Time-domain survey telescope array observation scheduling method based on multi-objective genetic algorithm

Abstract

The application discloses a time-domain patrol telescope array observation scheduling method based on a multi-objective genetic algorithm, which comprises the following steps: S1, determining constraint conditions and targets of a time-domain patrol telescope array observation scheduling problem; S2, constructing the time-domain patrol telescope array observation scheduling problem into a multi-objective optimization model based on the constraint conditions and the targets determined in the step S1; and S3, solving the multi-objective optimization model of the time-domain patrol telescope array observation scheduling by using a multi-objective genetic algorithm to obtain an observation sequence of the time-domain patrol telescope array. The method not only realizes the solution of the multi-objective optimization model of the time-domain patrol telescope array observation scheduling problem, but also guarantees a high time utilization rate and a stable patrol frequency compared with the prior art.

Description

Technical Field

[0001] This invention relates to the field of time-domain survey telescope array observation scheduling technology, and in particular to a time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm. Background Technology

[0002] The time-domain survey telescope array observation scheduling problem involves allocating the observation time of each telescope to complete a time-domain survey task for a set of sky regions and a set of telescopes. This problem must satisfy multiple constraints, including telescope performance and location, astronomical conditions during the observation period, and multiple objectives, such as time utilization and the frequency of repeated survey observations. Because this problem requires satisfying multiple constraints and simultaneously optimizing multiple objectives, it falls under the category of multi-objective constrained optimization problems. Multi-objective constrained optimization problems are NP-hard problems. Matthias and Xavier have comprehensively analyzed the complexity of various multi-objective constrained optimization problems, proving their NP-hardness. Compared to the scheduling problem of a single telescope, the scheduling problem of multiple telescopes also requires considering the flexible and organic combination and collaborative work of numerous telescopes, further increasing the difficulty. Therefore, designing and implementing a reliable and efficient time-domain survey telescope array observation scheduling method to organize multiple telescopes together to complete a time-domain survey task is extremely challenging.

[0003] Currently, telescope (array) observation scheduling algorithms are mainly classified into the following categories: 1) Mathematical optimization methods, including integer linear programming and mixed integer linear programming. Mathematical optimization methods have significant advantages in solution accuracy, but their solution complexity is often limited by the problem size, resulting in high time and space costs. 2) Heuristic algorithms, including genetic algorithms, particle swarm optimization algorithms, simulated annealing algorithms, ant colony optimization algorithms, and tabu search algorithms. While heuristic algorithms are not as accurate as mathematical optimization methods, they significantly improve the solution speed when solving large-scale problems and can utilize prior knowledge or empirical rules during the search process to find solutions faster. 3) Greedy algorithms, which generally consider maximizing scientific value and minimizing observation time. Although greedy algorithms are simple, easy to implement, and fast, they cannot adapt to complex scenarios and multi-constraint situations.

[0004] Considering that the time-domain survey telescope array observation scheduling problem is a multi-objective constrained optimization problem, and the number of telescopes and sky areas is large, heuristic algorithms are an effective choice. They have the advantage of quickly solving large-scale multi-objective constrained optimization problems and can find a high-performing solution set in a short time.

[0005] Among numerous heuristic multi-objective optimization algorithms, NSGA-II is a widely used method. NSGA-II belongs to the multi-objective genetic algorithm family and was proposed by Deb et al. Based on the basic genetic algorithm, NSGA-II proposes several improvements, including non-dominated sorting, crowding sorting, simulated binary crossover operator, multinomial mutation operator, binary tournament selection, elite retention strategy, and truncation selection strategy, significantly improving the diversity, uniformity, and convergence speed of the solution set distribution. Due to its convenience, efficiency, fast computation speed, and good convergence performance, NSGA-II has achieved excellent results in solving complex problems and is one of the most commonly used algorithms for multi-objective optimization problems. However, when dealing with certain complex problems, the NSGA-II algorithm may get stuck in local optima and fail to find the global optimum. This is a limitation of the algorithm, mainly reflected in the non-dominated sorting strategy. The non-dominated sorting value of each individual only reflects the dominance level but cannot fully reflect the density of the individual's surroundings. Individuals with the same non-dominated level but different surrounding densities have the same probability of inheriting to the next generation, thus affecting the diversity of the population distribution. Summary of the Invention

[0006] The purpose of this invention is to provide a time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm to solve the scheduling problem of geographically distributed multi-telescope collaborative sky survey missions.

