.

(1) Establishing optimized mathematical model

The software project P, including the number {0, 1.,. M +1} altogether, is divided into M +2 tasks, where task 0 and task M +1 are dummy jobs (a dummy job is a job that consumes no resources and has a time of execution of 0), representing the start and end of the software project, respectively, and the set of tasks is M. The total required set of development language skills s for the software project P is J = {1,2,.., s }. The project has N research and development personnel who can be called and master multi-development language skills, and the set of the research and development personnel is N = {1, 2. i, J and d respectively represent research personnel, development language skills and tasks, wherein i is more than or equal to 1 and less than or equal to N, J is more than or equal to 1 and less than or equal to s, d is more than or equal to 1 and less than or equal to M, namely i belongs to N, J belongs to J and d belongs to M.

As shown in fig. 3, each task requires multiple development language skills, each development language skill is mastered by multiple developers, each developer has different development language skills and the mastered development language skills are different in efficiency, and can be described by a three-layer architecture of work (task) -skill-manpower, and a three-layer architecture of a project scheduling problem of multiple development language skills and human resource constraints.

The GPRs represent general precedence relationship constraints A1-AJ to represent J work or tasks, 1-K represent that the work needs K development language skills, namely the development language skills owned by research and development personnel participating in the project, the development language skills mastered by each research and development personnel are different, and 1-S represent that S development language skill type employees are shared.

The basic assumption of the problem is as follows:

(1) The number of multiple development language skill developers in the whole project period is kept unchanged;

(2) The cost of the software project is the sum of the wages of research personnel participating in the project, the wages of the staff are influenced by the skill value of the development language mastered by the staff, and the higher the skill value is, the higher the wage is;

(3) In the calculation of the progress of the software project, the task preemption is not considered, and the time lag is not considered. Assuming that the completion time of a process immediately before the process is the starting time of the process, and no time interval exists between the completion time and the starting time, and the work conversion time and the preparation time are not considered;

(4) Each task can not be interrupted in the midway, namely, a research and development personnel allocated to one task can only be allocated to the next task after the task is finished;

(5) Each employee can only participate in one task at the same time, but cannot participate in multiple tasks at the same time.

T _ijd Indicating the time that the developer i engaged in task d using development language skills j.

The shortest completion time when the development language skill j is used in the task d is shown, the development language skill j is the highest level of all the development language skills j in the enterprise, the time required for the task d to be done by the research personnel with the highest level in the enterprise is shown, j is more than or equal to 1 and less than or equal to s, and d is more than or equal to 1 and less than or equal to m.

E _ij Representing the level of the development language skill j possessed by the developer i, i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to s, E _ij ∈[0,1]，E _ij =1 indicates that the level of development language skills j possessed by the developer i is the highest level of the enterprise; e _ij =0, indicating that the developer i does not have the development language skill j.

Indicates that the developer i has the level of development language skill j at the beginning of the software project, and->

As is known, can be managed by a project manager,And the project technical supervisor and the related responsible persons judge according to the knowledge, the capability and the like of the staff.

Indicating the level of development language skills j that the developer i possesses at the start of task d.

FT _d Indicating the completion time of the task.

ST _d Indicating the start time of the task.

FT _Pd Indicating the completion time of the preamble work.

T _d Indicating the duration of task d.

P _d A set of immediately preceding tasks representing task d.

J _d Represents the set of total number of required development language skills for task d.

Indicates whether task d requires a development language skill j, and if so->

Otherwise->

1≤j≤s，1≤d≤m；C _i The salary of the employee i within a certain time (such as month, week and day) is represented, and the average wage of each development language skill mastered by the developer i is more than or equal to 1 and less than or equal to n.

Indicating the working time of the developer i at the d-th task.

a _ij A learning operator representing the skill j of the employee i.

b _ij A forgetting operator representing employee i skill j.

x _ijd Is a decision variable of 0-1, i is more than or equal to 1 and less than or equal to n, and j is more than or equal to 1 and less than or equal to js,1 is not less than d and not more than m. If x _ijd =1, indicating that the developer i participates in the task d using the development language skill j, otherwise zero.

y _ijdt Is an auxiliary variable of 0 to 1, i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to s, and d is more than or equal to 1 and less than or equal to m. If y _ijdt =1, indicating that the developer i participates in the task d using the development language skill j during the time period t, and otherwise is zero.

