CN116258090A

CN116258090A - Differential evolution deep space orbit design method and system based on double-stage information migration

Info

Publication number: CN116258090A
Application number: CN202310544452.5A
Authority: CN
Inventors: 彭雷; 袁卓铭; 戴光明; 王茂才; 宋志明; 陈晓宇
Original assignee: China University of Geosciences
Current assignee: China University of Geosciences
Priority date: 2023-05-16
Filing date: 2023-05-16
Publication date: 2023-06-13
Anticipated expiration: 2043-05-16
Also published as: CN116258090B

Abstract

The invention provides a differential evolution deep space orbit design method and a system based on double-stage information migration, wherein the method comprises the following steps: initializing a father population and preset parameters, including the highest function evaluation times; randomly distributing individuals in the father population with the same sub-population scale to obtain three sub-populations; retaining partial individuals with low objective function values in the sub-population, and randomly reassigning the rest individuals; performing mutation, crossover and selection on the sub-species group after reassignment by utilizing a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-species group; comparing the function evaluation times of the global optimal solution with the highest function evaluation times, and returning to the global optimal solution if the function evaluation times of the global optimal solution are larger than the highest function evaluation times. Thus, the invention can maintain diversity by reserving part of individuals and randomly distributing the rest individuals; and by controlling the migration of the optimal individuals, the later stage of population evolution is prevented from falling into a local optimal solution, and the convergence and development capability are improved.

Description

Differential evolution deep space orbit design method and system based on double-stage information migration

Technical Field

The invention relates to the field of aerospace engineering application, in particular to a differential evolution deep space orbit design method and system based on double-stage information migration.

Background

The design and optimization of the deep space exploration orbit is one of the key problems of deep space exploration system engineering, and the deep space exploration task of remote stars (such as wooden stars, earth stars and asteroid) is particularly important.

In the existing solution to the deep space exploration orbit design problem, the search space presents high nonlinearity, and small variation (such as 0.001) of independent variables can cause the order of magnitude of the function value. Highly nonlinear sensitive search spaces can easily lead to premature population individuals, meaning that population individuals prematurely converge in a local region and cannot proceed toward the local region where the globally optimal solution is located. This feature requires a strong "pit" strategy for the algorithm to be able to continually jump from one local area to another. Also, the local area where the global optimum is often very narrow, even enclosed in an area that appears to have no search value, the so-called "companion". In a prior global search, individuals of the population will typically move from such "no search value seemingly" areas to "seemingly very search value" areas.

Disclosure of Invention

The embodiment of the invention provides a differential evolution deep space orbit design method and a differential evolution deep space orbit design system (English name: TITS-DE) based on double-stage information migration, which can maintain diversity and better balance the capability of algorithm exploration and development; meanwhile, the population is prevented from being trapped in a local optimal solution in the middle and later stages of evolution, and the convergence and development capacity of the algorithm in the later stages are improved.

The invention provides a differential evolution deep space orbit design method based on double-stage information migration, which comprises the following steps:

initializing a parent population and preset parameters, including:

determining a detector deep space track design problem M to be solved;

constructing an objective function f (x), a decision vector x, and an upper boundary vector x of the detection region for the problem M ^ub And a lower boundary vector x ^lb Setting the dimension D of the decision vector x; the objective function f (x) is used to find the cumulative speed change of the detector in the problem M

；

Initializing the highest function evaluation frequency MAX_FES, the lowest function evaluation frequency MIN_FES and the current function evaluation frequency FES of the objective function;

initializing evolution algebra G of father population and population scale NP _init ；

At x ^ub And x ^lb Random initialization generation NP in range _init Individual x _i As a solution vector of the problem M, constructing the parent population;

Randomly distributing individuals in the parent population with the same sub-population scale to obtain three sub-populations; the random assignment of individuals in the parent population on the same subspecies population scale comprises:

initializing population minimum size NPs for said sub-populations _min A tolerance factor Q and a migration factor T;

initializing a stall parameter M of a global operator _op (op=1, 2, 3), each of said sub-populations corresponding to a stagnation parameter; the global operator is used for searching the whole detection area to obtain a global optimal solution with the lowest objective function value;

initializing a local search initiation control parameter prob of a local operator _ls The method comprises the steps of carrying out a first treatment on the surface of the The local operator is used for determining a local search space and performing secondary search calculation to obtain a local optimal solution with the lowest objective function value in the local search space so as to update the global optimal solution;

retaining partial individuals with low objective function values in the sub-population, and randomly reassigning the rest individuals;

performing mutation, crossover and selection on the sub-species group after reassignment by utilizing a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-species group;

comparing the function evaluation times of the global optimal solution with the highest function evaluation times, and returning to the global optimal solution with the lowest objective function value if the function evaluation times of the global optimal solution are larger than the highest function evaluation times, namely the minimum value of the cumulative speed change of the detector in the deep space orbit design problem M.

Further, the initializing parent population includes:

the j-th dimension variable x of the i-th said individual _j,i The following parent population initialization formula is satisfied:

and, in addition, the method comprises the steps of,

for the j-th dimension variable of said upper boundary vector,>

x is the j-th dimension variable of the lower boundary vector _j,min Rand is the first randomly distributed variable, which is the minimum of all individual j-th dimensional variables.

Further, the performing mutation, crossover and selection on the sub-species group after reassignment by using a differential evolution algorithm comprises:

comparing the stagnation parameter with the tolerance factor, and if the stagnation parameter is smaller than the tolerance factor, performing mutation, crossover and selection on the subspecies by using a differential evolution algorithm; and/or if the stagnation parameter is not smaller than the tolerance factor, updating the individual with the highest objective function value in the sub-population to be a global optimal solution, and carrying out mutation, crossover and selection on the sub-population.

Further, the performing mutation, crossover and selection on the sub-population after the reassignment by using a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-population, and the method further comprises:

determining the improvement rate of the evolved sub-population according to the objective function value and the variable value corresponding to the optimal individual in the new generation sub-population and the objective function value and the variable value corresponding to other individuals;

And based on the improvement rate and the function evaluation times of the sub-population, and the highest function evaluation times and the minimum population scale, updating the new generation sub-population scale by adopting a linear decrementing strategy.

Further, the preset parameters include: a second randomly distributed variable; the comparing the function evaluation times of the global optimal solution with the highest function evaluation times comprises the following steps:

comparing the function evaluation times of the global optimal solution with the minimum function evaluation times, if the function evaluation times of the global optimal solution are smaller than the minimum function evaluation times, reserving partial individuals with low objective function values in the sub-population and randomly distributing the rest individuals; and/or comparing the second random distribution variable with a local search starting control parameter if the function evaluation frequency of the global optimal solution is not more than the highest function evaluation frequency and not less than the lowest function evaluation frequency, and not starting a local operator and returning to the global optimal solution if the second random distribution variable is not less than the local search starting control parameter.

