CN106156891A - A kind of Scheduling method based on Pareto multiple target ant colony optimization algorithm - Google Patents
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Abstract
The present invention relates to Scheduling field, more specifically, relate to a kind of Scheduling method based on Pareto multiple target ant colony optimization algorithm, Scheduling method based on Pareto multiple target ant colony optimization algorithm disclosed by the invention, including S1, the Formica fusca of pathway figure of looking for food employee is converted into to(for) the engagement of task；S2, the pathway figure of looking for food of initialization Formica fusca, arrange non-disaggregation and the initial value of being dominant；S3, pathway figure of looking for food according to every Formica fusca i foundation construct feasible solution Si, and assess feasible solution SiFeasibility；S4, update non-disaggregation PS that is dominant, until algorithm runs to certain iterations, just terminate circulation and export the non-solution being dominant in disaggregation i.e. Pareto disaggregation (PS), otherwise enter above-mentioned steps 3, Scheduling problem can be effectively solved within the less time, in major part example, obtain the solution more excellent than classical NSGA II algorithm, and can obtain there is the less project development cycle.
Description
Technical field
The present invention relates to Scheduling field, more particularly, to one based on Pareto multiple target ant group optimization
The Scheduling method of algorithm.
Background technology
Along with software industry develops rapidly, software project becomes more and more huger and complicated, breaks out in Software Development
Go out a lot of problem: incomplete Project Management and the most rigorous software development process control to cause various software quality problem
Occuring frequently, now, Scheduling problem becomes of crucial importance and is rich in challenge.
Real-life Scheduling problem is the most extremely complex, and is difficult to ask in polynomial time
Solve, it is impossible to utilize deterministic algorithm effectively to solve, the existing method solving Scheduling multi-objective optimization question
Mostly utilize following algorithm: single goal ant colony combinatorial optimization algorithm, NSGA-II, SPEA2, PAES etc..
Single goal combinatorial optimization algorithm is that multi-objective optimization question utilizes mathematical combination strategy be converted into single target letter
Number, recycling single object optimization algorithm solves.The method can only solve and obtain a combination optimal solution, but this solution is not necessarily
Meet the demand of software project managers, such as project administrator sometimes need to take into account simultaneously development cost is minimum and the duration
The conflicting target of short the two, Pareto solution is to solve for the more rational decision scheme of multiple target optimization problem simultaneously,
It is the compromise optimal solution considering each optimization aim.
The multi-objective Evolutionary Algorithm of this kind of classics of NSGA-II, SPEA2 and PAES uses bionics principle, can be in certain journey
Solve Scheduling multi-objective optimization question on degree, it is thus achieved that one group of Pareto optimal solution, but these results are not met by
The demand of actual software project management.It is primarily present following two problem: it is relatively low that (1) solves time efficiency；(2) decision support
Information is inadequate.
Prior art shortcoming: existing based on classical multi-objective Evolutionary Algorithm or single goal Combinatorial Optimization ant group algorithm soft
Part project scheduling method is primarily present and solves time efficiency lowly, and solving result can not meet the need of actual software project administrator
Ask, and the defect that information for supporting some decision is not enough.Information for supporting some decision deficiency refers to, in the face of existing method solves a group of generation
Pareto optimal solution, manager, in addition to considering desired value attribute, does not has other reference informations, especially meets demand in desired value
A series of solutions in be difficult to select, thereby increases and it is possible to the stability of solution selected is very poor, there is greater risk.
It is therefore proposed that a kind of Scheduling based on Pareto multiple target ant colony optimization algorithm solving the problems referred to above
Method is the most necessary.
Summary of the invention
The present invention is to overcome at least one defect (not enough) described in above-mentioned prior art, it is provided that a kind of many based on Pareto
The Scheduling method of target ant colony optimization algorithm.