[0007] Therefore, the technical solution of the present invention is as follows:

[0008] A time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm, comprising the following steps:

[0009] S1. Determine the constraints and objectives of the time-domain survey telescope array observation scheduling problem. The constraints include: the observable range of the telescope, the influence of air masses, the effective observation period, the sky background conditions, and the lunar phase. The objectives include: maximizing observation quality and priority; maintaining a uniform number of observations for each sky region; and maximizing telescope utilization.

[0010] S2. Based on the constraints and objectives determined in step S1, the time-domain survey telescope array observation scheduling problem is constructed as a multi-objective optimization model, the steps of which are as follows:

[0011] S201, Based on observations from a time-domain survey telescope array, N o N unobserved sky regions m One available telescope, N t If there is a time window, then:

[0012] 1) Define set O as the set of all celestial regions, O = {o i ,i=1,2,3,…,N0};

[0013] 2) Define set T as the set of all available time windows, T = {t i i = 1, 2, 3, ..., N t};

[0014] 3) Define set M as the set of all available telescopes, M = {m} i i = 1, 2, 3, ..., N m};

[0015] 4) Define variable Q otm Let represent the observation quality of each sky region within each time window, where 'o' represents the i-th sky region, 't' represents the i-th time window, and 'm' represents the i-th telescope; where

[0016] Based on the observations of the i-th telescope o on the i-th sky region m within the i-th time window t, the observation quality Q otm The calculation method is as follows:

[0017] i) If telescope o can effectively observe the sky region m, then Q1 = 1; otherwise, Q1 = 0.

[0018] ii) By adopting a standardization method that maps values ​​in the range of [1,2] to values ​​in the range of [0,1], the size of the air mass between telescope o and sky region m is converted into a standardized value in the range of [0,1], namely Q2.

[0019] iii) If the time window t is within the effective observation period, then Q3 = 1; otherwise, Q3 = 0.

[0020] iv) If the moon's brightness within the time window t is less than or equal to the set brightness, then Q4 = 1; otherwise, Q4 = 0.

[0021] v) If the angle between the right ascension and declination of the center point of the day region m and the center point of the moon is greater than or equal to the set angle, then Q5 = 1; otherwise, Q5 = 0.

[0022] vi) Calculate variable Q otm Result: Q otm =Q1×Q2×Q3×Q4×Q5;

[0023] 5) Define variable p ot Let represent the observation priority of the i-th observation target o in the i-th time window t, with a value range of (0,1]. Before each round of scheduling, the observation priorities of all observation targets o are adjusted based on the time of their most recent observation: Step 1) Set all observation targets o to have the same observation priority at the initial time, and their observation priority p otThe value of each is 1; Step 2) Obtain the difference e between the most recent observation time and the current time for each observation target o. o And sum all the differences to get the sum of the differences ∑e o Step 3) Based on the difference e between the most recent observation time and the current time for each observation target o o and the sum of the differences ∑e o The observation priority adjustment coefficient λ for each observation target o is obtained: λ = e o / ∑e o Step 4) Based on the current observation priority p of each observation target o ot Update the observation priority of each observation target o to λ×p ot ;

[0024] 6) Define variable a pqm And set when a pqm =1 indicates that telescope m observes these two sky regions consecutively, with sky region p first and sky region q second, when a pqm A value of 0 indicates that the aforementioned situation does not exist;

[0025] S202. Construct a mathematical model for sky survey scheduling, including:

[0026] The first objective function is expressed as follows:

[0027] maximize∑ m∈M ∑ t∈T ∑ o∈O Q otm d otm *∑ m∈M ∑ t∈T ∑ o∈O p ot d otm ,

[0028] In the formula, d otm d is the decision variable. otm ∈{0, 1}, o∈O, t∈T, m∈M; Q otm For observation quality; p ot Priority of the observed target o within time window t;

[0029] The second objective function is expressed as follows:

[0030]

[0031] The third objective function is expressed as follows:

[0032] minimize(waitTime+slewTime),

[0033] Where waitTime is the total idle time, and its expression is:

[0034]

[0035] In the formula, length_of_timeslot is the length of the time window;

[0036] slewTime is the rotation time taken for telescope m to turn from target p to target q, and its expression is:

[0037] slewTime=∑ m∈M ∑ p∈O ∑ q∈O slew(p, q, m)a pqm ,

[0038] Each telescope can observe at most one area of ​​the sky per time window (i.e., observe one area of ​​the sky or remain idle), and its expression is:

[0039]

[0040] In the formula,

[0041] S3. Using a multi-objective genetic algorithm, solve the multi-objective optimization model for the observation scheduling of the time-domain survey telescope array to obtain the observation sequence of the time-domain survey telescope array; wherein, in the multi-objective genetic algorithm, the population consists of several chromosomes, and is based on N m One telescope, N t A time window and N o For each observation area, the number of genes on a chromosome is set to N. m ×N t ×N o Each gene has a value of 0 or 1, meaning that one chromosome composition represents one observation scheme. At the same time, during the truncation selection operation, the new population sorts all individuals according to the subdominance ranking value and the crowding degree. The subdominance ranking value is obtained by adding the nondominance rank value of each individual to the number of all individuals that dominate that individual.

[0042] Furthermore, the specific implementation steps of step S3 are as follows:

[0043] S301, Set the encoding scheme, the number of individuals in the population, and the number of iterations for the algorithm;

[0044] S302, Adaptive crossover and mutation operations: Two chromosomes to be crossed are arranged according to the crossover probability p. c The crossover operation is performed, and the chromosomes to be mutated are selected according to the mutation probability p. m Perform mutation operation; where p c and p mThe value is adaptively adjusted based on the number of iterations and the individual fitness, and its calculation formula is as follows:

[0045]

[0046]

[0047]

[0048] In the formula, gen is the current iteration number, gen_max is the total iteration number, pop_size is the population size, and a is the proportion of individual fitness to the total fitness.

[0049] S303. Calculate the non-dominated ordination value based on the binding density. The specific steps are as follows:

[0050] S3031. Calculate the non-dominated rank value for each individual, that is, in the population P, the non-dominated rank of each individual on the Pareto optimal front is 1;

[0051] S3032. Remove individuals with a non-dominance level of 1 on the Pareto optimal front, and form a new population P' with the remaining individuals; at this time, the non-dominance level of each individual on the Pareto optimal front is 2; and so on, calculate the non-dominance level of all remaining individuals.

[0052] S3033. Add the number of all individuals that dominate that individual to the non-dominance rank value of each individual to obtain the non-dominance ranking value of that individual.

[0053] S304. Crowding Degree Calculation: Crowding degree is represented by crowding distance, which is the sum of the differences between all objective function values ​​of the (i-1)th individual and the (i+1)th individual;

[0054] S305, Truncated Selection Operation: Merge the parent population and child population into a new population; sort all individuals in the new population according to the non-dominated ranking value and crowding degree, and truncate them according to the set population size.

[0055] S306, increment the population iteration count by 1, and determine whether the number of iterations set in step S301 is satisfied: if satisfied, end the iteration, and the parent population obtained in step S305 is the optimal solution for the population, i.e., the observation sequence of the survey telescope array; otherwise, return to step S302 and start a new round of iteration.

[0056] S307. End the algorithm iteration process and output the population optimal solution and the corresponding observation sequence.

[0057] Furthermore, in step S301, the population size is set to 100, and the number of algorithm iterations is set to 1000.