The model takes the cost and the progress of a software project and the time balance of research personnel as objective functions and optimizes the cost, the progress and the time balance of the research personnel and the research personnel.

The objective function is as follows (1) to (3).

In a software project, the main cost is derived from the cost of the developers participating in the project, so the cost of the software project can be considered as the sum of the wages of the developers participating in the software project. The payroll level of the research and development personnel is influenced by the skill value of the multiple development languages mastered by the research and development personnel, and the skill value of the multiple development languages mastered by the research and development personnel can be evaluated by an expert group consisting of a project manager, a research and development technical supervisor, a responsible person and the like. If the developer has a higher value of multi-development language skills, the corresponding payroll is higher. Defining the initial value of the multi-development language skills mastered by the research and development personnel participating in the project as E _ij The product of the initial value of a certain development language skill mastered by the developer and the average skill payroll of the employee is the actual payroll of the development language skill mastered by the multi-development language skill developer. The software project cost objective function equation is shown in (1), and represents minimizing the software project cost.

The completion time for each task in a software project is the maximum time within the task for the developer to use the skills. The progress of the whole software project is the deadline of the last completion task in the software project, namely the time of the task with the longest completion time in all the tasks is the final completion time of the whole project. The greater the skill value of the employee means that the more skilled the skill of the employee, the shorter the time the employee will take to complete the task. The software project progress objective function formula is shown in (2), and represents the minimized software project progress.

/>

In a software project, developers need to be used in a balanced manner, the situation that one developer has long working time and the other developer has short working time cannot occur in one task, the working time of the developers needs to be balanced, and the developers are used reasonably, so that the software project is more practical. The extreme difference of the working time of the research and development personnel is defined, and as shown in formula (3), the extreme difference of the working time of the research and development personnel is minimized, and the working time of the research and development personnel in the project is balanced.

The constraint conditions in the model are set as shown in (4) to (16). Due to the fact that

The shortest completion time of the development language skills j when the task d is completed, namely the time taken for the task d to be done by the research and development personnel having the highest level of the development language skills j in the enterprise, the time taken for any one research and development personnel i to participate in the task d by using the development language skills j is related to the level of the development language skills of the research and development personnel. The larger the ratio of the developer's development language skill value to the highest level in the enterprise, the shorter the time for the developer to participate in the task using that skill, so the time for the developer i to participate in the task d using the development language skill j is as shown in equation (4):

the completion time of a task in a software project is determined by the longest completion time of a certain development language skill J used by a developer i in the task, that is, the longest completion time of all development language skills J in a development language skill set J required for a task d determines the final completion time of the task, so the completion time of the task d is as shown in formula (5):

in the software project, the order constraint relationship between tasks is as follows. Wherein (6) indicates that the completion time of task d is the sum of its start time and its actual duration; (7) The starting time of the task d is the completion time of the task immediately before the task d, the time interval is not considered between the tasks, and the default is that after the previous task is completed, the next task is immediately started; (8) The completion time of the preorder task of the task d is represented as the maximum time spent in the preorder task; (9) Meaning that if a task has no predecessor, then the completion time for that predecessor is zero.

In a software project, each development language skill required by a task must be completed by only one developer with the development language skill, one development language skill J in a development language skill set J required by a certain task cannot be completed by two or more employees with the development language skill J, and each developer can participate in a task by only using one development language skill, and cannot use two development language skills simultaneously in one task by one employee. One research and development personnel can only participate in one task at the same time, namely, the research and development personnel can only participate in one task in a project by using one development language skill at the same time, and after the task is completed, the research and development personnel can redistribute and participate in the subsequent tasks. (10) Each development language skill indicating each task requires and is only completed by one person, (11) each developer can only participate in the same task using one development language skill. (12) Indicating that one developer can only participate in the same task at the same time, (13) indicating the total working time of the developer i in the software project.

/>

If the developer i participates in the task d by using the development language skill j in the time period t, the developer i is indicated to use the development language skill in the task d, namely y _ijdt =1, then x _ijd =1, otherwise if y _ijdt =0, then x _ijd ＝0。

Wherein y is _ijdt And x _ijd With values of 0 or 1, the constraints are set as (14), (15) and (16).

x _ijd ＝{0,1},1≤i≤n,1≤j≤s,1≤d≤m (15)

y _ijdt ＝{0,1},1≤i≤n,1≤j≤s,1≤d≤m (16)

And (3) a software development project scheduling model based on the learning effect of research and development personnel.