Further, the method further comprises:

if the second random distribution variable is smaller than the local search starting control parameter, starting a local operator for the global optimal solution, determining a local search space according to the global optimal solution and a control parameter probls, and carrying out search calculation on the local search space to obtain a local optimal solution with the lowest objective function value in the local search space;

Comparing the objective function value of the local optimal solution with the objective function value of the global optimal solution, if the objective function value of the local optimal solution is smaller than the objective function value of the global optimal solution, updating the local optimal solution into the global optimal solution, and returning to the global optimal solution.

Further, the method further comprises: and if the objective function value of the local optimal solution is not smaller than the objective function value of the global optimal solution, overlapping the function evaluation times of the local optimal solution to the function evaluation times of the global optimal solution, and comparing the overlapped function evaluation times of the global optimal solution with the highest function evaluation times.

The invention also provides a differential evolution deep space orbit design system based on the double-stage information migration, which is characterized by comprising the following steps:

the initialization module is used for initializing the father population and preset parameters, and comprises the following steps:

determining a detector deep space track design problem M to be solved;

；

the processing module is used for randomly distributing individuals in the father population to obtain three populations according to the same subspecies population scale; the random assignment of individuals in the parent population on the same subspecies population scale comprises:

initializing a stall parameter M of a global operator _op (op=1, 2, 3), each of said sub-populations corresponding to a arrest parameter; the global operator is used for searching the whole detection area to obtain a global optimal solution with the lowest objective function value;

the processing module is also used for reserving part of individuals with low objective function values in the sub-population and randomly reassigning the rest individuals;

The processing module is also used for carrying out mutation, crossover and selection on the sub-species group after the reassignment by utilizing a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-species group;

and the output module is used for comparing the function evaluation times of the global optimal solution with the highest function evaluation times, and if the function evaluation times of the global optimal solution are larger than the highest function evaluation times, the global optimal solution with the lowest objective function value is the minimum value of the cumulative speed change of the detector in the deep space orbit design problem M.

The beneficial effects provided by the invention are as follows:

1. the invention discloses a differential evolution deep space orbit design method based on double-stage information migration, which comprises the following steps: TITS-DE first stage information migration: each population keeps the continuous development of the excellent individuals of the part of the previous generation, and the residual individuals of all the populations of the previous generation are randomly distributed to each population so as to maintain the diversity of the populations, so that the exploring and developing capability of the algorithm can be balanced better.

2. The invention discloses a differential evolution deep space orbit design method based on double-stage information migration, which comprises the following steps: TITS-DE second stage information migration: by controlling migration of optimal individuals in the population, various populations are prevented from being trapped into a local optimal solution in the later stage of evolution, and convergence and development capacity of the later stage of an algorithm are further improved.

Drawings

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

FIG. 2 is a schematic diagram of the interplanetary transfer orbits MGA-DSMs of the method of the present invention;

FIG. 3 is a schematic diagram of a system architecture of the method of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

In the following description, suffixes such as "module", "component", or "unit" for representing elements are used only for facilitating the description of the present invention, and have no specific meaning per se. Thus, "module," "component," or "unit" may be used in combination.

As shown in fig. 1, an embodiment of the present invention provides a differential evolution deep space track design method based on dual-stage information migration, where the method includes:

step S101: initializing a father population and preset parameters; wherein, the preset parameters include: the highest function evaluation times;

step S102: randomly distributing individuals in the parent population with the same sub-population scale to obtain three sub-populations;

step S103: retaining partial individuals with low objective function values in the sub-population, and randomly reassigning the rest individuals;

Step S104: performing mutation, crossover and selection on the sub-species groups after the reassignment by utilizing a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-species groups;

step S105: comparing the function evaluation times of the global optimal solution with the highest function evaluation times, and returning to the global optimal solution if the function evaluation times of the global optimal solution are larger than the highest function evaluation times.

The blanking method is executed by the terminal. The terminals may be various types of terminals; for example, the terminal may be, but is not limited to being, at least one of: a server, computer, tablet, or other electronic device.

In some embodiments, initializing the parent population and the preset parameters includes:

determining a detector deep space track design problem M to be solved;

；

At x ^ub And x ^lb Random initialization generation NP in range _init Individual x _i As a solution vector to problem M, the parent population is constructed.

For example, determining a deep space orbit design problem M to be solved, and setting a decision vector x of the problem M, wherein the dimension of the decision vector is D; setting a detection area of the problem M and an upper boundary vector x of the detection area ^ub And a lower boundary vector x ^lb The method comprises the steps of carrying out a first treatment on the surface of the Setting evolution algebra g=1 and initial parent population size NP _init =18×D。

One implementation manner of the step S101 is as follows: setting a detection area and a decision vector, and setting an upper boundary vector x of the detection area ^ub And a lower boundary vector x ^lb The method comprises the steps of carrying out a first treatment on the surface of the At x ^ub And x ^lb Random initialization generation NP in range _init Individual x _i Constructing the parent population; wherein the j-th dimension variable x of the i-th said individual _j,i The following parent population initialization formula is satisfied:

and, in addition, the method comprises the steps of,

for the j-th dimension variable of said upper boundary vector,>

Here, the individual can be understood as a solution vector of the problem M.

In some embodiments, the upper boundary vector x of the detection region ^ub And a lower boundary vector x ^lb The value range of each deep space orbit design variable in the expression formula corresponding to the decision vector x; assuming that the deep space orbit detection problem M comprises orbits of n planets, the expression formula of the decision vector x of the problem M is as follows:

wherein t is ₀ Is the emission time, V _∞ U, v define the speed v of the hyperbola of the driving-off transfer track _∞ The direction of the center of gravity, r _pi For the lowest safe fly-by radius,

t is the angle measured in the plane of the planet _i Is auxiliary planet P of spacecraft from gravitation _i-1 To P _i Is a transfer time of (2);

given transfer time T _i And the variable η with respect to each track i _i The transfer time eta of the spacecraft in the deep space orbit detection problem M can be calculated along the kepler transfer orbit _i T _i 。

The deep space track design problem M in step S101 may be: the objective function f (x) is used for solving the cumulative speed change of the detector in the problem M

；

The deep space track design problem M in step S101 may also be: cumulative energy variation of detector during computer deep space detection task

The objective function f (x) is used to determine the cumulative energy change of the detector in the problem M >

。

Here, a larger value of the objective function indicates a worse individual, and a smaller value of the objective function indicates a better individual.

It can be appreciated that the larger the objective function value corresponding to the solution vector individual is, the accumulated energy change of the detector during the computer deep space detection task

The larger the corresponding more energy is consumed in the detection process, the worse the individual is; the smaller the objective function value corresponding to the solution vector individual is, the accumulated energy change of the detector during the computer deep space detection task is

The smaller the corresponding less energy expended in the detection process, the better the individual.

Similarly, the larger the objective function value corresponding to the solution vector individual is, the cumulative speed change of the detector during the computer deep space detection task

The larger the corresponding more energy is consumed in the detection process, the worse the individual is; the smaller the objective function value corresponding to the solution vector individual is, the accumulated speed change of the detector during the computer deep space detection task is +.>

The smaller the corresponding less energy is expended in the detection process, the more the individualAnd (3) the advantages are good.