[0058] Compared with existing technologies, this time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm abstracts and formalizes the constraints and objectives of the scheduling problem, and constructs it into a multi-objective optimization model based on the Pareto principle. Simultaneously, it improves population diversity by proposing binary-based adaptive crossover and mutation operators to optimize the NSGA-II algorithm. By combining a density-based non-dominated sorting strategy, the algorithm can more effectively search the solution space, solving the problem that the NSGA-II algorithm may get trapped in local optima when dealing with certain complex problems. Ultimately, it not only solves the multi-objective optimization model of the time-domain survey telescope array observation scheduling problem, but also ensures both high time utilization and a stable survey frequency compared to existing methods. Attached Figure Description

[0059] Figure 1 This is a flowchart of the time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm according to the present invention;

[0060] Figure 2 This is a flowchart of step S3 in the time-domain survey telescope array observation scheduling method based on multi-objective genetic algorithm of the present invention;

[0061] Figure 3 This is a flowchart of the truncation selection process of the multi-objective genetic algorithm in step S3 of the time-domain survey telescope array observation scheduling method based on multi-objective genetic algorithm of the present invention;

[0062] Figure 4 This is a schematic diagram of starlight propagation used to calculate the size of an air mass in step S1 of the time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm of the present invention.

[0063] Figure 5(a) is a comparison of time slice utilization between the time-domain survey telescope array observation scheduling method based on multi-objective genetic algorithm of the present invention and the greedy algorithm based on observation quality.

[0064] Figure 5(b) is a comparison of the uniformity of observation times between the time-domain survey telescope array observation scheduling method based on multi-objective genetic algorithm of the present invention and the greedy algorithm based on observation quality.

[0065] Figure 5(c) is a comparison of the uniformity of observation time intervals between the time-domain survey telescope array observation scheduling method based on multi-objective genetic algorithm of the present invention and the greedy algorithm based on observation quality. Detailed Implementation

[0066] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0067] See Figure 1 The specific implementation steps for determining the observation mode of a time-domain survey telescope array at a certain location using the multi-objective genetic algorithm-based time-domain survey telescope array observation scheduling method of this application are as follows:

[0068] S1. Determine the constraints and objectives of the time-domain survey telescope array observation scheduling problem;

[0069] Specifically, the implementation steps of step S1 are as follows:

[0070] S101. Determine the constraints for scheduling observations using the time-domain survey telescope array, including: the telescope's observable range, air mass effects, effective observation periods, sky background conditions, and lunar phase; among which,

[0071] 1) The observable range of a telescope, that is, the area of ​​the sky that can be effectively observed, which is determined based on the telescope's limited height pointing range;

[0072] 2) Air mass influence, i.e., the quality of observation determined by air mass size; among which, the relationship between air mass size and the quality of observation is determined by human judgment based on experience;

[0073] The size of an air mass is approximately equal to the secant of the zenith angle; therefore, the formula for calculating the air mass size, airmass, is: airmass ≈ 1 / cosθ, where θ is the zenith angle; see [link to relevant documentation]. Figure 4 The formula for calculating air mass size is further expanded to: airmass≈1 / cosθ=BC / AC, where BC is the atmospheric optical thickness of the observed sky area relative to the observation location of the specified telescope, and AC is the atmospheric optical thickness of the specified telescope location in the zenith direction. The larger the value of airmass, the thicker the atmosphere between the observed target (i.e., the observed sky area) and the observation site (i.e., the telescope location), and therefore the worse the observation effect. Specifically, in this embodiment, the calculation of air mass size is implemented using the AirmassConstraint function in the Python toolkit astroplan. Based on practical experience, airmass=2 is set as the upper limit of observation quality. Since the value range of cosθ is [0,1] and the value range of 1 / cosθ is [1,+∞], that is, airmass=1 is the lower limit of observation quality. Therefore, the value range of air mass size is [1,2].

[0074] 3) Effective observation period, which is the period during which the telescope can effectively observe the sky area;

[0075] In this embodiment, since all time-domain survey telescopes are optical telescopes, these telescopes can only observe targets at night. That is, the effective observation period is the observation night period, which is the time between astronomical dawn (when the solar altitude is -18 degrees). Specifically, the calculation and limitation of this effective observation period is implemented using the twilight_astronomical function in the Python toolkit astroplan.

[0076] 4) Sky background conditions, that is, the brightness of the moon must be below the set brightness to achieve effective observation (moon brightness ≤ set brightness);

[0077] In this embodiment, the calculation and constraint of the sky background conditions are implemented using the MoonIlluminationConstraint function in the Python toolkit astroplan; wherein, the brightness is set to 0.65, that is, when the moon's brightness is ≤0.65, the time domain survey telescope can achieve effective observation;

[0078] 5) Lunar phase, meaning the observation target must be at least 30 degrees of separation from the moon; the separation angle is determined by the right ascension and declination of the center point of the observation target (i.e., the observation area) and the center point of the moon.