The constraint conditions in the model are set as shown in (1) to (16) above. Wherein the constraints (17) to (18) represent learning effects of the developer under consideration. Due to consideration of skilled staffLearning effect, so in a software development project, when a skill type employee i uses a skill j to participate in a task d, if the employee i does not use the skill j to participate in other tasks before the task d, namely before the starting time STd of the task d, the skill value of the skill j when the skill type employee starts to participate in the task d is considered as the initial skill value; when the skilled worker has engaged in other tasks using skill j for a portion of the time after the project begins and before task d begins, the total time to engage in other tasks is:

according to the learning curve model of Wu and Sun research, the skill value of the skill-type employee i when participating in the project d is:

when the skilled employee has used skill j to participate in other tasks at all times after the start of the project and before the start of task d, i.e., before the start time STd of task d, then the skill value of the skilled employee when participating in project d is, according to the learning curve model of the Wu and Sun studies:

therefore, when considering the learning effect of the employee, the skill value of the skill type employee i when using the skill j to participate in the task d is shown in the formula (17):

after the project is finished, because the learning effect of the skill type employee is considered, the final skill of the skill type employee participating in the project is increased compared with the initial skill value, and if the skill j of the employee i is not participated in the project in the whole project, the level of the skill j of the employee i after the project is finished is the initial value; if the skill j of the employee i participates in the project in the whole projectThen we accumulate the time that the employee used skill j over the entire project period for the project as:

according to the learning curve model of the Wu and Sun studies, the skill value of the skill j of the employee i after the project is finished is:

therefore, when considering the learning effect of the employee, the skill level value of the skill j of the skill type employee i after the software project is finished is shown in the formula (18):

and (3) a software development project scheduling model based on a learning forgetting effect.

In the software development project, because the learning forgetting efficiency of the skill type employee is considered, when the skill type employee i participates in the task d by using the skill j, if the employee i starts the task d at the starting time ST _d If skill j has not been previously used to participate in any task, then the skill value of skill j for a person i participating in task d is:

if employee i begins time ST at task d _d Skill j has been used previously to participate in other tasks, then the skill value of skill j for employee i when participating in task d is:

if employee i begins time ST at task d _d If the skill j has been used only part of the time before, then the time to use the skill j is calculated, i.e. the time to use the skill j is calculated

Then at the beginning of task d there is noThe time to use skill j is:

then the skill value of skill j for employee i when participating in task d is:

therefore, when the forgetting effect of the employee is comprehensively considered, the skill value of the skill type employee i when using the skill j to participate in the task d is shown in the formula (19):

after the project is finished, due to the fact that the learning forgetting effect of the skill type employees is considered, the skill value of the final skill of the skill type employees participating in the project is changed from the initial skill value, when the time for the skill type employees i to use the skill j in the project is longer than the time for not using the j, the skill value of the skill j of the skill type employees i is increased, and when the time for the skill type employees i to use the skill j in the project is shorter than the time for not using the j, the skill value of the skill j of the skill type employees i is reduced. If the skill j of employee i is not involved in the project throughout the project, the level of skill j for employee i after the project ends is:

if employee i has consistently used skill j to participate in the project throughout the project, the level of skill j for employee i after the project is completed is, based on the learning forgetting curve developed by Attia and Nembard:

if the skill j of the employee i participates in the project in the whole project, the learning effect of the employee is considered, and the employee i is firstly calculated in the whole projectThe time to use skill j in is:

/>

then the time that employee i has not used skill j throughout the project is:

according to the learning forgetting curve of the Attia and Nembhard studies, the level of skill j for employee i after the end of the project is:

therefore, when the learning forgetting effect of the skill type employee is considered, the skill level value of the skill j of the skill type employee i after the software project is finished is shown as the formula (20):

the invention provides a specific example, which comprises the following components:

a large software development project P of a certain software development company S has 10 tasks, namely D1, D2, \ 8230, D10, wherein 8 development language skills are needed, namely S1, S2 \8230, and S8, each task needs multiple development language skills, each development language skill is carried out in parallel, the initial value of the development language skill of an employee is given by an expert group consisting of a technical supervisor, a responsible person, a project manager and the like in the project through evaluation, and the total number of developers who can participate in the software project is 40.

The precedence between tasks and the skills required for each task are shown in table 1.

