CN107944623A - A kind of optimization method and its application based on saccharomycete budding breeding - Google Patents

Abstract

A kind of optimization method and its application based on saccharomycete budding breeding, the present invention relates to fleet retention optimization method, the problem of in order to solve the prior art when fleet retention Optimized model optimal solution is not unique, optimal fleet retention can not be obtained.Culture medium is considered as the range constraint of optimization problem continuous type solution by the present invention；Inoculation yeast bacterium process is considered as initial solution generating process；Budding breeding of the saccharomycete on culture medium is considered as majorization of solutions process：It is excellent solution that the saccharomycete bred, which is fallen into culture medium, can survive and can continue to breed；Otherwise it is then inferior solution, it is impossible to which survival is also impossible to continue to breed.Continuous type optimal solution in view of optimization problem is probably the situation that zonal cooling or initial solution drop into non-culture medium, and the inferior solution allowed in non-culture medium can be found and move to optimal populated regions and be bred.The region that the excellent solution set bred is covered is exactly the continuous type optimal solution of optimization problem.The present invention is used for aircraft maintenance management domain.

Description

Optimization method based on yeast budding propagation and application thereof

Technical Field

The invention relates to a yeast budding propagation-based chemical method and application thereof.

Background

The modern aviation maintenance thought is a reliability-centered maintenance thought. The reliability-centered maintenance decision is made without considering maintenance resources and maintenance cost, the reliability is used as the only target of maintenance planning arrangement, and the decision model has the advantages that the reliability of the airplane is ensured very high, and the disadvantages that the maintenance resources are overloaded, the maintenance cost is wasted, and the retention rate of the airplane fleet cannot meet the requirement. Most of the existing aviation maintenance models are aimed at civil aviation, and the maintenance targets are single and aimed at single unit utilization rate from the perspective of an airplane. Air force troops are more concerned about enough airplanes to complete tasks under special conditions, and need to arrange maintenance plans from the perspective of the fleet to ensure the minimum guarantee rate requirement of the fleet.

The existing single-target optimization method mainly comprises the following steps: deterministic methods and stochastic methods. Deterministic methods, such as steepest descent, conjugate gradient, newton descent, generally search for ordered iterations of the solution space, and finally converge to a local or global optimum; stochastic methods, such as simulated degenerate algorithms, differential evolution algorithms, genetic algorithms, particle swarm algorithms, generally generate a finite number of initial solutions, then perform heuristic search on the solution space, and finally converge to a solution. For the problem of airplane fleet retention rate optimization with non-unique optimal solution, no better solution method exists at present. The invention provides a method for solving an optimization problem of a continuous solution form simulating a budding propagation process of saccharomycetes in a culture medium by taking the propagation process of organisms in the culture medium as reference.

Disclosure of Invention

The invention aims to solve the problem that in the prior art, when the optimal solution of a fleet retention rate optimization model is not unique, all solutions of the fleet retention rate model cannot be obtained, so that the optimal fleet retention rate cannot be obtained, and provides an optimization method based on yeast budding propagation and application thereof.

An optimization method based on yeast budding propagation comprises the following steps:

inputting: an objective function f (x), an initial population size n (inoculation scale), the number z of inferior solutions selected for migration in the neighborhood searching step based on a Particle Swarm Optimization (PSO), the side length epsilon of a continuous solution unit (CSE), and a relaxation variable xi;

and (4) termination conditions: the fluctuation range of the number of continuous solution units reaching the maximum iteration number S or in the latest triple iteration EP is within 1 percent; EP is the output data set (corresponding to the maintenance time of each aircraft in the fleet);

the method comprises the following steps: generating an initial solution;

n seeds were randomly generated: x is the number of ¹ ,x ² ,...,x ⁿ X is to ¹ ,x ² ,...,x ⁿ Converting the continuous solution unit into a continuous solution unit, and adjusting the continuous solution unit to the central position of the grid;

step two: carrying out budding propagation on the reproducible optimal solution MS in the initial solution generated in the step one, and defining the neighborhood of the MS as a budding position;

step three: performing neighborhood search on the budding position defined in the second step by adopting a particle swarm algorithm, if the obtained solution is less than or equal to MS (the solution can be less than or equal to or greater than the MS according to an actual objective function, if the solution is minimized, the solution is less than or equal to, and if the solution is maximized, the solution is greater than or equal to), storing the position of the solution into an optimal position data set (OPS), adding the solution stored into the optimal position data set into the EP, emptying the optimal position data set, and if the solution is greater than the MS, eliminating (not recording);

step four: adjusting the solution added into the EP in the step three to the central position of the located grid (by adopting the same method as the step one);

step five: and (5) iteratively executing the step one to the step four until an iteration termination condition is met, and outputting the EP.

The method for optimizing the airplane fleet survival rate based on the yeast budding propagation optimization is applied to the airplane fleet survival rate optimization process.