In some embodiments, the objective function f (x) of the deep space trajectory design problem may be expressed as:

Wherein, the liquid crystal display device comprises a liquid crystal display device,

due to the track transfer node P _j-1 And P _j Accumulated speed variation caused by deep space maneuvers in between,

is the emission speed, +.>

Representing the required speed change from start to end at each transfer track segment, +.>

Is the maneuver speed required to reach the target track. />

In one embodiment, the cumulative velocity variation of the spacecraft in the deep space orbit design problem M is determined according to the objective function f (x)

Continuously running, said cumulative speed variation +.>

The amount of speed variation caused by deep space maneuvers during orbit transfer for the spacecraft.

Exemplary, the inter-planet transfer orbits MGA-DSMs are shown schematically in FIG. 2, initial time t ₀ At the moment, the spacecraft is at speed Deltav ₀ Starting from the earth and passing through the earth and the planet P ₁ The change of speed caused by deep space maneuver of the initial section transfer track between the two is

Transfer time T ₁ The method comprises the steps of carrying out a first treatment on the surface of the By orbital rotationMobile node P ₁ And P _i The speed change caused by deep space maneuver of the intermediate transfer rail between them is +.>

Transfer time T _i The method comprises the steps of carrying out a first treatment on the surface of the Through track transfer node P _i And P _N The deep space maneuver induced speed variation of the final segment transfer track in between is +.>

Transfer time T _N The method comprises the steps of carrying out a first treatment on the surface of the The orbit transfer node is here understood to be an attraction-assisted planet through which the orbit is to pass in a deep space exploration task. It can be seen that the spacecraft is able to propel an engine during each section of transfer orbit to achieve deep space maneuver effects.

The preset parameters in step S101 include: a first random distribution variable, a second random distribution variable, and a third random distribution variable.

Here, the first random distribution variable, the second random distribution variable and the third random distribution variable are independent of each other, and each random distribution variable is rand, which is a random distribution variable with a value range of [0,1 ].

The initializing preset parameters in step S101 further includes: maximum number of function evaluations max_fes, minimum number of function evaluations min_fes, initial number of function evaluations FES, minimum population size NP _min Stagnation parameter M _op (op=1, 2, 3), tolerance factor Q, migration factor T, local search start control parameter prob _ls 。

Here, the highest function evaluation number is a given value, for example, 150000.

Here, the number of function evaluations is the number of times the objective function is called, and in each iteration, each individual of the population is evaluated once until the iteration stagnates; it will be appreciated that the number of evaluations is the number of population individuals multiplied by the number of iterations.

Here, the minimum function evaluation number may be determined according to the maximum function evaluation number, for example, min_fes=0.85max_fes.

Here, the initial population size is the parent population size at the time of initialization.

Here, the minimum population size is a given value, for example, 4.

Here, the stall parameter initial value is 0.

Here, the arrest parameter is an arrest parameter of a sub-population; each of the subspecies corresponds to a stagnation parameter.

Here, the tolerance factor is a given value, for example, 64.

Here, the migration factor is a given value, for example, 0.3.

Here, the local search start control parameter initial value is 0.1.

The randomly assigning individuals in the parent population at the same subspecies scale in step S102 includes:

initializing a local search initiation control parameter prob of a local operator _ls The method comprises the steps of carrying out a first treatment on the surface of the The local operator is used for determining a local search space and performing secondary search calculation to obtain a local optimal solution with the lowest objective function value in the local search space so as to update the global optimal solution.

The same subspecies group size is NP _op,G (op=1, 2, 3), it being understood that initially the subspecies size may be one third of the parent size.

In some embodiments, the step S103 includes: determining a first scale of retention using a rounding function based on the subspecies population scale and the migration factor; and determining the difference between the initial population size and the reserve size as a remaining second size.

Exemplary, according to the subspecies population scale NP _op,G (op=1, 2, 3) and the migration factor T, the first scale of the subspecies group retention is determined using a rounding function Round ():

wherein NP _op,G (op=1, 2, 3) is the subspecies size of the previous generation;

a second scale of the remaining second portion of individuals determined from the difference between the initial population size and the first scale is:

。

it is understood that the subspecies sizes include: current subspecies group size and previous generation subspecies group size; initially, the previous generation subspecies size was 0.

In some embodiments, the step S103 includes: calculating the objective function value of the individuals in the sub-population according to the objective function; sorting the individuals in the sub-population from small to large according to the objective function value; retaining individuals of a first scale in the sub-population that have a low prior objective function value; re-randomly assigning the remaining second-size individuals of the subspecies population, and updating each of the subspecies population.

It will be appreciated that initially, the first scale is 0 and that all individuals are reassigned randomly; thereafter, if the first scale is not 0, individuals with low objective function values remain for development, and individuals without retention are randomly assigned to each subspecies.

Therefore, the embodiment of the invention can keep part of excellent individuals for continuous development based on the objective function value, and randomly distribute the unreserved individuals to each sub-population to maintain population diversity, so as to better balance the exploration and development capability of the algorithm.

In some embodiments, the step S104 includes: comparing the stagnation parameter with the tolerance factor, and if the stagnation parameter is smaller than the tolerance factor, performing mutation, crossover and selection on the subspecies by using a differential evolution algorithm.

Here, the stagnation parameters of each of the subspecies are compared with tolerance factors.

The three subspecies are exemplified by P ₁ 、P ₂ And P ₃ Comparing said subspecies P ₁ Comparing the retention parameters of subspecies group P with the tolerance factor ₂ Comparing the retention parameters of subspecies group P with the tolerance factor ₃ And the tolerance factor.

In other embodiments, the step S104 further includes: and if the stagnation parameter is not smaller than the tolerance factor, updating the individual with the highest objective function value in the sub-population into a global optimal solution, and carrying out mutation, crossover and selection on each sub-population.

Here, the three subspecies group P ₁ 、P ₂ And P ₃ ，P ₁ The successor population of (2) is P ₃ ，P ₂ The successor population of (2) is P ₁ ，P ₃ The successor population of (2) is P ₂ 。

It will be appreciated that if the stall parameter is not less than the tolerance factor, then a second stage information migration strategy is initiated, and the worst individual (highest objective function value) in the sub-population will be updated to the globally optimal individual (lowest objective function value).

In one embodiment, the updating the individual with the highest objective function value in the sub-population to the globally optimal solution includes: judging the sub-population where the global optimal solution is located, and if the global optimal solution does not belong to the previous population of the current sub-population, reserving the global optimal solution.

In another embodiment, the updating the individual with the lowest objective function value in the sub-population to the globally optimal solution further includes: and if the global optimal solution belongs to the successor population of the current sub-population, updating the individual with the highest objective function value in the current sub-population as the global optimal solution.

Illustratively, if the subspecies group stagnates and the current globally optimal solution is located in a preceding population of the subspecies group, replacing the individual in the subspecies group with the globally optimal solution having the highest objective function value.