[0079] In this embodiment, the calculation and constraint of the lunar phase are implemented using the MoonSeparationConstraint function in the Python toolkit astroplan; the separation angle is set to 45°, that is, the separation angle between the moon and the sky region must be at least 45° to achieve effective observation.

[0080] S102. Determine the objectives of the time-domain survey telescope array observation scheduling problem, including:

[0081] 1) Maximize observation quality and priority;

[0082] 2) The number of observations for each sky region remains uniform;

[0083] 3) Maximize the utilization of the telescope.

[0084] S2. Based on the constraints and objectives determined in step S1, the time-domain survey telescope array observation scheduling problem is constructed as a multi-objective optimization model.

[0085] Specifically, the construction steps of the multi-objective optimization model in step S2 are as follows:

[0086] S201, Based on observations from a time-domain survey telescope array, N o N unobserved sky regions m One available telescope, N t If there is a time window, then:

[0087] 1) Define set O as the set of all celestial regions, O = {o i ,i=1,2,3,…,N0};

[0088] 2) Define set T as the set of all available time windows, T = {t i i = 1, 2, 3, ..., N t In this embodiment, the length of the time window is set to 30 minutes. Taking a scheduling time of 1 day as an example, the corresponding number of time windows is 48.

[0089] 3) Define set M as the set of all available telescopes, M = {m} i i = 1, 2, 3, ..., N m};

[0090] 4) Define variable Q otm The variable Q represents the observation quality of each sky region within each time window, where o represents the i-th sky region, t represents the i-th time window, and m represents the i-th telescope; otm The larger the value, the higher the observation quality, meaning it can be prioritized in the scheduling process;

[0091] Specifically, define variable Q. otm The relationship between the value of and the various constraints in step S101 is as follows:

[0092] Taking the observation of the i-th sky region m by the i-th telescope o in the i-th time window t as an example, its corresponding observation quality Q otm The process of determining is as follows:

[0093] i) If the telescope is able to effectively observe the sky region, then Q1 = 1; otherwise, Q1 = 0.

[0094] ii) Using a standardization method that maps values ​​in the range of [1,2] to values ​​in the range of [0,1], the airmass between the telescope and the sky region is converted into a standardized value in the range of [0,1], i.e., Q2.

[0095] iii) If the time window falls within the valid observation period, then Q3 = 1; otherwise, Q3 = 0.

[0096] iv) If the moon's brightness within this time window is less than or equal to the set brightness (i.e., 0.65), then Q4 = 1; otherwise, Q4 = 0.

[0097] v) If the angle between the sky region and the moon is greater than or equal to the set angle (i.e., 45°), then Q5 = 1; otherwise, Q5 = 0.

[0098] vi) Calculate variable Q otmQ otm =Q1×Q2×Q3×Q4×Q5;

[0099] Through the above calculations, a total of N results were obtained to characterize the observation quality of each telescope for different sky regions under different time windows. o ×N m ×N t One, and the observation quality result Q otm The value range of Q is [0,1]; when Q otm A value of 0 indicates unobservable; when Q... otm When the value is greater than 0, it indicates that it is observable, and Q otm The larger the value, the better the observation quality;

[0100] 5) Define variable p ot This represents the observation priority of the i-th observation target o in the i-th time window t, with a value range of (0,1]. This observation priority is positively correlated with the difference between the most recent observation time of the observation target o and the current time. That is, the further back the time of the most recent observation is from the current time, the higher the observation priority of the observation target o, and it should be observed first. At the same time, it is set that before each round of scheduling, the observation priority of each observation target o is adjusted according to the most recent observation time of all observation targets o to ensure the uniformity of the sky survey in time.