The invention has the beneficial effects that:

the solution form of the existing optimization problem is a discrete solution, and for the optimization problem of which the solution form is a continuous function, no better solution method exists at present. The invention provides a method for solving an optimization problem of a continuous solution form simulating the budding propagation process of saccharomycetes in a culture medium by using the propagation process of organisms in the culture medium, which has the basic idea that: the culture medium is regarded as the regional constraint of the continuous solution of the optimization problem; the yeast inoculation process is regarded as an initial solution generation process; the budding propagation of the yeast on the culture medium is regarded as the optimization process of solution: the bred microzyme falls into the culture medium for optimal solution, can survive and can be bred continuously; the yeast after propagation falls into a non-culture medium, is inferior, cannot survive and cannot propagate continuously. Considering the condition that the continuous optimal solution of the optimization problem is possibly in a segmented continuous manner or the initial solution falls into a non-culture medium, the invention provides a neighborhood search method based on particle swarm, so that the inferior solution in the non-culture medium can be searched and transferred to an optimal propagation area for propagation. Finally, the area covered by the propagated optimal solution set is the continuous optimal solution of the optimization problem. The method adopts 2 engineering problems to test the method, and the experimental result shows the correctness and the effectiveness of the method.

Drawings

FIG. 1 is a piecewise continuous optimal solution form diagram;

FIG. 2 is a diagram showing the propagation process of yeast in the culture medium;

FIG. 3 is a schematic illustration of a propagation process;

FIG. 4 is a representation of an optimal solution in a 1-dimensional space;

FIG. 5 is a representation of an optimal solution in a 2-dimensional space; in the figure (c) ₁ ,c ₂ ) The coordinate of the central point of the solution unit is shown, and epsilon is the side length of the solution unit;

FIG. 6 is a representation of an optimal solution in a 3-dimensional space;

FIG. 7 is a schematic diagram of the budding process of yeast;

FIG. 8 is a diagram showing a multistage budding pattern of yeast;

FIG. 9 shows the sprouting pattern of the maternal solution in 1-dimensional space;

FIG. 10 shows the sprouting pattern of the maternal solution in 2-dimensional space;

FIG. 11 shows the germination pattern of the maternal solution in 3-dimensional space;

FIG. 12 shows the sprouting patterns of two adjacent parents in 2-dimensional space;

FIG. 13 is a propagation diagram of a solution unit under a dimensional space;

FIG. 14 is a diagram illustrating a neighborhood search of a inferior solution unit in dimensional space;

FIG. 15 is a process diagram of the transformation of 10 random solutions of the dimensional space into CSE;

FIG. 16 is a map of the overlap of regions during propagation;

FIG. 17 is a diagram of an optimal solution under CSE location normalization;

FIG. 18 is a diagram of an optimal solution without CSE location normalization;

FIG. 19 is a schematic diagram of a particle swarm-based neighborhood search;

FIG. 20 is a block diagram of an unnormalized continuous solution found;

FIG. 21 is a normalized continuum solution unit;

FIG. 22 is a schematic representation of re-inoculation;

FIG. 23 is a diagram illustrating the optimization results of the retention rate model shown in formula (9) in the first embodiment;

FIG. 24 is a diagram illustrating the optimization results of the retention rate model shown in the first embodiment (10);

FIG. 25 is a Gantt chart of two retention optimization models of the model shown in formula (9) in example I;

FIG. 26 is a Gantt chart of two retention optimization models of the model shown in formula (10) in example I.

Detailed Description

The first embodiment is as follows: an optimization method based on yeast budding propagation comprises the following steps:

in each iterative optimization, the OA/BPY holds the following data:

initial population: x is a radical of a fluorine atom ¹ ,x ² ,...,x ⁿ ∈Ω。

F ¹ ,F ² ,...,F ⁿ : wherein F ⁱ Is solving for x ⁱ The fitness value of (a).

f ^* : optimal value in the current population.

Optimal position data set (OPS): for storing the optimal locations found during the PSO-based domain search.

Output data set (EP): used to store all the normalized CSE during propagation.

Inputting: an objective function f (x), an initial population size n (inoculation scale), the number z of inferior solutions selected for migration in the neighborhood search step based on a Particle Swarm Optimization (PSO), the side length epsilon of a continuous solution unit (CSE), and a relaxation variable xi;

and (4) termination conditions: the fluctuation range of the number of continuous solution units reaching the maximum iteration number S or in the latest triple iteration EP is within 1 percent; EP is the output data set (corresponding to the maintenance time of each aircraft in the fleet);

the method comprises the following steps: generating an initial solution;

randomly generating n seeds: x is the number of ¹ ,x ² ,...,x ⁿ X is to be ¹ ,x ² ,...,x ⁿ Converting the continuous solution unit into a continuous solution unit, and adjusting the continuous solution unit to the central position of the grid;