It can be understood that only if the stagnation parameter is not less than the tolerance factor, it is determined that the current sub-population falls into a local optimum and is stagnated, and the original global optimum solution needs to be replaced by the individual with the highest objective function value in the current sub-population so as to jump out of the local optimum solution.

Therefore, the embodiment of the invention can judge that the subspecies are in local optimum and stagnate based on the stagnation parameter not smaller than the tolerance factor, and update the global optimum solution, and jump out of the local optimum solution, so as to avoid premature whole algorithm caused by early migration of the global optimum solution to each subspecies.

In one embodiment, the step S104 includes: selecting a number of individuals with the objective function values ranked first from small to large; assigning a unique mutation operator to each subspecies group according to table 1; wherein, table 1 is as follows:

table 1 three mutation operators

Wherein the mutation operator in DE (differential evolution) can be expressed in the form of DE/x/y, x represents the source of the base vector, e.g. if rand represents that the base vector is randomly selected, if pbest represents that the base vector is randomly selected from the top% p solution in the current generation population _pbest,G The method comprises the steps of carrying out a first treatment on the surface of the y represents the number of differential quantities based on the basis of the basis vector; with archive means that the base vector is selected in the population and external archive, while with archive means that the base vector is selected only in the population; i not equal to r ₁ ≠r ₂ ≠r ₃ Is a random integer, x _r1,G And x _r3,G X is the individual selected randomly from the parent population _r2,G For the individual selected from the parent population and the external storage space A, V _i,G For variant individuals, x _pbest,G Is in a populationThe objective function values rank from small to large for the top 25% of individuals.

Exemplary subspecies group P ₁ Subspecies group P using DE/current-to-pbest with archive/1 variation ₂ Subspecies group P using DE/current-to-pbest without archive/1 variation ₃ DE/weighted-rand-to-pbest variation was used.

In one embodiment, the step S104 includes: the initializing preset parameters comprises the following steps: the crossover rate Cr; performing cross operation on each subspecies group by using a first cross formula, a second cross formula and a third cross formula; wherein, the liquid crystal display device comprises a liquid crystal display device,

the first crossover formula is as follows:

and u _i,j For the experimental vector u _i The j-th variable value of rand machine distribution variable;

the second crossover formula is as follows:

and j _rand Is [1, D]Random integers in (a);

the third formula is as follows:

and L is the experimental vector u _i From the test vector x _i The number of inherited variables.

Here, the second crossover formula may be a two-term crossover operator, and the third crossover formula may be an exponential crossover operator.

Here, the experimental vector may be understood as an individual in the sub-population, and the test vector may be understood as an individual in the sub-population that is different from the experimental vector.

In one embodiment, the step S104 includes: selecting the individuals after the evolution of each sub-population by using a selection formula, selecting the individuals with low objective function values to determine a new generation sub-population, and updating the function evaluation times; wherein, the selection formula is as follows:

and u _i,G For the experimental vectors, x, in the G generation sub-population _i,G The test vectors, x, in the G generation sub-population _i,G+1 The test vectors in the G generation sub-population.

Exemplary, if the experimental vector u _i,G The objective function value is smaller than the test vector x _i,G Then the experimental vector u in the G generation sub-population is calculated _i Screening a new population of the new generation, namely G+1 generation; at the same time, update the experimental vector u _i,G The number of function evaluations is the sum of the number of primitive function evaluations and the subspecies group size, i.e., fes=fes+np.

Therefore, the embodiment of the invention can change, cross and select the subspecies based on the differential evolution algorithm, further control the migration of the optimal individuals in the subspecies to the subspecies of the new generation, avoid each population from sinking into a local optimal solution in the middle and later stages of evolution, and further improve the convergence and development capacity of the algorithm in the later stages.

In one embodiment, the step S104 includes: if the objective function value of the optimal individual in the determined new generation sub-population is not less than the objective function value of the optimal individual in the sub-population before evolution, the stagnation parameter of the sub-population is increased by 1; and/or if the objective function value of the optimal individual in the determined new generation sub-population is smaller than the objective function value of the optimal individual in the sub-population before evolution, setting the stagnation parameter to 0.

By way of example only, and not by way of limitation,

optimal individuals in the G generation for the op-th sub-population, +.>

Optimal individuals of the op sub-population in the G+1st generation; if->

(op=1, 2, 3), i.e. the objective function value of the optimal individual of the g+1st generation is smaller than the objective function value of the optimal individual of the G generation, then M _op =0; otherwise M _op =M _op +1.

Therefore, the invention can update the stagnation parameters based on comparing the objective function value of the individual in the sub-population before evolution with the objective function value of the individual in the sub-population of the new generation after evolution, and ensure the continuous progress of evolution.

In some embodiments, the step S104 includes: and determining the improvement rate of the evolved sub-population according to the objective function value and the variable value corresponding to the optimal individual in the new generation sub-population and the objective function value and the variable value corresponding to other individuals.

Illustratively, based on the size of the sub-population of the new generation, the first dimension variable value of the optimal individual in the sub-population and the first dimension variable values of other individuals, determining the diversity parameter of the sub-population of the new generation by using a diversity parameter calculation formula; wherein, the diversity parameter calculation formula is as follows:

and D is _op Is the diversity parameter of the op sub-population, NP _op The sub-population size for the op sub-population,

is the optimal individual in the op sub-population +.>

Is the j-th dimensional variable value of->

Is the ith individual in the op subfamily

A j-th dimensional variable value of (2);

based on the diversity parameters of all the sub-species groups, determining the diversity ratio of the sub-species groups of the new generation by using a diversity ratio calculation formula; wherein, the diversity ratio calculation formula is as follows:

and DR (digital radiography) _op Is the diversity ratio of the op sub-population,

is the sum of all subspecies population diversity ratios;

determining a solution quality ratio of the next generation of the sub-population by using a solution quality calculation formula based on the objective function value of the optimal individual in the sub-population and the objective function values of other individuals; the solution quality calculation formula is as follows:

And QR _op Is the solution mass ratio of the op sub-population,

is the objective function value of the optimal individual in the op sub-population,/->

Is the sum of objective function values of the optimal individuals in all sub-populations;

determining an improvement rate of the new generation of the sub-population by using an improvement rate calculation formula based on the diversity ratio and the resolution ratio; wherein, the improvement rate calculation formula is as follows:

and, IRV _op Op (op)Improvement rate of sub-populations.

In some embodiments, the step S104 further includes: and updating the new generation subspecies scale by adopting a linear decreasing strategy based on the improvement rate of the subspecies and the function evaluation times of the optimal individuals, and the highest function evaluation times and the minimum population scale.

Here, the whole population composed of the subspecies of the new generation is the father population of the new generation.