[0101] Specifically, the observation priority p of all observed targets o ot The adjustment method is as follows:

[0102] Step 1: Set all observation targets o to have the same observation priority at the initial time, and their observation priority p ot The value of is 1;

[0103] Step 2: Obtain the difference e between the most recent observation time and the current time for each observation target o. o And sum all the differences to get the sum of the differences ∑e o ;

[0104] Step 3: Based on the difference e between the most recent observation time and the current time for each observation target o o and the sum of the differences ∑e o The observation priority adjustment coefficient λ for each observation target o is obtained: λ = e o / ∑e o ;

[0105] Step 4: Based on the current observation priority p of each observation target o ot Update the observation priority of each observation target o to λ×p ot ;

[0106] 6) Define variable a pqm And set when a pqm =1 indicates that telescope m observes the two sky regions consecutively, with sky region p first and sky region q second; when a pqm A value of 0 indicates that the aforementioned situation does not exist; the variable a pqm The objective is to minimize the distance between sky region p and sky region q in subsequent calculations, thereby saving the time required for telescope turning.

[0107] S202. Based on the physical quantities defined in step S201, construct a mathematical model for sky survey scheduling, which consists of three objective functions, including:

[0108] The first objective function corresponds to the first objective set in step S102, which is to maximize observation quality and priority; therefore, the first objective function is set as the convolution of the two, and its expression is:

[0109] maximize∑ m∈M ∑ t∈T ∑ o∈O Q otm d otm *∑ m∈M ∑ t∈T ∑ o∈O p ot d otm ,

[0110] In the formula, d otm d is the decision variable. otm ∈{0, 1}, o∈O, t∈T, m∈M; Q otm For observation quality; p ot Priority of the observed target o within time window t;

[0111] The second objective function corresponds to the second objective set in step S102, which aims to keep the number of observations for each sky region uniform. Therefore, the second objective function uses the standard deviation of the number of observations to represent uniformity, and the smaller the standard deviation of the number of observations, the better the uniformity. The expression for the second objective function is:

[0112]

[0113] The third objective function corresponds to the third objective set in step S102, which is to maximize the utilization of the telescope, that is, to minimize the sum of idle time and rotation time; where,

[0114] The expression for the total idle time waitTime is:

[0115]

[0116] In the formula, length_of_timeslot is the length of the time window. As mentioned earlier, the length of the time window in this embodiment is 30 minutes.

[0117] To facilitate the calculation of telescope rotation time, this application ignores the telescope's limiting problem and simplifies the telescope's rotation process into a uniformly accelerated rotation model with the same angular acceleration and deceleration. Furthermore, since the altazimuth and elevation axes need to rotate simultaneously when the altazimuth telescope changes sources, the rotation time from the current position to the next source position is taken as the longest time on both axes, i.e., the expression is:

[0118] slewTime=∑ m∈M ∑ p∈O ∑ q∈O slew(p, q, m)a pqm ,

[0119] In the formula, slew(p, q, m) represents the rotation time taken for telescope m to turn from target p to target q; a pqm As a variable, a pqm ∈{0,1};

[0120] Therefore, the expression for the third objective function is:

[0121] minimize(waitTime+slewTime),

[0122] Each telescope can observe at most one area of ​​the sky per time window (i.e., observe one area of ​​the sky or remain idle), and its expression is:

[0123]

[0124] In the formula, the decision variable d otm The value of can only be 0 or 1, that is:

[0125] S3. Using a multi-objective genetic algorithm, solve the multi-objective optimization model for the observation scheduling of the time-domain survey telescope array to obtain the observation sequence of the time-domain survey telescope array.

[0126] See Figure 2 The specific implementation steps of step S3 are as follows:

[0127] S301. Sequentially set the encoding scheme, the number of individuals in the population, and the number of iterations:

[0128] As can be seen from steps S1 and S2, the time-domain survey telescope array observation scheduling problem of this application is refined into a multi-objective 0-1 planning problem. Therefore, in order to simplify the calculation process and facilitate crossover and mutation operations, the solution steps adopt a binary encoding method; specifically, for N m One telescope, N t One time window, N o For the problem of scheduling observations by a time-domain survey telescope array over a single observation area, the number of genes on a chromosome can be set to N. m ×N t ×N o Each gene has a value of 0 or 1, and one chromosome composition represents one observation scheme. Meanwhile, considering the algorithm execution time and the accuracy of the solution, the population size is set to 100 and the number of algorithm iterations is set to 1000.