step two: carrying out budding propagation on the reproducible optimal solution MS in the initial solution generated in the step one, and defining the neighborhood of the MS as a budding position;

step three: performing neighborhood search on the budding positions defined in the step two by adopting a particle swarm algorithm, if the obtained solution is less than or equal to MS (the solution can be less than or equal to or greater than the MS according to an actual objective function, if the solution is minimized, the solution is less than or equal to, and if the solution is maximized, the solution is greater than or equal to), storing the positions of the solutions into an optimal position data set (OPS), adding the solutions stored into the optimal position data set into EP, emptying the optimal position data set, and if the solutions are greater than MS, eliminating (not recording);

step four: adjusting the solution added into the EP in the step three to the central position of the grid (by adopting the same method as the step one);

step five: and (5) iteratively executing the step one to the step four until an iteration termination condition is met, and outputting the EP.

The optimization algorithm based on the budding propagation of the yeast is a process of 1 cycle of 'inoculation' and 'migration', and can avoid the situation that 1 time of 'inoculation' or 'migration' is carried out, solution does not fall into COS and cannot propagate and cover the whole 'culture medium'. As in fig. 22, after 2 "inoculations" and "migrations", the COS on the right would be found, followed by a reproduction to cover all COS.

According to the method provided by the invention, the continuous solution optimization problem can be solved according to the following steps:

(1) Continuous solution optimization problem and solution thinking

For the optimization problem shown in formula (1), the optimal solution can be obtained by adopting mathematical derivationIs a continuous 2-dimensional function, and only f (x) can be obtained by adopting the optimization method ₁ ,x ₂ ) One discrete solution in (a), the entire continuous region cannot be obtained.

As shown in fig. 1, if the optimal solution is in the form of 3 piecewise continuous regions, the current optimization method is difficult to support the solution process.

FIG. 2 is a microscopic image showing the propagation and growth of yeast by budding of the mother. FIG. 3 is a schematic diagram showing the propagation and growth process of yeast seeds inoculated into the culture medium. Three irregular culture mediums with the numbers of 1,2 and 3 are respectively arranged in the container, the yeast seeds are inoculated into the container, wherein three yeast seeds respectively fall on the culture medium with the number of 1,2, and the rest fall on a non-culture medium area. Three yeast seeds in the medium began to multiply and grow until the entire medium was covered. While the remaining yeast seeds die due to lack of reproductive conditions.

Therefore, the invention provides an optimization problem solving method for simulating the continuous optimal solution form of the propagation process of the microzyme in the culture medium by taking the propagation process of the microzyme in the culture medium as a reference, which comprises the following steps: the yeast inoculation process is an initial solution generation process, the culture medium is used as the reproductive constraint of the initial solution, and the propagation process of the yeast is an optimization process: the budded yeast falls into the culture medium to be dominant solution and can survive and continue to reproduce; the budded yeasts fall into a non-culture medium area, which is a disadvantage solution and cannot survive and cannot propagate continuously. The actual inoculation of yeast may result in a culture medium (e.g., medium No. 3 in fig. 3) that is not inoculated with yeast, i.e., the initial solution does not fall into the continuous optimal solution region, and no propagation (optimization) process occurs in this region. To solve this problem, it is assumed here that yeast seeds falling in non-culture medium will find and migrate to the nearest culture medium for propagation, based on the property that organisms constantly find the optimal living environment for propagation, namely: the initial solution falling into the non-optimal solution area is propagated by searching the optimal solution area closest to the initial solution by a neighborhood search method. Finally, the propagated yeast covers all the culture medium, namely, the continuous optimal solution is obtained.

(2) Continuous optimal solution form and continuous solution unit definition in optimization problem

As discussed in the introduction, there is an optimization problem in actual engineering where the optimal solution is continuous. According to different decision space dimensions of optimization problems, a Continuous Optimal Solution (COS) form is represented as a plurality of non-connected space closed regions. For example, COS is represented in one-, two-, and three-dimensional decision spaces as shown in fig. 4 to 6, and c-letter in fig. 4 to 6 represents the coordinates of the center point.

In the 1-dimensional space, COS is a plurality of interval sets; in 2-dimensional space, COS is a collection of planes with irregular boundaries; in the 3-dimensional space are several 3-dimensional stereo sets with irregular surfaces.

Definition 1. Continuous solution unit (CSE) which is a basic linear unit in the decision space of the optimization problem, here denoted g (-).

As shown in fig. 4-6: the 1-dimensional CSE is an interval, the length of which is represented by epsilon, and the midpoint of which is c; the 2-dimensional CSE is a square, the length of which is represented by ε, and the midpoint is (c) ₁ ,c ₂ ) (ii) a The 3-dimensional CSE is a cube with ε representing the length of the square and the midpoint being (c) ₁ ,c ₂ ,c ₃ ) (ii) a For more than 3 dimensions (n)&gt, 3), the CSE is a hypercube with side length of epsilon and midpoint of (c) ₁ ,c ₂ ,...,c _n )。

Cos is the limit for a series of CSE combinations expressed as:

in the formula: phi is COS;

X＝(x ₁ ,x ₂ ,...,x _n ) N represents the dimension of the decision space;

g (. Epsilon., i) represents the ith CSE of length ε.