For solving above-mentioned technical problem, technical scheme is as follows: a kind of based on Pareto multiple target ant group optimization
The Scheduling method of algorithm, comprises the following steps；
S1, employee is converted into for the engagement of task the pathway figure of looking for food of Formica fusca；
S2, the pathway figure of looking for food of initialization Formica fusca, arrange non-disaggregation and the initial value of being dominant；
S3, pathway figure of looking for food according to every Formica fusca i foundation construct feasible solution Si, and assess feasible solution SiFeasible
Property；
S4, update the non-disaggregation that is dominant；
If S5 algorithm runs to certain iterations, just terminate circulation and export the most non-solution that is dominant of Pareto disaggregation
Solution in collection (Pareto Set, PS), otherwise enters above-mentioned steps 3.
Further, in described step S1, comprise the steps；
S11, one node city the 0th of generation arrange as start node；
S12, j node of structure as first employee for candidate's engagement node of each task；
S13, construct the engagement node of other employees；
S14, one node city E+1 of generation arrange as terminal node；
S15, the limit produced between the node connecting each neighbours row.
Further, described when constructing one and solving, Formica fusca can only select a node to pass through in each column, each
Employee has for each task and an only engagement.
Further, in described step S2, comprise the steps；
S21, the non-disaggregation PS=Ф that is dominant is set；
S22, the initial value of pheromone is set to 1.
Further, in described step S3, comprise the steps；
S31, construction solution Si, carry out structure by every Formica fusca i according to its heuristic information, pheromone information and probability matrix
Make feasible solution Si。
S32, assessment solve Si, calculate feasible solution SiProject cost cost and two desired values of project duration duration, and
The feasibility that assessment solves.
Further, in described step S4, comprise the steps；
S41, update PS, if non-disaggregation PS that is dominant does not exists any solution can be dominant solution Si, just by feasible solution SiAdd PS
In, and remove all by feasible solution S from PSiThe solution being dominant.
S42, renewal Pheromone Matrix, for every Formica fusca i, if feasible solution SiEpicycle is added in PS,
Just the pheromone information of Formica fusca i place group is updated.
S43, current optimal solution xi of renewal subproblem i, if the neighbours that current optimal solution xi is taken turns middle Formica fusca i by this produce
Optimal solution SxIt is dominant, then xi=S is setx。
Compared with prior art, technical solution of the present invention provides the benefit that:
By Scheduling problem being solved based on the multiple target ant colony optimization algorithm decomposed, it is thus achieved that one group
Pareto optimal solution, then these solutions are carried out Monte Carlo Experiment, analyze it the most true in data parameters " employee's maximum engagement "
Robustness time fixed or unstable, and it is visualized as software by Pareto leading surface bubble chart and threshold value screening leading surface figure
Project administrator provides more information for supporting some decision, contrasts, with this, the robustness that each Pareto solves.Experiment shows, proposition
Algorithm can effectively solve Scheduling multi-objective optimization question within the only about half of time of classical NSGA-II algorithm, and
The robust analysis method proposed can provide more rich decision support for software project managers.
The multiple target ant colony optimization algorithm based on Pareto that this patent proposes, it is possible to effectively ask within the less time
Solve Scheduling problem, major part example obtains the solution more excellent than classical NSGA-II algorithm, and can obtain and have
The less project development cycle.The robust analysis method solving Pareto proposed can judge the robustness and the stability that solve,
And be dissolved in Pareto leading surface and carry out visual presentation, provide except each optimization aim to software project managers
Information for supporting some decision outside value.
Accompanying drawing explanation
Fig. 1 is Scheduling problem model example in the present invention；
Fig. 2 is ant colony feeding structure figure in the present invention；
Fig. 3 is the robust analysis flow chart that in the present invention, Pareto solves；
Fig. 4 is the PF figure that in the present invention, 15e_10t_g10 obtains；
Fig. 5 is the PF figure that in the present invention, 5e_10t_p5 obtains；
Fig. 6 is the PF figure that in the present invention, 10e_20t_p7 obtains；
Fig. 7 is the PF figure that in the present invention, 15e_30t_g10 obtains；
Fig. 8 is the average operating time figure of example set G1 in the present invention；
Fig. 9 is the average operating time figure of example set G2 in the present invention；
Figure 10 is the average operating time figure of example set G3 in the present invention；
Figure 11 is the average operating time figure of example set G4 in the present invention；
Figure 12 is the robustness indicatrix of 24 POS* in example 5e_10t_p5 in the present invention；
Figure 13 is the robustness information visuallization figure of example 5e_10t_p5 in the present invention；
Figure 14 is the robustness indicatrix of 24 POS* in example 15e_30t_p7 in the present invention；
Figure 15 is the robustness indicatrix of 24 POS* in example 10e_10t_g5 in the present invention；
Figure 16 be in the present invention robustness information at the visualization figure of Pareto leading surface.