For example, firstly, determining the scale of the new generation parent population by utilizing a linear decreasing formula for the whole population of the new generation, namely the new generation parent population, based on the scale of the parent population before evolution, the minimum population scale, the highest function evaluation times and the function evaluation times of the global optimal solution; wherein the linear decreasing formula is as follows:

And NP (NP) _G+1 Is the parent population scale of the G+1st generation, NP _G Is the G generation parent population scale, and NP is at the initial iteration _G =NP _init ；

Based on the scale of the parent population of the new generation and the improvement rate of the sub population, updating the scale of the sub population of the new generation by using a sub population scale updating formula; wherein, the subspecies group scale updating formula is as follows:

and NP (NP) _op,G+1 Is the G+1st generation op subspecies group scale, NP _op,G Is the size of the G generation op subspecies group,

is the sum of all subspecies improvement rates.

In some embodiments, the step S105 further includes: and comparing the function evaluation times of the global optimal solution with the minimum function evaluation times, and if the function evaluation times of the global optimal solution are smaller than the minimum function evaluation times, reserving partial individuals with low objective function values in the sub-population and randomly distributing the rest individuals.

Illustratively, if the function evaluation number FES of the global optimal solution is smaller than the minimum function evaluation number min_fes, that is, FES < min_fes, a part of individuals with low objective function values in the sub-population of the new generation are reserved, and the rest individuals are randomly reassigned.

In other embodiments, the step S105 also includes: and if the function evaluation frequency of the global optimal solution is not more than the highest function evaluation frequency and not less than the lowest function evaluation frequency, comparing the second random distribution variable with a local search starting control parameter, and if the second random distribution variable is not less than the local search starting control parameter, not starting a local operator and returning to the global optimal solution.

Illustratively, if the function evaluation number FES of the globally optimal solution is not less than the minimum function evaluation number min_fes and is less than the maximum function evaluation number of fish, that is, min_fes is less than or equal to FES is less than or equal to max_fes; comparing the second random distribution variable rand with the local search start control parameter prob _ls If the second random distribution variable is not smaller than the local search start control parameter, namely rand is larger than or equal to prob _ls And not starting the local operator, and returning to the global optimal solution in the new generation population.

In one embodiment, if the second random distribution variable is not smaller than the local search initiation control parameter, not initiating a local operator, and returning to the globally optimal solution, further including: and updating the local search starting control parameter to be 0.01.

Exemplary, the local search initiation control parameter prob is updated _ls As such, the present invention may assign the local search initiation parameter to 0.01, which is much smaller than 0.1, in case the objective function value of the individual determined by the local operator is higher, to reduce the probability of initiating the local operator for the next iteration.

In some embodiments, the step S105 includes: if the second random distribution variable is smaller than the local search control parameter, starting a local operator for the global optimal solution to obtain a local optimal solution; comparing the objective function value of the local optimal solution with the objective function value of the global optimal solution, if the objective function value of the local optimal solution is smaller than the objective function value of the global optimal solution, updating the local optimal solution into the global optimal solution, and returning to the global optimal solution.

Exemplary, the second random distribution variable rand is compared with a local search initiation control parameter prob _ls If the second random distribution variable is smaller than the local search initiation control parameter, namely rand < prob _ls Comparing the local optimal solution x _ls And the global optimal solution x _gmin Is set according to the objective function value of (1); if the objective function value of the locally optimal solution is smaller than the objective function value of the globally optimal solution, i.e., f (x) _ls )＜ f(x _gmin ) The local optimal solution is a better individual than the global optimal solution, and the local optimal solution x is further calculated _ls Replacing the global optimal solution x _gmin Updating the global optimal solution to x _ls 。

The method includes the steps of starting a local operator on the global optimal solution to obtain a local optimal solution, and searching a detection area near the global optimal solution to obtain an individual with the lowest objective function value in the detection area near the global optimal solution. Therefore, the embodiment of the invention can search the detection area with the search value near the global optimal solution based on the local operator, further determine the individual with the lower objective function value than the global optimal solution, and obtain the better solution.

In some embodiments, if the objective function value of the locally optimal solution is smaller than the objective function value of the globally optimal solution, updating the locally optimal solution to be the globally optimal solution, and returning to the globally optimal solution, further includes: updating the local search starting control parameter to be 0.1, updating the function evaluation frequency of the global optimal solution to be the sum of the function evaluation frequency of the global optimal solution before updating and the function evaluation frequency of the local optimal solution, and comparing the function evaluation frequency of the updated global optimal solution with the highest function evaluation frequency.

Exemplary, updating to update the local search initiation control parameter prob _ls =0.1. In this way, the invention can assign the local search starting parameter to 0.1 which is much larger than 0.01 under the condition that the objective function value of the individual determined by the local operator is lower, so as to improve the probability of starting the local operator in the next iteration.

Illustratively, the globally optimal solution is x _ls The function evaluation times are the local optimal solution x _ls The number of times of function evaluation and the global optimal solution x _gmin Is the sum of the number of functional evaluations, i.e., fes=fes+fes _ls The method comprises the steps of carrying out a first treatment on the surface of the And comparing the updated function evaluation times of the global optimal solution with the highest function evaluation times.

In other embodiments, the step S105 includes: and if the objective function value of the local optimal solution is not smaller than the objective function value of the global optimal solution, returning to the global optimal solution.

Illustratively, the objective function value of the locally optimal solution is not less than the objective function value of the globally optimal solution, i.e., f (x) _ls )≥f(x _gmin ) The globally optimal solution is the optimal individual.

In the embodiment of the invention, initializing the father population and the preset parameters comprises the following steps: the highest function evaluation times; randomly distributing individuals in the parent population with the same sub-population scale to obtain three sub-populations; retaining partial individuals with low objective function values in the sub-population, and randomly reassigning the rest individuals; performing mutation, crossover and selection on the sub-species groups after the reassignment by utilizing a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-species groups; comparing the function evaluation times of the global optimal solution with the highest function evaluation times, and returning to the global optimal solution if the function evaluation times of the global optimal solution are larger than the highest function evaluation times. Therefore, the invention can be based on retaining part of excellent individuals, and randomly distributing the rest individuals to each sub-population, so as to maintain population diversity and better balance the exploration and development capability of the algorithm; meanwhile, the migration of the optimal individuals in the sub-population is controlled based on a differential evolution algorithm, so that the situation that the partial optimal solution falls into in the middle and later stages of evolution is avoided, and the convergence and development capacity of the algorithm in the later stages are improved.