(3) Method for solving continuous solution optimization problem

(a) Propagation process of Jiejie

As described above, after yeast seeds are seeded in the medium, the yeast is propagated in the medium as a mother body by budding. Referring to fig. 7-8, the germination process and the random (multi-stage) germination pattern of yeast are shown, and one parent can simultaneously germinate and propagate in a plurality of nutrient-rich and suitable propagation positions.

By taking the budding propagation mode of the yeast as a reference, the invention establishes the budding propagation mode of solving the optimization problem of different spatial dimensions. In the continuous solution optimization problem, an initial solution is given in the form of CSE, and if it is judged by evaluation (evaluation method is to calculate objective function value) that the initial solution is within the range of COS, the initial solution starts to propagate as a "maternal solution" (MS), and the budding direction of the MS during propagation is defined as shown in fig. 9 to 12.

The breeding process is continued, as shown in FIG. 13, CSE is propagated by 2 times of budding, the covered area is expanded to the area enclosed by the red solid line frame, and the COS can be obtained after the process is continued. If the initial solution is judged to have no reproductivity by evaluation, the initial solution (inferior solution) is searched and moved to the nearest nutrient-rich and suitable reproduction position (maternal budding position) for reproduction. FIG. 14 shows a poor solution to the nearest budding site in the neighborhood search process.

(b) Determination of the reproductive Properties of solutions

From the above, it can be seen that yeast can multiply when it falls within a medium, which is a constraint on the reproductivity of yeast. The culture medium is equivalent to COS in the optimization problem, is the final solving target of the problem, and cannot be used for judging the solution reproductive performance in the optimization process. Therefore, the present invention defines the current continuous optimal solution area as the 'culture medium' for each optimization process in the following way to support the budding propagation of solutions in the 'culture medium'.

Definition 3: current continuous optimal solution area (CCOSD): CCOSD is a neighborhood of the best solution found in the current solution space, and solutions falling within the neighborhood are all defined as MS capable of budding.

The expression of CCOSD is:

|f(x)-f ^* |≤ξ (3)

where f (-) is the objective function, f (x) is the solution corresponding to the current x, f ^* Is the optimal solution that has been obtained and ξ is the relaxation variable.

(c) Several problems in initial solution generation

Initial solution generation step (inoculation):

step1. Generation of n random points x ¹ ,x ² ,...,x ⁿ E.g. omega. (as shown in FIG. 15, 10 random points are randomly generated);

step2. The present invention converts n random points into coordinate index and position index using formulas (4) and (5), and CSE is expressed using coordinate index and position index, which is equivalent to converting random points into CSE, as shown in fig. 16. This process amounts to adjusting the position of the random point to the grid position in the decision space closest to it, normalizing its position.

p _i ＝round((|x _i |+ε/2)/ε) (5)

Why is the position of the initial solution normalized in step 2? There are two reasons:

1. as shown in fig. 16, if the CSE location is not normalized, in the propagation process, a region overlap (region repeat search) may occur, which affects the efficiency of the propagation covering COS.

2. If the COS of the optimization problem is a circle (curve), compare the results of the optimization with the CSE normalized and unnormalized shown in FIG. 17 and FIG. 18: obviously, after the normalization processing, the number of CSEs obtained by solving is small and limited; under non-normalization, theoretically there could be an infinite number of CSEs overlapping on the continuous optimal solution area, which would cause a dead-loop of the optimal solution.

(d) Neighborhood search algorithm based on particle swarm

When a CSE is not fertile, it will find the nearest nutrient-rich, suitable location for propagation (maternal emergence location) in the decision space for propagation. The invention improves the PSO, provides a neighborhood search algorithm based on the PSO and supports the optimization process of CSE. The basic idea of the algorithm is described here by taking the COS of an optimization problem as an example of a region as shown in fig. 17.

1. Randomly generating 6 particles { a, b, c, d, e, f }, and converting the formulas (3) and (4) into CSE in space to serve as an initial solution of an optimization problem;

2. judging a in the 6 initial solutions as the current optimal solution by adopting an objective function for the initial solution central value, determining CCOSD (culture medium) according to 3.2 sections, wherein only solution a exists in the culture medium range, so that a has reproductive performance and 4 budding positions;

{ b, c, d, e, f } falls outside the "medium", called the inferior solution set, and the optimal position on the medium needs to be found, so the direction to { n } starts ₁ ,n ₂ ,n ₃ ,n ₄ 4 budding sites were migrated.