Detailed description of the invention
Accompanying drawing being merely cited for property explanation, it is impossible to be interpreted as the restriction to this patent；In order to the present embodiment is more preferably described, attached
Scheme some parts to have omission, zoom in or out, do not represent the size of actual product；To those skilled in the art,
In accompanying drawing, some known features and explanation thereof may be omitted and be will be understood by.
In describing the invention, it should be noted that unless otherwise clearly defined and limited, term " is installed ", " even
Connect " should be interpreted broadly, connect for example, it may be fixing, it is also possible to be to removably connect, or be integrally connected；It can be machine
Tool connects, it is also possible to be electrical connection；Can be to be joined directly together, it is also possible to be to be indirectly connected with by intermediary, it may be said that two
The connection of element internal.For the ordinary skill in the art, can understand that above-mentioned term is in the present invention with concrete condition
Concrete meaning.With embodiment, technical scheme is described further below in conjunction with the accompanying drawings.
In the present invention, the English word or the english abbreviation that relate in literary composition are explained as follows:
Pareto: Pareto, is technical term, the name of a mathematician get.
NSGA-II: English full name is Non-dominated Sorting GeneticAlgorithm II, is to NSGA
The modified version of algorithm.NSGA-II Chinese is typically translated as: quickly non-dominated sorted genetic algorithm.
RPS:Reference Pareto Set, translator of Chinese is: with reference to Pareto disaggregation.
POS:Pareto Optimal Solution, translator of Chinese is: Pareto optimizes solution
RI:Robustness Index, translator of Chinese is: robustness index
SPEA2:Strength Pareto Evolutionary Algorithm 2 (SPEA2), translator of Chinese is: improve
The Pareto evolution algorithm of intensity.
PAES:Pareto Archived Evolution Strategy (PAES), translator of Chinese is: Pareto achieve into
Change policing algorithm
Unit: unit
Duration: the duration
Cost: cost
Effort: contribution degree
Skills: technical ability
PF:Pareto Front, Pareto leading surface
MOEA/D-ACO: algorithm full name is: Multi-Objective Evolutionary Algorithm-Ant
Colony Optimization based on Decomposition.
MOEA/D-ACO_MOSPSP: algorithm full name is: Multi-Objective Evolutionary Algorithm-
Ant Colony Optimization algorithm based on Decomposition for Multi-Objective
Software Project Scheduling Problem. translator of Chinese is: be used for solving Scheduling multiple-objection optimization
The multiple target ant group algorithm based on decomposition of problem.
For ease of understanding the present invention, below each accompanying drawing is illustrated:
As it is shown in figure 1, illustrate a software project example to be solved.Related resource is mainly employee and task, its
Middle employee has with properties: the vocational skills of employee, wage and maximum functional amount etc..And each task there is one must
Indispensable skill collection (skills) and required engagement (effort).The deadline of each task is required to meet task
Sequence chart (Task Precedence Graph, TPG).
Realize multiple target ant colony optimization algorithm based on Pareto and solve the first step of Scheduling problem, be by soft
In part project scheduling, employee is converted into the pathway figure of looking for food of Formica fusca for the engagement of task.The Food Recruiment In Ants that each task is corresponding
Figure is as shown in Figure 2.Wherein Unit is that an employee puts into angle value for the minimum of a task, and this numerical value can manually be arranged.Often
Individual employee is for multiple that the engagement of any task is all Unit.