As a specific embodiment, the method further comprises:

step S201: initializing a parent population and preset parameters;

illustratively, determining a deep space orbit design problem M to be solved; setting an objective function f (x) of the problem M for calculating accumulated energy variation during the deep space exploration task

The method comprises the steps of carrying out a first treatment on the surface of the Setting a decision vector x of the problem M and a dimension D of x; setting an upper boundary vector x of a detection region in the problem M ^ub And a lower boundary vector x ^lb The method comprises the steps of carrying out a first treatment on the surface of the Initializing a prescribed evolution algebra g=1, the highest function evaluation frequency max_fes=150000, the lowest function evaluation frequency min_fes=0.85max_fes, and the current function evaluation frequency fes=0; initializing population size NP _init =18×d, population minimum scale NP _min =4; setting stagnation parameters M of sub-populations _op =0 (op=1, 2, 3), tolerance factor q=64, migration factor t=0.3, local search start control parameter prob _ls =0.1。

Step S202: initializing three sub-populations, and randomly distributing individuals in the parent population with the same sub-population scale to obtain three sub-populations;

step S203: retaining partial individuals with low objective function values in the sub-population, and randomly reassigning the rest individuals;

step S204: judging whether the stagnation parameter is not less than the tolerance factor, if so, executing step S205; if not, executing step S206;

Step S205: determining the individuals with the lowest objective function values in all the sub-populations after the reassignment as global optimal solutions;

step S206: performing mutation, crossover and selection operation on the sub-population by using a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-population;

step S207: judging whether the objective function value of the global optimal solution of the new generation is smaller than the objective function value of the global optimal solution before evolution; if yes, go to step S208; if not, executing step S209;

step S208: the stop parameter is set to 0, and step S210 is executed;

step S209: the stagnation parameter is increased by 1, and step S210 is executed;

step S210: determining the improvement rate of the new generation sub-population according to the objective function value and the variable value of the optimal individual in the new generation sub-population and the objective function value and the variable value of other individuals;

here, the optimal individual is the individual having the lowest objective function value.

Here, the three sub-populations of the determined new generation may constitute a parent population of the new generation.

Step S211: based on the minimum population scale, the highest function evaluation times and the function evaluation times of the global optimal solution, updating the parent population scale of the new generation by adopting a linear decreasing strategy;

Step S212: updating the new generation subspecies group scale based on the new generation parent group scale and the improvement rate of the subspecies;

step S213: judging whether the function evaluation times of the global optimal solution are not more than the highest function evaluation times and not less than the lowest function evaluation times; if yes, go to step S214; if not, executing step S219;

step S214: judging whether the second random distribution variable is smaller than a local search starting control parameter or not; if yes, go to step S215; if not, executing step S220;

step S215: starting a local operator to obtain a local optimal solution;

step S216: judging whether the objective function value of the local optimal solution is smaller than the objective function value of the global optimal solution; if yes, go to step S217; if not, go to step S218;

step S217: updating the local optimal solution to a global optimal solution, and executing step S220;

step S218: superposing the function evaluation times of the local optimal solution to the global optimal solution, updating the function evaluation times of the global optimal solution, and executing step S219;

step S219: judging whether the function evaluation times of the global optimal solution are larger than the highest function evaluation times; if yes, go to step S220; if not, executing step S203;

Step S220: and returning to the global optimal solution.

For example, the task of detecting the Kacini by the earth star (English is called Cassini1 for short) aims at capturing the earth star by the attraction of the earth star on an orbit with a near-heart radius of 108950 km and an eccentricity of 0.98, and the planetary force-borrowing sequence is earth, golden star, earth, wooden star and earth star; the invention determines for this task that the minimum of the total speed variation deltav of the detection task, first,

the upper and lower boundary vectors of the set detection region are respectively the lower boundary vector x ^lb = [-1000, 30, 100, 30,400, 1000]Upper boundary vector x ^ub =[0, 400, 470, 400, 2000, 6000]；

Initializing a plurality of individual solution vectors by using the parent population initialization formula based on the upper and lower boundary vectors, randomly distributing the parent population into three sub-populations, reserving part of individuals in the sub-populations, and randomly distributing the rest individuals;

finally, performing mutation, intersection and selection on the sub-species group after reassignment by utilizing a differential evolution algorithm to obtain a global optimal solution with the lowest objective function value in the new generation of sub-species group, wherein the corresponding decision vector x= [ -789.8117,158.302027105278, 449.385873819743, 54.7489684339665, 1024.36205846918,4552.30796805542]; wherein, the liquid crystal display device comprises a liquid crystal display device,

x ₁ = -789.8117 refers to the task start time calculated with 1/2000 as the start time,

x ₂ 158.302027105278 refers to the number of days spent by the detector flying from earth to gold star,

x ₃ 449.385873819743 refers to the number of days it takes for the detector to fly around a golden star,

x ₄ the = 54.7489684339665 indicates that the detector leaps from the golden star toThe number of days spent by the earth,

x ₅ 1024.36205846918 refers to the number of days it takes for a detector to fly from earth to a star,

x ₆ = 4552.30796805542 refers to the number of days spent by the detector flying from the wooden star to the earth star, captured by it;

and the objective function value corresponding to the global optimal solution is 4.9307 km/s, namely the optimal value of the cumulative speed change of the detector in the detection task of the Tuxing detection Kaschinib.

Exemplary, 67P/Churyumov-Gerasimenko (Church Mo Fu-Gracilobujia) comet detection Rostata task (English: rosetta) whose planetary power-borrowing order is earth, mars, earth, 67P/Churyumov-Gerasimenko comet; the present invention determines for this task that the overall speed change av of the detection task is minimized by, first,

the upper and lower boundary vectors of the set detection region are respectively the lower boundary vector x ^lb = [1460, 3, 0, 0, 300,150, 150, 300, 700, 0.01, 0.01, 0.01, 0.01, 0.01, 1.05, 1.05, 1.05, 1.05, -π,-π, -π, -π]Upper boundary vector x ^ub =[1825, 5, 1, 1, 500, 800, 800, 800, 1850, 0.9, 0.9, 0.9, 0.9, 0.9, 9, 9, 9,9,π,π,π,π]；

Finally, the variation, the intersection and the selection are carried out on the sub-species group after the reassignment by utilizing a differential evolution algorithm, so as to obtain a global optimal solution with the lowest objective function value in the new generation of sub-species group, and corresponding decision variables are obtained: x= [1543.30669582458,4.62591297553792, 0.735711649721644, 0.751372228132414, 365.24128038597,704.776990594467, 258.110840823509, 730.484771806871, 1849.99995454174,0.341009328525255, 0.808663668992205, 0.376496220185218, 0.171287567923826,0.431489206122146, 3.07135208604219, 1.06000000320681, 1.41824842842757,1.39748724339122, -1.39587494176148 1.77647871470111, -2.52771948343642, -1.58247504575273]; wherein, the liquid crystal display device comprises a liquid crystal display device,

x1= 1543.30669582458 means a task start time calculated with 1/2000 as a start time;

x2= 4.62591297553792 refers to the initial hyperbolic residual speed (km/s);

x3= 0.735711649721644 and x4= 0.751372228132414 refer to the angle (polar coordinate system) of the hyperbolic residual speed;

x5= 365.24128038597 refers to the number of days it takes for the detector to fly around the earth;

x6= 704.776990594467 refers to the number of days it takes for the detector to fly from earth to Mars;

x7= 258.110840823509 refers to the number of days spent by the detector flying from Mars to earth;

x8 = 730.484771806871 refers to the number of days it takes for the detector to fly around the earth;

x9= 1849.99995454174 refers to the number of days spent by the detector from earth leap to 67P/Churyumov-gerasimienko comet;

x10= 0.341009328525255 refers to the time interval from the detector flying around the earth to deep space maneuver taking place;

x11= 0.808663668992205 refers to the time interval in which the detector takes place from earth flight to mars deep space maneuver;

x12= 0.376496220185218 refers to the time interval from the flight of the detector from Mars to the maneuvers of the earth's deep space;

x13= 0.171287567923826 refers to the time interval during which the detector maneuver around earth in deep space occurs;

x14= 0.431489206122146 refers to the time interval in which the detector maneuvers from earth to 67P/Churyumov-gerasimienko comet deep space;

x15= 3.07135208604219, x16= 1.06000000320681, x17= 1.41824842842757 and x18= 1.39748724339122 refer to the fly radius (planetary radius);

x19 = -1.39587494176148, x20 = 1.77647871470111, x21 = -2.52771948343642 and x22 = -1.58247504575273 refer to angles measured in the B-plane of the planetary approach vector;

and the objective function value corresponding to the global optimal solution is 1.3878 km/s, namely the optimal value of the accumulated speed change of the detector in the task of detecting the Rosmarin by 67P/Churyumov-Gerasimenko comet.