4. Adopting a neighborhood search algorithm based on particle swarm to ensure that a rogue solution set { b, c, d, e, f } is directed to a budding position n ₁ Migration is an example to introduce the whole search process. As shown in FIG. 19, the disadvantaged set { b, c, d, e, f } is directed to the sprouting position n ₁ Direction shift, passing j times (S in the figure) _bj Representing element b migrated j times), d finds a ratio n ₁ The better solution (because it falls into COS), so after step j, { b, c, e, f } changes the original migration direction and starts to migrate towards d. b, c, e, f are respectively passed through S _bk ,S _cl ,S _em ,S _fn COS was also found after the migration step. FIG. 20 is an optimal location without duplication where records are stored during migration. FIG. 21 is a CSE normalized for the optimal location found during migration.

Unlike the location update procedure of the conventional PSO: bud n ₁ Is defined as a global optimum position at initializationIf the inferior solution b, c, d, e, f is in the migration path and a position which can be propagated is found (i.e. the fitness is better), updatingEach particle no longer stores the optimum position it finds, but rather usesAs the optimal location during the { b, c, d, e, f } migration (this optimal location may also fall outside the COS region, but it is optimal in the migrated path location). Based on the above modifications to the PSO, the new velocity is updated to equation (5) and the location update is equation (6).

v _i,j (t+1)＝wv _i,j (t)+c ₁ r ₁ (xp _j (t)-x _i,j (t))+c ₂ r ₂ (xg _j (t)-x _i,j (t)) (6)

x _i,j (t+1)＝x _i,j (t)+v _i,j (t+1) (7)

Where w is the inertial weight, c ₁ And c ₂ Is a learning factor, r ₁ And r ₂ To obey the random number of uniformly distributed U (0, 1).

PSO-based neighborhood search algorithm (NS/PSO):

1) Determining a budding position n requiring neighborhood search _b (e.g., n in the above ₁ )；

2) Initializing an optimal position data set, and adding the budding position determined in Step 1) into the data set;

3) Selecting z distances n from CSE (inferior solution) falling outside CCOSD _b Nearest (distance n for faster migration efficiency) _b Closer CSE requires less number of transitions, e.g. FIG. 19-21 choosing { b, c, d } to transition to n ₁ ) As an initial particle group IP;

4) The PSO parameters are initialized. N is to be _b Is arranged asSelecting a distance n from the best individual in IP _b The most recent one is set as

5) The particles in P are "migrated".

a) Respectively updating the speed and the position of z particles in the IP according to the equations (6) and (7);

b) Determining the reproductivity of the solution of the newly obtained particles of a);

c) UpdatingAnd

d) The optimal location storage data set (OPS) is updated. Randomly selecting one particle from the OPS, emptying the OPS if the fitness of the newly obtained particle is better than the randomly selected particle, and adding the newly obtained particle into the OPS. Adding the particle into the OPS if the fitness of the newly obtained particle is equal to the fitness of the randomly selected particle;

e) Duplicate data in OPS is removed. As shown in FIGS. 19-21, { b, c, d, e, f } is migrating to n ₁ The optimal positions found in the process are stored:in order to avoid repeated addition of optimal positions falling into the same CSE, the data set is screened according to the formulas (4) and (5), and only one CSE can exist in one network position.

f) And (4) terminating: if a predefined termination condition (e.g., the maximum number of iterations or the range of changes in the positions of the particle group over the last few optimization processes) is satisfied, the optimal position set is terminated and output. Otherwise, returning to the step a).

The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the step one, x is ¹ ,x ² ,...,x ⁿ The specific process of converting the continuous solution unit into the continuous solution unit and adjusting the continuous solution unit to the central position of the grid is as follows:

randomly generating n seeds, namely n random points, and converting the n random points into a coordinate index and a position index by adopting the following formula;

whereinFor the j-th dimension of the i-th seed,is composed ofJ =1,.. M, m is the dimension, i =1,. N;is composed ofRound is the rounding function.

Other steps and parameters are the same as those in the first embodiment.

The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: the specific process of carrying out budding propagation on the reproducible optimal solution MS in the initial solution generated in the step one in the step two is as follows:

step two is as follows: calculating an objective function value of each seed, wherein the objective function value of the ith seed is recorded as f ⁱ ，f ⁱ ＝f(x ⁱ )；

Step two: recording the minimum value (the maximum value or the minimum value can be selected according to the actual objective function, namely the optimal value) in the n objective function values obtained in the step two I as f ^* ；

Step two and step three: continuous solution units satisfying the following formula are all defined as MS, and the neighborhood of MS is defined as a budding position;

|f(x ⁱ )-f ^* |≤ξ。

other steps and parameters are the same as those in the first or second embodiment.

The fourth concrete implementation mode is as follows: the aircraft fleet survival rate optimization method based on yeast budding propagation optimization is applied to the aircraft fleet survival rate optimization process.