The processing procedure that a task in project is divided into a Food Recruiment In Ants figure is described as follows:
(1) produce a node city the 0th to arrange as start node.
(2) j node of structure as first employee for candidate's engagement node of each task.
(3) the engagement node of other employees is constructed as shown in Figure 2.
(4) produce a node city E+1 to arrange as terminal node.
(5) limit between the node connecting each neighbours row is produced.
Ant colony is looked for food after figure constructed, and the search that starts to look for food on figure of every Formica fusca solves.Formica fusca is from start node, warp
Cross the 1st row in directed graph, the 2nd row ..., E arranges, then to terminal node.Just can try to achieve each according to the path that Formica fusca selects
Employee is for the input angle value of each task.Therefore, have passed through the looking for food in figure of the structure of all tasks in TPG when a Formica fusca
After all row, a candidate solution about this Scheduling problem just is constructed out.
Noting, when constructing one and solving, Formica fusca can only select a node to pass through in each column, because each employee couple
Have and an only engagement (may be 0) in each task.
When Formica fusca scans for construction solution, the method for this patent have employed following two heuristic information strategy:
(1) degree of distribution and employee compensation's information (being designated as H1).This heuristic information strategy refers to each bar limit in figure
Heuristic information is relevant with the wage of the distribution degree that this employee puts in other tasks and this employee.When the wage of employee is got over
Low, and existing distribution degree is the lowest in other tasks, then heuristic information is the biggest.
(2) the total engagement of mission requirements and employee's degree of distribution (being designated as H2).I.e. heuristic information is asked by this required by task
Total engagement and employee in other tasks existing distribution degree determine.When the total engagement of required by task is the biggest, and this member
Work existing engagement in other tasks is the lowest, then heuristic information is the biggest.
When Formica fusca walks in the drawings with construction solution, in figure, the choice of Formica fusca path is played very by the heuristic information on each limit
Big impact.If Formica fusca have selected the node of l row that article of limit as terminal in arranging with kth in the drawings, then this employee for
The engagement of this task is equal to the product of l Yu Unit.
The algorithm utilizing multiple target ant colony optimization algorithm based on decomposition to solve Scheduling problem is referred to as MOEA/
D-ACO_MOSPSP, the detailed process of this algorithm is described as follows:
Input:
-Scheduling example
Output:
-PS, Pareto disaggregation (Pareto Set), the most non-disaggregation that is dominant.
Step 1) initialize.
Step 1.1) PS=Ф is set.
Step 1.2) initial value of pheromone is set to 1.
Step 2) construction solution.
Step 2.1) construction solution Si.Every Formica fusca i carrys out structure according to its heuristic information, pheromone information and probability matrix
Make feasible solution Si。
Step 2.2) assessment solution Si.Calculate two desired values of project cost cost and project duration duration solving Si,
And assess the feasibility of solution.
Step 3) update.
Step 3.1) update PS.If non-disaggregation PS that is dominant does not exists any solution can be dominant solution Si, just by SiAdd PS
In, and remove all by S from PSiThe solution being dominant.
Step 3.2) update Pheromone Matrix.For every Formica fusca i, if solving SiEpicycle is added in PS,
Just the pheromone information of Formica fusca i place group is updated.
Step 3.3) update subproblem i current optimal solution xi.If current optimal solution xi is taken turns the neighbours of middle Formica fusca i by this
Optimal solution S producedxIt is dominant, then xi=S is setx。
Step 4) iteration ends.If meeting end condition, just terminating circulation and exporting the solution in PS.On otherwise entering
State step 3.
The robust analysis of 1.Pareto disaggregation
Problem is standardized by Scheduling model, idealization processes modeling.The data ginseng of Scheduling problem
Number as shown in table 1, its assume all these data parameters all it is known that wherein the maximum engagement acquiescence of employee be all set to
1.0.But employee's maximum engagement of reality is difficult to accurately estimate, and change can occur over time.Above Algorithm for Solving is obtained
The non-disaggregation that is dominant of Pareto carry out robust analysis, investigate its robust disposition when employee's maximum engagement parameter instability
Condition.