Table 1 task precedence relationships in the project

Task name	Task immediately before	Required skill
			D1	——	S1,S2,S3,S5,S7
D2	——	S1,S2,S3,S5,S7
			D3	D2	S2,S5,S6,S7
D4	——	S1,S2,S3,S5,S7
			D5	D1,D2	S2,S4,S6,S8
D6	D1,D4	S3,S5,S7,S8
			D7	D3,D5	S3,S5,S7,S8
D8	D3	S3,S5,S7,S8
			D9	D6,D7,D8	S3,S5,S7,S8
D10	D9	S3,S5,S7,S8

A project task node network diagram of tasks in a project is given according to table 1, as shown in fig. 4, where task S and task E are virtual processes.

The development language skills required for each task in the project and the minimum development time for the required development language skills are shown in table 2.

TABLE 2 shortest time requirement for skills in task (unit: month)

The average payroll for the development language skills of these 40 employees is shown in table 3.

TABLE 3 average payroll (Yuan/moon) of skills held by the employee

The skills of the development language and the initial level values of the skills mastered by each developer are shown in table 4.

TABLE 4 staff and skill value for each skill

The multi-skill staff scheduling multi-target experiment result based on the learning effect is as follows:

the learning rate is set to 0.91 and the upper limit of the learning curve is set to 1 during encoding. Running the code through Matlab results in:

an iteration graph of the learning effect construction period is shown in fig. 5, wherein the abscissa represents the iteration number, and the ordinate represents the construction period f 1.

As shown in fig. 6, the abscissa represents the number of iterations, and the ordinate represents the f2 cost.

The learning effect pareto frontier chart is shown in fig. 7, and the abscissa is the construction period f1, the ordinate is the cost f2, and the vertical coordinate is the staff equilibrium value f 3.

The 10 solutions were selected from the pareto frontier of fig. 7 and the cost and progress values of the 10 solutions were listed, as shown in table 5:

TABLE 5 software project progress and cost

Table 6 gives the skilled employee scheduling schemes corresponding to these 10 solutions.

TABLE 6 skill type employee scheduling scheme

/>

/>

The multi-skill staff scheduling multi-target optimization experiment result based on the learning forgetting effect is as follows:

the learning rate is set to 0.91, the forgetting rate is set to 0.04, the upper limit of the learning forgetting curve is set to 1, and the lower limit is set to 0.2. Obtaining by running the code Matlab:

learning a forgetting effect construction period iteration curve chart, as shown in fig. 8, the abscissa is the number of iterations, and the ordinate is the construction period f 1;

learning a forgetting effect cost iteration curve graph, as shown in fig. 9, the abscissa is the iteration number, and the ordinate is the f2 cost;

learning a forgetting effect pareto frontier chart, as shown in fig. 10, the abscissa is the construction period f1, the ordinate is the cost f2, and the vertical coordinate is the staff equilibrium value f 3.

The 10 solutions were selected from the pareto frontier of fig. 10 and the cost and progress values of the 10 solutions are listed, as shown in table 7:

TABLE 7 software project progress and cost

Cost of software project	Software project progress
		1022732.5	34.8
1037779.2	34.9
		1061631.3	35.0
1019637.6	35.0
		1013704.4	35.4
1016632.9	35.4
		1025197.3	35.7
1032221.3	35.7
		1057848.0	36.1
1019376.6	36.4

Table 8 gives the skilled employee scheduling schemes for these 10 solutions:

TABLE 8 skill type employee scheduling scheme

/>

/>

The data comparison can be obtained, when only the learning effect of the developer is concerned, although the progress is improved, the cost is increased, when the learning forgetting efficiency of the developer is comprehensively considered, the cost and the progress are in a moderate state, the cost and the progress are optimized more accurately, the scheduling corresponding to the cost and the progress is more scientific, and the requirement of an actual project is met more.

According to the scheduling method based on the learning-forgetting effect, provided by the embodiment of the invention, when the learning efficiency and the learning-forgetting efficiency of developers are comprehensively considered, the cost and the progress of a project are in a moderate state, the cost and progress optimization result is more accurate, and the scheduling corresponding to the cost and the progress is more scientific, so that the requirements of the actual project are better met.