The fifth concrete implementation mode: the fourth difference between the present embodiment and the specific embodiment is that: the specific process of applying the method to the fleet retention rate optimization process is as follows:

taking a fleet comprising 5 airplanes shown in formula (9) in the first embodiment of the specification as an example (formula (10) is an example in which the fleet comprises 10 airplanes, and the description is not repeated here):

inputting: the method comprises the steps that an objective function f (x) is optimized through coincidence degree of maintenance time of a fleet, the smaller the coincidence degree of the maintenance time of the fleet is, the greater the retention rate of the fleet is, the size n =100 of an initial population (the number of solutions of a maintenance plan of the fleet), the number z =20 of inferior solutions selected for migration in a neighborhood searching step based on a particle swarm optimization algorithm, the side length epsilon =0.5 of a continuous solution unit, and a relaxation variable xi =1;

termination conditions were as follows: the maximum iteration number is 1500, or the fluctuation range of the number of continuous solution units in the latest triple iteration EP is within 1%; EP is the output data set;

the method comprises the following steps: generating an initial solution;

randomly generating 100 fleet maintenance plans (seeds), one fleet maintenance plan containing the maintenance time of each aircraft in the fleet: x is a radical of a fluorine atom ¹ ,x ² ,...,x ⁿ ， Represents the maintenance time of the jth aircraft in the ith fleet maintenance plan, j =1 ¹ ,x ² ,...,x ⁿ Converting the solution into a continuous solution unit, and adjusting the continuous solution unit to the central position of the maintenance time decision space grid; the number of aircraft in the fleet is the dimension of the maintenance time decision space, and if the aircraft comprises 5 aircraft as shown in formula (9) in the first embodiment of the specification, the aircraft is considered to be in the maintenance time decision space

Step two: defining the solution with the minimum aircraft fleet maintenance time contact ratio in the initial solutions generated in the first step as a reproducible optimal aircraft fleet maintenance plan MS, carrying out budding reproduction, and defining the neighborhood of the MS as a budding position, namely a decision space position of the optimal aircraft fleet maintenance plan most possibly obtained;

step three: performing neighborhood search on the budding position defined in the step two by adopting a particle swarm algorithm, if the coincidence degree of the fleet maintenance time corresponding to the obtained solution is less than or equal to the coincidence degree of the fleet maintenance time corresponding to the MS, storing the fleet maintenance plan corresponding to the solution into an optimal fleet maintenance plan data set, adding the solution stored into the optimal fleet maintenance plan data set into the EP, emptying the optimal position data set, and if the coincidence degree of the fleet maintenance time corresponding to the MS is greater than or equal to the coincidence degree of the fleet maintenance time corresponding to the MS, knowing that the fleet retention rate is not optimal, and executing a elimination program;

step four: adjusting the solution added into the EP in the step three to the central position of the maintenance time decision space grid;

step five: and (5) iteratively executing the step one to the step four until an iteration termination condition is met, and outputting the EP.

Other steps and parameters are the same as those in the fourth embodiment.

The sixth specific implementation mode: the fourth or fifth embodiment is different from the specific embodiment in that: in the first step, x is ¹ ,x ² ,...,x ⁿ The specific process of converting the continuous solution unit into the continuous solution unit and adjusting the continuous solution unit to the central position of the maintenance time decision space grid is as follows:

randomly generating n fleet maintenance plans, wherein each seed represents one fleet maintenance plan, namely the n randomly generated fleet maintenance plans, and converting the n fleet maintenance plans into a coordinate index and a position index in a maintenance time decision space by adopting the following formula;

whereinThe maintenance time for the jth aircraft scheduled for the ith fleet maintenance,is composed ofA coordinate index of the decision space at maintenance time, j = 1., m, m being a maintenance time decision space dimension, i = 1., n;is composed ofAnd in the position index in the maintenance time decision space, round is a rounding function.

The other steps and parameters are the same as those in the fourth or fifth embodiment.

The seventh embodiment: this embodiment is different from one of the fourth to sixth embodiments in that: in the second step, the solution with the minimum crew maintenance time contact ratio in the initial solutions generated in the first step is defined as the reproducible optimal crew maintenance plan MS, and the specific process of budding reproduction is as follows:

step two, firstly: calculating an objective function value of each fleet maintenance plan, wherein the objective function value of the ith fleet maintenance plan is recorded as f ⁱ ，f ⁱ ＝f(x ⁱ )；

Step two: recording the minimum value (the minimum airplane fleet maintenance time contact ratio) in the n objective function values obtained in the step two and the step one as f ^* ；

Step two and step three: continuous solution units satisfying the following formula are all defined as MS, and the neighborhood of the MS is defined as a budding position;

|f(x ⁱ )-f ^* |≤ξ

other steps and parameters are the same as those of one of the fourth to sixth embodiments.