Based on employee's maximum engagementThis unstability parameter, is set to 5% by unstability index α, to software item
The non-solution that is dominant of Pareto that mesh Scheduling Problem obtains carries out robust analysis.When α=5%, employee's maximum engagement sample
This interval is expressed as follows:
With " employee's maximum engagement " this uncertain data parameters in Scheduling multi-objective optimization question
As point of penetration, by Monte Carlo simulation experiment, the solving result of algorithm is carried out robust analysis, to provide except two
Robustness information outside optimization target values (i.e. project cost and construction cycle) is for policymaker's reference.Software project managers exists
Optimization object function value and the robustness information of Pareto solution can be considered during decision-making, thus obtain and not only there is more excellent target
Value, and the solution that target function value robustness is higher when little range.It follows that the program can reduce to a certain extent
The risk of whole Scheduling multi-objective optimization question.
Implement flow chart as shown in Figure 3.
In the present invention, the selection of data set, have selected online disclosed test data set.This data set have 36 soft
The test data instance of part project scheduling.These 36 examples are that Spain scholar Alba et al. opens according to actual software project situation
The random generator sent out produces.Having employee and two main bodys of task, the headcount in each group example is respectively 5,10 or 15,
Task quantity is then 10,20 or 30.These data sets can be divided into 4 groups, and often group comprises 9 and has the soft of different employee or task
Part project testing example.In first two groups, total technical ability number is undefined.Test case in latter two groups then has solid
Fixed total technical ability number: 5 or 10.Example table in first group (G1) is shown as Ee_Tt_p5, as example 5e_10t_p5 indicates 5
The technical ability number that individual employee, 10 tasks, and employee possess is 4 or 5.Equally, the example Ee_Tt_p7 in second group (G2) is skill
Can number be 6 or 7.Example in rear two groups (G3 and G4) is represented as Ee_Tt_gS, as 10e_20t_g10 indicates 10
Employee, 20 tasks, and a total of 10 kinds of technical ability.In 36 groups of test data set, the maximum functional of all employees puts into angle value
It is defaulted as 1.0, represents all employees and can be fully immersed in the work of this project.The situation such as following table institute of concrete data set
Show.
One, the selection of method
Classic algorithm NSGA-II that contrast forefathers propose, the Pareto optimum face obtained from Algorithm for Solving and operation time
Two aspects compare.
Two, Pareto optimal solution compares
Have selected the most representational experimental result to show the characteristic of algorithm.RPF reference plane (Reference Pareto
Front, RPF) be made up of the optimal result in these part Experiment all.
In Fig. 4, MOEA/D-ACO_H1 and MOEA/D-ACO_H2 represent respectively use heuristic information H1 and H2 based on
The multiple target ant group algorithm MOEA/D-ACO_MOSPSP decomposed.It is observed that in example 15e_10t_10g MOEA/D-
The solution of ACO_H2 algorithm is all than the Xie Gengyou of NSGA-II.And MOEA/D-ACO_MOSPSP algorithm is also solving 10e_30t_g5,
Performance better than NSGA-II during these examples of 10e_10t_10g and 15e_20t_g10.
Fig. 5 illustrates the solution major part ratio that MOEA/D-ACO_MOSPSP algorithm obtains when solving example 5e_10t_p5
The Xie Gengyou of NSGA-II, and have the trend obtaining the solution with less exploitation duration target.At other 12 examples
In have also discovered same result, these examples are: 10e_10t_p5,10e_20t_p5,15e_10t_p5,15e_30t_p5,
10e_10t_p7,15e_10t_p7,15e_30t_p7,10e_10t_g5,15e_10t_g5,15e_20t_g5,15e_30t_g5
And 5e_10t_g10.