As shown in fig. 3, the embodiment of the present invention further provides a differential evolution deep space track design system based on dual-stage information migration, where the system includes: an initialization module 301, a processing module 302, an output module 303; wherein, the liquid crystal display device comprises a liquid crystal display device,

the initializing module 301 is configured to initialize a parent population and preset parameters, and includes:

determining a detector deep space track design problem M to be solved;

；

the processing module 302 is configured to randomly allocate individuals in the parent population with the same sub-population size, so as to obtain three sub-populations; the random assignment of individuals in the parent population on the same subspecies population scale comprises:

initializing a local search initiation control parameter prob of a local operator _ls The method comprises the steps of carrying out a first treatment on the surface of the The local calculationThe sub-module is used for determining a local search space and performing secondary search calculation to obtain a local optimal solution with the lowest objective function value in the local search space so as to update the global optimal solution;

the processing module 302 is also configured to reserve a part of individuals with low objective function values in the sub-population, and randomly reassign the remaining individuals;

the processing module 302 is further configured to perform mutation, crossover and selection on the sub-population after reassignment by using a differential evolution algorithm, so as to obtain a global optimal solution with the lowest objective function value in the new generation of sub-population;

the output module 303 is configured to compare the function evaluation times of the globally optimal solution with the highest function evaluation times, and if the function evaluation times of the globally optimal solution are greater than the highest function evaluation times, return to the globally optimal solution with the lowest objective function value, that is, the minimum value of the cumulative speed change of the detector in the deep space orbit design problem M.

In some embodiments, the system further comprises:

the initialization module is used for setting a detection area, a decision vector x and an upper boundary vector x of the detection area ^ub And a lower boundary vector x ^lb ；

At x ^ub And x ^lb Random initialization generation NP in range _init Individual x _i Constructing the parent population; wherein the j-th dimension variable x of the i-th said individual _j,i The following parent population initialization formula is satisfied:

and, in addition, the method comprises the steps of,

for the j-th dimension variable of said upper boundary vector,>

x is the j-th dimension variable of the lower boundary vector _j,min For the minimum of all individual j-th-dimension variables, rand isA first randomly distributed variable.

In some embodiments, the system further comprises:

the processing module is used for comparing the stagnation parameter with the tolerance factor, and if the stagnation parameter is smaller than the tolerance factor, the variation, the intersection and the selection of the subspecies are carried out by utilizing a differential evolution algorithm; and/or the processing module is used for updating the individual with the highest objective function value in the sub-population into a global optimal solution if the stagnation parameter is not smaller than the tolerance factor, and carrying out mutation, crossover and selection on the sub-population.

In some embodiments, the system further comprises:

The processing module is used for determining the improvement rate of the sub-population after evolution according to the objective function value and the variable value corresponding to the optimal individual in the new generation sub-population and the objective function value and the variable value corresponding to other individuals;

the processing module is used for updating the new generation subspecies scale by adopting a linear decreasing strategy based on the improvement rate and the function evaluation times of the subspecies and the highest function evaluation times and the minimum population scale.

In some embodiments, the system further comprises:

the processing module is used for comparing the function evaluation times of the global optimal solution with the lowest function evaluation times, and if the function evaluation times of the global optimal solution are smaller than the lowest function evaluation times, reserving a part with a low objective function value in the sub-population and randomly distributing the rest individuals; and/or the number of the groups of groups,

the processing module is further configured to compare the second random distribution variable with a local search start control parameter if the function evaluation number of the global optimal solution is not greater than the highest function evaluation number and not less than the lowest function evaluation number, and not start a local operator if the second random distribution variable is not less than the local search start control parameter, and return the global optimal solution.

In some embodiments, the system further comprises:

the processing module is configured to start a local operator for the globally optimal solution if the second random distribution variable is smaller than the local search start control parameter, and to start the local operator according to the globally optimal solution and the control parameter prob _ls Determining a local search space, and carrying out search calculation on the local search space to obtain a local optimal solution with the lowest objective function value in the local search space;

the processing module is configured to compare the objective function value of the locally optimal solution with the objective function value of the globally optimal solution, and if the objective function value of the locally optimal solution is smaller than the objective function value of the globally optimal solution, update the locally optimal solution to be the globally optimal solution, and return to the globally optimal solution.

In some embodiments, the system further comprises:

and the processing module is used for overlapping the function evaluation times of the local optimal solution to the function evaluation times of the global optimal solution if the objective function value of the local optimal solution is not smaller than the objective function value of the global optimal solution, and comparing the function evaluation times of the overlapped global optimal solution with the highest function evaluation times.

As an example, the present invention compares the proposed method with other methods. Refer to table 2.

TABLE 2 comparison of TITS-DE with Friedman results from other design methods

Wherein j2020 (DifferentialEvolution Algorithm for Single Objective Bound-Constrained Optimization: algorithm j 2020) is an improved Algorithm based on adaptive differential evolution algorithms jDE and jDE100, jDE (A Self-Adaptive Differential Evolution) is an adaptive differential evolution Algorithm, jDE100 (The 100-Digit change: algorithm jDE 100) is a differential evolution Algorithm with 100-bit digital challenges;

IDE-EDA (An improved differential evolution byhybridizing with estimation-of-distribution algorithm) is a hybrid algorithm improved by a differential evolution algorithm and a distribution estimation algorithm;

OLSHADE-CS (Differential evolution with orthogonalarray-based initialization and a novel selection strategy) is a differential evolution algorithm based on population initialization of orthogonal tables and a new selection strategy;

DISH (Distance Based Parameter Adaptation forSuccess-History Based Differential Evolution Algorithm), an improvement of distance-based parameter adaptation based on a success history differential evolution algorithm;

APGSK-IMODE (training-Sharing Knowledge BasedAlgorithm with Adaptive Parameters Hybrid with IMODE Algorithm) is a mixed algorithm based on a parameter self-adaptive gain sharing knowledge algorithm and an IMODE algorithm;

AL-SHADE (A novel adaptive L-SHADE algorithm), which is a new adaptive L-SHADE algorithm, SHADE (Success-HistoryBased Parameter Adaptation for Differential Evolution), which is a differential evolution parameter adaptive algorithm based on Success history, L-SHADE (Improving the SearchPerformance of SHADE Using Linear Population Size Reduction), which is an improved SHADE algorithm that utilizes linear population reduction to improve algorithm search performance;

UMOEAs-II (United Multi-operator evolutionary Algorithm-II), is a joint Multi-operator evolutionary algorithm II;

EBOwithCMAR (Improving the local search capability ofEffective Butterfly Optimizer using Covariance Matrix Adapted Retreat phase), which is a high-efficiency butterfly optimization algorithm for improving local searching capability by adopting a covariance matrix adaptive backoff stage;

IMODE (Improved Multi-operator DifferentialEvolution), is an Improved Multi-operator differential evolution algorithm;

MadDE (Improving Differential Evolution throughBayesian Hyperparameter Optimization), which is a differential evolution algorithm based on Bayesian super-parameter optimization.