The first embodiment is as follows:

flight Maintenance Planning (FMP) is a very important decision-making problem, aiming at maximizing the survival rate of the fleet on the premise that the safety of the aircraft, the Flight mission and Maintenance are met.

The fleet's retention rate is more important to the air force troops because the air force troops need to have enough warplanes to meet daily training needs and to deal with safety issues. The invention establishes a fleet retention rate optimization model as shown in the formula (10) under the requirements of considering airplane safety and minimum fleet retention rate. The main purpose of this model is to maximize fleet retention by reducing the repair coincidence time of any two aircraft in the fleet. And the decision maker can select the starting maintenance time of different airplanes in the fleet as the optimization variable of the model according to the actual situation.

In the formula: l represents the total number of airplanes of the fleet; delta is the aircraft maintenance time contact ratio;

t _i (i =1, \8230;, l) is the time to start maintenance of the ith aircraft in the fleet;

d _i (i =1, \8230;, l) is the time of maintenance of the ith aircraft (the time of maintenance is usually determined by the degree of damage to the structure, the complexity of the structure, a service manual and the experience of the maintenance together);

availability (t) is the fleet's retention at time t;

min _ retention is the minimum retention requirement for the fleet;

PoF(t _i ) Is that the aircraft i is at t _i The failure rate at the moment.

According to the invention, parameters in a model (8) are initialized according to parameters of two actual aircraft fleets, and two specific optimization problems are obtained, wherein the models are shown as (9) and (10). In the model represented by equation (9), the fleet has 5 aircrafts in total, and the time to start maintenance of the aircrafts 1 and 5 is used as the optimization variable of the model (t in equation (9)) ₁ ,t ₅ ) The time to start maintenance of the other aircraft remains unchanged due to the smaller approach to deadline (aircraft 2 and 3 in fig. 25) or maintenance of critical structures (aircraft 5 in fig. 26, periodic engine detection and maintenance). In the model represented by equation (10), the fleet has 10 airplanes, and the start maintenance time of airplanes 1, 5, and 6 is used as the optimization variable of the model (t in equation 12) ₁ ,t ₅ ,t ₆ ) The time to start maintenance of the other aircraft remains unchanged. The optimization results are shown in fig. 23 and 24, respectively.

As can be seen from FIG. 23, the model optimization result shown in equation (9) is divided into twoA region and two intervals, from which the invention selects a solution t ₁ ＝85,t ₅ =215, and a maintenance plan of the fleet is represented by a Gantt chart shown in fig. 25. As can be seen from FIG. 24, the model optimization result shown in equation (10) is composed of two regions from which the present invention selects a solution t ₁ ＝320,t ₅ ＝116,t ₆ =140, and a maintenance plan of the fleet is represented by a Gantt chart shown in fig. 26. As can be seen from fig. 25 and 26, the maintenance plan obtained optimizes the retention rate of the fleet over the entire maintenance period while meeting the requirements of aircraft safety (the Deadline in fig. 24 and 25 indicates the time to failure of the aircraft) and fleet minimum retention rate (the top of fig. 25 and 26 is the retention rate in the fleet maintenance plan).

The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (7)

1. An optimization method based on yeast budding propagation is characterized in that: the optimization method based on the budding propagation of the yeast comprises the following steps:

inputting: the method comprises the following steps of (1) selecting an objective function f (x), an initial population size n, the number z of inferior solutions to be migrated, the side length epsilon of a continuous solution unit and a relaxation variable xi in the neighborhood searching step based on a particle swarm optimization algorithm;

and (4) termination conditions: the fluctuation range of the number of continuous solution units reaching the maximum iteration number S or in the latest triple iteration EP is within 1 percent; EP is the output data set;

the method comprises the following steps: generating an initial solution;

n seeds were randomly generated: x is the number of ¹ ,x ² ,...,x ⁿ X is to be ¹ ,x ² ,...,x ⁿ Converting the continuous solution unit into a continuous solution unit, and adjusting the continuous solution unit to the central position of the grid;

step two: carrying out budding propagation on the reproducible optimal solution MS in the initial solution generated in the step one, and defining the neighborhood of the MS as a budding position;

step three: performing neighborhood search on the budding positions defined in the second step by adopting a particle swarm algorithm, if the obtained solution is less than or equal to MS, storing the solution positions into an optimal position data set, adding the solution stored into the optimal position data set into EP, emptying the optimal position data set, and if the solution is greater than MS, eliminating;

step four: adjusting the solution added into the EP in the step three to the central position of the located grid;

step five: and (5) iteratively executing the step one to the step four until an iteration termination condition is met, and outputting the EP.

2. The yeast budding propagation-based optimization method according to claim 1, wherein: in the step one, x is ¹ ,x ² ,...,x ⁿ The specific process of converting the continuous solution unit into the continuous solution unit and adjusting the continuous solution unit to the central position of the grid is as follows:

randomly generating n seeds to be n random points, and converting the n random points into coordinate indexes and position indexes by adopting formulas (1) and (2);

whereinFor the j-th dimension of the i-th seed,is composed ofJ =1,.. M, m is the dimension, i =1,. N;is composed ofRound is a rounding function.