But, in test case 10e_20t_p7, the result of NSGA-II is better than the MOEA/D-ACO_ of current setting
MOSPSP algorithm, concrete outcome is as shown in Figure 6.And similar result also appears in following 10 examples: 5e_20t_p5,
10e_30t_p5,15e_20t_p5,5e_10t_p7,5e_20t_p7,10e_30t_p7,5e_10t_g5,5e_20t_g5,5e_
30t_5 and 10e_20t_g5.
It addition, when software project problem is considerably complicated, MOEA/D-ACO_MOSPSP algorithm and NSGA-II can only obtain
To a small amount of solution.Fig. 7 shows that in complex example 15e_30t_g10 the Pareto solution that two algorithms are obtained is all few, wherein
MOEA/D-ACO_MOSPSP algorithm can obtain the solution more excellent than NSGA-II algorithm.And at example 5e_20t_g10,10e_20t_
G10,10e_30t_g10 and 5e_30t_p5 also has similar situation.
Riming time of algorithm compares
It can be seen that MOEA/D-ACO_MOSPSP algorithm spends the fewest one than NSGA-II from its result Fig. 8 to Figure 11
The operation time of half.In figure, all of time is the meansigma methods taken after each algorithm runs 10 times.
The visualization of robust analysis result
Extracting 3 groups of representational data from 36 groups of test data to test, it is respectively example 5e_10t_p5,
15e_30t_p7 and 10e_10t_g5.
Scheduling problem-instance 5e_10t_p5 creates after 1000 iteration that 1000 Pareto are non-to be dominant
Solving set, totally 64000 POS solve.From RPF, choose 24 representative reference solution POS* (eliminate comparison close
Solve), the robust analysis result of these 24 POS* is added up as shown in figure 12.In figure, each robustness index solved is uneven,
Illustrate that non-being dominant solves the unstability concentrating each solution.
The robustness information visuallization of Pareto leading surface is as shown in figure 13.Wherein figure (a) exhibition in the way of bubble chart
Having shown the robustness of 24 POS*, diameter of a circle is the biggest, and to represent robustness the strongest.By figure (a) can be more visible which is found out
The robustness solved is higher, and the robustness which solves is the most weak.As in example 5e_10t_p5, close to the district that Duration value is maximum
The solution robustness in territory is the most weak, and the strong robustness of the less solution of Duration value.If it addition, policymaker wants to take
Duration < 20 and the solution of Cost < 780000, as can be seen from the figure the solution in this interval class has 9, and wherein
The robustness of that solution that Duration value is minimum is the strongest.
Figure 13 (b) has then filtered out the robustness index solution more than 40%, is that one disturbs information visuallization form less,
The most practical at special scenes.For example 5e_10t_p5, in its 24 POS*, only 6 solutions meet RI > 40%.Now, certainly
Plan person can choose the feasible solution of oneself expectation target value relatively easily in the solution meeting robustness index request.
The robustness indicatrix of example 15e_30t_p7 and 10e_10t_g5 is distinguished the most as shown in Figure 14 and Figure 15, corresponding band
Shown in robustness bubble chart such as Figure 16 (a) and Figure 16 (b).
By above Experimental results show and analysis, it can be seen that the robustness of Scheduling multi-objective optimization question
Analyze the most valuable to project decision person.The Pareto leading surface visualization figure embedding robustness information is expressing each mesh solved
While offer of tender numerical value, moreover it is possible to clearly express the robustness information of solution, it is simple to make decision after policymaker is comprehensive, thus obtain more
Good solution.
In figure, position relationship being merely cited for property explanation is described, it is impossible to be interpreted as the restriction to this patent；Obviously, this
Bright above-described embodiment is only for clearly demonstrating example of the present invention, and not to embodiments of the present invention
Limit.For those of ordinary skill in the field, other multi-form can also be made on the basis of the above description
Change or variation.Here without also cannot all of embodiment be given exhaustive.All the spirit and principles in the present invention it
Interior made any amendment, equivalent and improvement etc., within should be included in the protection domain of the claims in the present invention.