An embodiment of the present invention further provides a scheduling system based on learning-forgetting effect, as shown in fig. 11, including:

the scheduling model building module is used for building a scheduling model according to the NSGA-II algorithm, the tasks and the personnel information;

The embodiment of the invention also provides a scheduling system based on the learning-forgetting effect, and the scheduling model building module comprises:

the double-layer coding module is used for adopting a double-layer coding algorithm, wherein the first layer of coding is sequential coding, and the second layer of coding is task assignment coding, so that a scheduling model is constructed;

the task comprises a task construction period;

the personnel information includes: personnel cost, initial skill value of personnel, and personnel skill use time.

The embodiment of the invention also provides a scheduling system based on learning-forgetting effect, wherein the learning effect scheduling model building module comprises:

and the learning effect scheduling model constructing submodule is used for constructing a learning effect scheduling model according to the learning operator and the scheduling model.

The embodiment of the invention also provides a scheduling system based on learning-forgetting effect, and the learning-forgetting effect scheduling model building module comprises:

The embodiment of the invention also provides a scheduling system based on the learning-forgetting effect, and the scheduling information acquisition module comprises:

The embodiment of the invention also provides a scheduling system based on learning-forgetting effect, and the learning effect value acquisition submodule comprises:

the learning effect task duration obtaining unit is used for obtaining the learning effect task duration according to the learning effect skill value and the task duration;

and the learning effect worker working time equilibrium value acquisition unit is used for acquiring a learning effect worker working time equilibrium value according to the learning effect skill value and the worker skill use time.

The embodiment of the invention also provides a scheduling system based on learning-forgetting effect, and the learning forgetting effect value acquisition submodule comprises:

the learning forgetting effect task construction period obtaining unit is used for obtaining the learning forgetting effect task construction period according to the learning forgetting effect technical value and the task construction period;

the learning forgetting effect personnel cost obtaining unit is used for obtaining the learning forgetting effect personnel cost according to the learning forgetting effect technical value and the personnel cost;

and acquiring the working time balance value of the learning forgetting effect worker according to the learning forgetting effect skill value and the worker skill use time.

According to the scheduling system based on the learning-forgetting effect, when the learning efficiency and the learning-forgetting efficiency of developers are comprehensively considered, the cost and the progress of a project are in a moderate state, the cost and progress optimization result is more accurate, the scheduling corresponding to the cost and the progress is more scientific, and the requirements of actual projects are better met.

The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the apparatus embodiment, since it is substantially similar to the method embodiment, it is relatively simple to describe, and reference may be made to some descriptions of the method embodiment for relevant points. Those skilled in the art will appreciate that the modules in the devices in the embodiments may be adaptively changed and arranged in one or more devices different from the embodiments. The modules or units or components of the embodiments may be combined into one module or unit or component, and furthermore they may be divided into a plurality of sub-modules or sub-units or sub-components. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and all of the processes or elements of any method or apparatus so disclosed, may be combined in any combination, except combinations where at least some of such features and/or processes or elements are mutually exclusive. Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise.

It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above may be implemented by a computer program, which may be stored in a computer readable storage medium and executed by a computer to implement the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.

The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A scheduling method based on learning-forgetting effect is characterized by comprising the following steps:

constructing a scheduling model according to the NSGA-II algorithm, tasks and personnel information;

constructing a learning effect scheduling model according to the scheduling model and the learning effect;

constructing a learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect;

acquiring scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model;

the method for constructing the scheduling model according to the NSGA-II algorithm, the tasks and the personnel information comprises the following steps:

a double-layer coding algorithm is adopted, the first layer of codes are sequential codes, the second layer of codes are task assignment codes, and a scheduling model is constructed; the task comprises a task construction period; the personnel information includes: personnel cost, initial skill value of personnel and personnel skill use time;

the step of constructing a learning effect scheduling model according to the scheduling model and the learning effect comprises the following steps:

acquiring a learning operator according to the learning effect, the sequence code and the task assignment code; constructing a learning effect scheduling model according to the learning operator and the scheduling model;

the method for constructing the learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect comprises the following steps:

acquiring a forgetting operator according to the learning forgetting effect, the sequence codes and the task assignment codes; constructing a learning forgetting effect scheduling model according to the forgetting operator and the scheduling model;

in the learning effect scheduling model, a skill value of a skill type employee i when using a skill j to participate in a task d is calculated by adopting an equation (17):

the skill level value for skill j of a skilled employee i after the software project is completed is calculated using equation (18):