The method is used for solving seven well-known deep space orbit detection tasks, and the performance of the method is verified to be superior to that of other design methods. The seven deep space exploration tasks are respectively as follows: the earth star detection Cascinia task (English abbreviations: cassini1 and Cassini 2), the asteroid TW229 detection task (English abbreviations: gtoc 1), the 67P/Churyumov-Gerasimenko comet detection Rostuta task (English abbreviations: rosetta), the flying wooden star detection task (English abbreviations: sagas), the water star intersection detection Messenger number task (English abbreviations: messenger and Messenger-Full).

Table 2 shows Friedman analysis of various design results, and the lower the algorithm score, the better the performance of the corresponding design method. TITS-DE scored lowest in the comparison method, 2.1429, indicating that TITS-DE design capacity is superior to the comparison method over the seven deep space orbit design tasks described above.

On the Cassini1 task, UMOEAs-II, EBOwithCMAR, madDE and TITS-DE gave optimal values 4.9307, both superior to other comparison algorithms, and the mean value 5.2833 of TITS-DE was superior to the mean value of other comparison methods. On the Cassini2 task, UMOEAs-II gave an optimum of 8.6247, both superior to other comparison methods, while TITS-DE's mean 11.2575 is superior to other comparison algorithms. On the Gtoc1 task, the EBOwithcMAR optimum is-1578915.7, which is superior to other comparison algorithms, and the average value of AL-SHADE-1237576.2 is superior to other comparison algorithms. On the Rosetta task, IDE-EDA gave an optimal value of 1.3575, which is better than that of other comparison algorithms, and EBOwithcmar gave a mean of 1.9682, which is better than that of other comparison methods. On the Sagas task, the APGSK-IMODE gave an optimal value of 18.1878, which is superior to other comparison methods, while TITS-DE mean 48.6826 is superior to other comparison methods. On the Messenger task, TITS-DE gets an optimal value 8.7020, which is superior to the optimal values of other comparison methods, and EBOwithcMAR gets a mean 11.2419, which is superior to the mean of other comparison methods. It is worth mentioning that the TITS-DE yields optimal values 5.7310 and means 9.8456 that are superior to other comparison algorithms on the most complex Messenger-Full task.

The innovation point of the invention is that:

(1) TITS-DE first stage information migration: each population keeps the continuous development of the excellent individuals of the part of the previous generation, and the residual individuals of all the populations of the previous generation are randomly distributed to each population so as to maintain diversity, so that the algorithm exploration and development capability can be balanced better;

(2) TITS-DE second stage information migration: by controlling migration of optimal individuals in the population, various populations are prevented from being trapped into a local optimal solution in the later stage of evolution, and convergence and development capacity of the later stage of an algorithm are further improved.

The beneficial effects of the invention are as follows: population diversity in the deep space exploration track design can be maintained, and algorithm exploration and development capability is balanced better; the method avoids sinking into a local optimal solution, and improves the later convergence and development capacity of the algorithm.

It should be noted that: the technical schemes described in the embodiments of the present invention may be arbitrarily combined without any collision.

The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within 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. The differential evolution deep space orbit design method based on double-stage information migration is characterized by comprising the following steps of:

initializing a parent population and preset parameters, including:

determining a detector deep space track design problem M to be solved;

；

At x ^ub And x ^lb Random initialization generation NP in range _init Individual x _i As a solution vector of the problem M, constructing the parent population; randomly distributing individuals in the parent population with the same sub-population scale to obtain three sub-populations; the random assignment of individuals in the parent population on the same subspecies population scale comprises:

initializing population minimum size NPs for sub-populations _min A tolerance factor Q and a migration factor T;

initializing a stall parameter M of a global operator _op (op=1, 2, 3) each of said sub-populations having a corresponding one of the parameters of arrest; the global operator is used for searching the whole detection area to obtain a global optimal solution with the lowest objective function value;

2. The method of claim 1, wherein initializing the parent population comprises:

and, in addition, the method comprises the steps of,

for the j-th dimension variable of said upper boundary vector,>

3. The method of claim 1, wherein the mutating, crossing and selecting the reassigned subspecies using a differential evolution algorithm comprises:

4. The method of claim 1, wherein the performing mutation, crossover and selection on the reassigned sub-population by using a differential evolution algorithm to obtain a global optimal solution with a lowest objective function value in the new generation sub-population, further comprises:

5. The method of claim 1, wherein the predetermined parameters include: a second randomly distributed variable; the comparing the function evaluation times of the global optimal solution with the highest function evaluation times comprises the following steps:

6. The method of claim 5, wherein the method further comprises:

if the second random distribution variable is smaller than the local search start control parameter, starting a local operator for the global optimal solution according to the global optimal solution and the control parameter prob _ls Determining a local search space, and carrying out search calculation on the local search space to obtain a local optimal solution with the lowest objective function value in the local search space;

7. The method of claim 6, wherein the method further comprises:

and if the objective function value of the local optimal solution is not smaller than the objective function value of the global optimal solution, overlapping the function evaluation times of the local optimal solution to the function evaluation times of the global optimal solution, and comparing the overlapped function evaluation times of the global optimal solution with the highest function evaluation times.

8. Differential evolution deep space orbit design system based on double-stage information migration, which is characterized by comprising:

；

the processing module is used for randomly distributing individuals in the father population to obtain three populations according to the same subspecies population scale;

the processing module is also used for reserving part of individuals with low objective function values in the sub-population and randomly reassigning the rest individuals; the random assignment of individuals in the parent population on the same subspecies population scale comprises:

initializing dead parameters of global operatorsNumber M _op (op=1, 2, 3) each of said sub-populations having a corresponding one of the parameters of arrest; the global operator is used for searching the whole detection area to obtain a global optimal solution with the lowest objective function value;

and the output module is used for comparing the function evaluation times of the global optimal solution with the highest function evaluation times, and returning to the global optimal solution with the lowest objective function value if the function evaluation times of the global optimal solution are larger than the highest function evaluation times, namely the minimum value of the cumulative speed change of the detector in the deep space orbit design problem M.