3. The yeast budding propagation-based optimization method according to claim 2, wherein: the specific process of carrying out budding propagation on the reproducible optimal solution MS in the initial solution generated in the step one in the step two is as follows:

step two, firstly: calculating an objective function value of each seed, wherein the objective function value of the ith seed is recorded as f ⁱ ，f ⁱ ＝f(x ⁱ )；

Step two: recording the minimum value of the n objective function values obtained in the first step as f ^* ；

Step two and step three: continuous solution units satisfying the formula (3) are defined as MS, and the neighborhood of the MS is defined as a budding position;

|f(x ⁱ )-f ^* |≤ξ (3)。

4. a fleet maintenance rate optimization method based on yeast budding propagation optimization based on the use of the method of claim 1, wherein: the method is applied to a fleet retention rate optimization process.

5. The fleet survival rate optimization method based on yeast budding propagation optimization according to claim 4, wherein: the specific process of applying the method to the fleet retention rate optimization process is as follows:

inputting: optimizing an objective function f (x) by the overlap ratio of the maintenance time of the fleet, wherein the initial population size n =100, selecting the number z =20 of inferior solutions to be migrated in the neighborhood searching step based on the particle swarm optimization algorithm, the side length epsilon =0.5 of a continuous solution unit, and the relaxation variable ξ =1;

termination conditions were as follows: the maximum iteration number is 1500 or the fluctuation range of the number of continuous solution units in the latest triple-iteration EP is within 1 percent; EP is the output data set;

the method comprises the following steps: generating an initial solution;

randomly generating 100 fleet maintenance plans, wherein one fleet maintenance plan comprises the maintenance time of each airplane in a fleet: x is a radical of a fluorine atom ¹ ,x ² ,...,x ⁿ ， Represents the maintenance time of the jth aircraft in the ith fleet maintenance plan, j =1 ¹ ,x ² ,...,x ⁿ Converting the solution into a continuous solution unit, and adjusting the continuous solution unit to the central position of the maintenance time decision space grid;

step two: defining the solution with the minimum maintenance time contact ratio in the initial solution generated in the step one as the reproducible optimal maintenance plan MS of the fleet, carrying out budding reproduction, and defining the neighborhood of the MS as a budding position;

step three: performing neighborhood search on the budding positions defined in the step two by adopting a particle swarm algorithm, if the coincidence degree of the fleet maintenance time corresponding to the obtained solution is less than or equal to the coincidence degree of the fleet maintenance time corresponding to the MS, storing the fleet maintenance plan corresponding to the solution into an optimal fleet maintenance plan data set, adding the solution stored into the optimal fleet maintenance plan data set into the EP, emptying the optimal position data set, and if the coincidence degree of the fleet maintenance time corresponding to the MS is greater than the coincidence degree, executing a elimination program;

step four: adjusting the solution added into the EP in the third step to the central position of the maintenance time decision space grid;

step five: and (5) iteratively executing the step one to the step four until an iteration termination condition is met, and outputting the EP.

6. The fleet conservation rate optimization method based on yeast budding propagation optimization according to claim 5, wherein: in the step one, x is ¹ ,x ² ,...,x ⁿ The specific process of converting the continuous solution unit into the continuous solution unit and adjusting the continuous solution unit to the central position of the maintenance time decision space grid is as follows:

randomly generating n fleet maintenance plans, wherein each seed represents one fleet maintenance plan, namely the n randomly generated fleet maintenance plans are converted into a coordinate index and a position index in a maintenance time decision space by adopting formulas (4) and (5);

whereinThe maintenance time for the jth aircraft scheduled for the ith fleet maintenance,is composed ofCoordinate indices in the maintenance time decision space, j =1, a, m, m being the maintenance time decision space dimension, i =1, a, n;is composed ofAnd in the maintenance time, the position index in the decision space is round, and round is an integer function.

7. The fleet conservation rate optimization method based on yeast budding propagation optimization according to claim 6, wherein: in the second step, the solution with the minimum aircraft fleet maintenance time contact ratio in the initial solutions generated in the first step is defined as the reproducible optimal aircraft fleet maintenance plan MS, and the specific process of budding propagation is as follows:

step two is as follows: calculating an objective function value of each fleet maintenance plan, wherein the objective function value of the ith fleet maintenance plan is recorded as f ⁱ ，f ⁱ ＝f(x ⁱ )；

Step two: recording the minimum value of the n objective function values obtained in the first step as f ^* ；

Step two and step three: continuous solution units satisfying the formula (6) are defined as MS, and the neighborhood of MS is defined as a budding position;

|f(x ⁱ )-f ^* |≤ξ (6)。