in the learning forgetting effect scheduling model, a skill value of a skill type employee i when using a skill j to participate in a task d is calculated by adopting an equation (19):

calculating the skill level value of the skill j of the skill-type employee i after the software project is finished by adopting an equation (20):

in the formula (I), the compound is shown in the specification,

indicating a level of skill i the skill type employee had at the beginning of the software project; ST (ST) _d Representing a start time of the task; a is a _ij A learning operator representing skill j of a skill type employee i; y is _ijdt Is an auxiliary variable of 0 to 1, i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to s, and d is more than or equal to 1 and less than or equal to m; if y _ijdt =1, indicating that the skill type employee i uses the skill j to attend the task d during the time period t, otherwise it is zero; x is the number of _ijd Is a decision variable of 0-1, i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to s, and d is more than or equal to 1 and less than or equal to m; if x _ijd =1, indicating that the skill type employee i uses the skill j to attend the task d, otherwise it is zero; t is a unit of _ijd Representing the time that a skill-type employee i engages in task d using skill j; b _ij A forgetting operator representing skills j of a skill type employee i; FT _d Representing the completion time of the task; n represents the total number of employees; m represents the total number of tasks;

the obtaining of the scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model includes:

acquiring a learning effect task construction period, learning effect personnel cost and a learning effect personnel working time balance value according to the learning effect scheduling model;

the method for acquiring the learning effect task construction period, the learning effect personnel cost and the learning effect personnel working time equilibrium value according to the learning effect scheduling model comprises the following steps:

acquiring a learning effect skill value according to the learning effect scheduling model, the personnel initial skill value and the learning effect formula;

acquiring a work time balance value of the learning effect personnel according to the learning effect skill value and the personnel skill use time;

the method for acquiring the project period of the learning forgetting effect task, the cost of the learning forgetting effect personnel and the working time balance value of the learning forgetting effect personnel according to the learning forgetting effect scheduling model comprises the following steps:

acquiring a learning forgetting effect skill value according to the learning effect scheduling model, the personnel initial skill value and a learning forgetting effect formula;

acquiring the learning forgetting effect task construction period according to the learning forgetting effect technical value and the task construction period;

2. A dispatch system based on the learning-forgetting effect, comprising:

the learning forgetting effect scheduling model building module is used for building a learning forgetting effect scheduling model according to the scheduling model and the learning forgetting effect; the scheduling information acquisition module is used for acquiring scheduling information according to the learning effect scheduling model and the learning forgetting effect scheduling model;

the scheduling model building module comprises:

the task comprises a task construction period;

the personnel information includes: personnel cost, initial skill value of personnel, and personnel skill use time;

the learning effect scheduling model building module comprises:

the learning effect scheduling model constructing sub-module is used for constructing a learning effect scheduling model according to the learning operator and the scheduling model;

the learning forgetting effect scheduling model building module comprises:

the forgetting operator obtaining sub-module is used for obtaining a forgetting operator according to the learning forgetting effect, the sequence codes and the task assignment codes; the learning forgetting effect scheduling model constructing submodule is used for constructing a learning forgetting effect scheduling model according to the forgetting operator and the scheduling model;

in the formula (I), the compound is shown in the specification,

indicating a level of skill i the skill type employee had at the beginning of the software project; ST (ST) _d Representing a start time of the task; a is _ij A learning operator representing skill j of a skill type employee i; y is _ijdt Is an auxiliary variable of 0 to 1, i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to s, and d is more than or equal to 1 and less than or equal to m; if y _ijdt =1, indicating that the skill type employee i uses the skill j to attend the task d during the time period t, otherwise it is zero; x is a radical of a fluorine atom _ijd Is a decision variable of 0 to 1, i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to s, and d is more than or equal to 1 and less than or equal to m; if x _ijd =1, meaning the skill type employee i uses the skill j to participate in the task d, otherwise it is zero; t is _ijd Representing a time at which a skill type employee i engages task d using skill j; b _ij A forgetting operator representing skills j of a skill type employee i; FT _d Representing the completion time of the task; n represents the total number of employees; m represents the total number of tasks;

the scheduling information obtaining module includes:

the learning forgetting effect value acquisition submodule is used for acquiring a learning forgetting effect task construction period, the learning forgetting effect personnel cost and the learning forgetting effect personnel working time balance value according to the learning forgetting effect scheduling model;