Claims (6)
1. a Scheduling method based on Pareto multiple target ant colony optimization algorithm, it is characterised in that include following
Step；
S1, employee is converted into for the engagement of task the pathway figure of looking for food of Formica fusca；
S2, the pathway figure of looking for food of initialization Formica fusca, arrange non-disaggregation and the initial value of being dominant；
S3, pathway figure of looking for food according to every Formica fusca i foundation construct feasible solution Si, and assess feasible solution SiFeasibility；
S4, update the non-disaggregation that is dominant；
If S5 algorithm runs to certain iterations, just terminate circulation and export the most non-disaggregation that is dominant of Pareto disaggregation
Solution in (Pareto Set, PS), otherwise enters above-mentioned steps 3.
Scheduling method based on Pareto multiple target ant colony optimization algorithm the most according to claim 1, it is special
Levy and be, in described step S1, comprise the steps；
S11, one node city the 0th of generation arrange as start node；
S12, j node of structure as first employee for candidate's engagement node of each task；
S13, construct the engagement node of other employees；
S14, one node city E+1 of generation arrange as terminal node；
S15, the limit produced between the node connecting each neighbours row.
Scheduling method based on Pareto multiple target ant colony optimization algorithm the most according to claim 2, it is special
Levying and be, described when constructing one and solving, Formica fusca can only select a node to pass through in each column, and each employee is for each
Task has and an only engagement.
Scheduling method based on Pareto multiple target ant colony optimization algorithm the most according to claim 1, it is special
Levy and be, in described step S2, comprise the steps；
S21, the non-disaggregation PS=Ф that is dominant is set；
S22, the initial value of pheromone is set to 1.
Scheduling method based on Pareto multiple target ant colony optimization algorithm the most according to claim 1, it is special
Levy and be, in described step S3, comprise the steps；
S31, construction solution Si, construct one by every Formica fusca i according to its heuristic information, pheromone information and probability matrix
Individual feasible solution Si。
S32, assessment solve Si, calculate feasible solution SiProject cost cost and two desired values of project duration duration, and assess
The feasibility solved.
Scheduling method based on Pareto multiple target ant colony optimization algorithm the most according to claim 1, it is special
Levy and be, in described step S4, comprise the steps；
S41, update PS, if non-disaggregation PS that is dominant does not exists any solution can be dominant solution Si, just by feasible solution SiAdd in PS,
And remove all by feasible solution S from PSiThe solution being dominant.
S42, renewal Pheromone Matrix, for every Formica fusca i, if feasible solution SiEpicycle is added in PS, just to ant
The pheromone information of ant i place group is updated.
S43, current optimal solution xi of renewal subproblem i, if the neighbours that current optimal solution xi is taken turns middle Formica fusca i by this produce
Excellent solution SxIt is dominant, then xi=S is setx。
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Cited By (2)
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| CN109460862A (en) * | 2018-10-22 | 2019-03-12 | 郑州大学 | The method that meta-heuristic algorithms based on MAB solve multi-objective optimization question |
| US20210390487A1 (en) * | 2018-01-15 | 2021-12-16 | Nmetric, Llc | Genetic smartjobs scheduling engine |
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2016
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| JING XIAO等: "Empirical Study of Multi-objective Ant Colony Optimization to Software Project Scheduling Problems", 《PROCEEDINGS OF THE 2015 ANNUAL CONFERENCE ON GENETIC AND EVOLUTIONARY COMPUTATION》 * |
| 肖菁等: "基于蚁群算法的多目标优化技术研究", 《华南师范大学学报（自然科学版）》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| US20210390487A1 (en) * | 2018-01-15 | 2021-12-16 | Nmetric, Llc | Genetic smartjobs scheduling engine |
| CN109460862A (en) * | 2018-10-22 | 2019-03-12 | 郑州大学 | The method that meta-heuristic algorithms based on MAB solve multi-objective optimization question |
| CN109460862B (en) * | 2018-10-22 | 2021-04-27 | 郑州大学 | Method for solving multi-objective optimization problem based on MAB (multi-object-based) hyperheuristic algorithm |
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