[0129] S302, Adaptive crossover and mutation operations:

[0130] Specifically, the two chromosomes to be crossed are arranged according to the crossover probability p. c The crossover operation is performed, and the chromosomes to be mutated are selected according to the mutation probability p. m Mutation operations are performed; among them, in order to maintain population diversity and prevent premature convergence, p c and p m The value is adaptively adjusted based on the number of iterations and the individual fitness, and its calculation formula is as follows:

[0131]

[0132]

[0133]

[0134] In the formula, gen is the current iteration number, gen_max is the total iteration number, pop_size is the population size, and a is the proportion of individual fitness to the total fitness.

[0135] S303. Binding density, calculate non-dominated ordination value:

[0136] The specific implementation steps of step S303 are as follows:

[0137] S3031. Calculate the non-dominated rank value for each individual, that is, in the population P, the non-dominated rank of each individual on the Pareto optimal front is 1;

[0138] S3032. Remove individuals with a non-dominance level of 1 on the Pareto optimal front, and form a new population P' with the remaining individuals; at this time, the non-dominance level of each individual on the Pareto optimal front is 2; and so on, calculate the non-dominance level of all remaining individuals.

[0139] S3033. Add the number of all individuals that dominate that individual to the non-dominance rank value of each individual to obtain the non-dominance ranking value of that individual.

[0140] S304. Congestion Calculation:

[0141] Crowding degree is represented by crowding distance, which is the sum of the differences between all objective function values ​​of the (i-1)th individual and the (i+1)th individual. The larger the crowding distance, the smaller the crowding degree. Generally, the optimal solutions in the solution set have higher objective function values ​​and lower crowding degree values ​​because they are more representative of the effective solutions in the solution space.

[0142] S305, Truncation Selection Operation:

[0143] The parent and child populations are merged into a new population; all individuals in the new population are ranked according to their non-dominant ranking value and crowding, and then truncated according to the set population size; specifically as follows: Figure 3 As shown, the upper half of the individual set with a size of N is selected to be retained, and all individuals exceeding the size are eliminated. The retained individual set serves as the parent population for the next generation to participate in evolution.

[0144] S306, increment the population iteration count by 1, and determine whether the number of iterations set in step S301 is satisfied: if satisfied, end the iteration, and the parent population obtained in step S305 is the optimal solution for the population, i.e., the observation sequence of the survey telescope array; otherwise, return to step S302 and start a new round of iteration.

[0145] S307. End the algorithm iteration process and output the population optimal solution and the corresponding observation sequence.

[0146] Furthermore, the method of this application was applied to specific data to verify its effectiveness.

[0147] The distribution of observation sites in the telescope array was simulated using the locations of 20 real global observatories from the astropy library in Python. Additionally, 1000 sky regions were generated for simulation, some of which were derived from real sky region data from the ZTF project. Furthermore, additional location coordinates were added to these data to achieve more comprehensive sky coverage. Meanwhile, in practical applications, the scheduling quality of the method in this application is measured using the following three indicators:

[0148] (1) Time slice utilization rate, which is the proportion of time successfully allocated under observation conditions to all available observation time;

[0149] (2) The uniformity of the number of observations is specifically measured by calculating the standard deviation of the number of observations for each day region in the scheduling results.

[0150] (3) Observation time interval uniformity, specifically by calculating the standard deviation of the time interval from the start of each observation to the end of the previous observation for each sky area as the result of this metric.

[0151] This application was tested multiple times under different survey telescope array sizes, different sizes of the sky area to be observed, and different scheduling durations. The scheduling performance of this method is shown in Table 1 below.

[0152] Table 1:

[0153]

[0154]

[0155] As shown in Table 1, the time-domain survey telescope array obtained by this method exhibits stable performance in terms of time slice utilization, uniformity of observation time intervals, and time slice utilization under different telescope array sizes, different numbers of observation sky areas, and different scheduling durations. This indicates that the method has good universality.

[0156] To better explore the superiority of the proposed method in solving the observation scheduling problem of time-domain survey telescope arrays, a series of comparative experiments were conducted with it and the greedy algorithm, which is widely used in astronomical scheduling. Specifically, the greedy algorithm provides a convenient entry point for automatic scheduling and is widely used in astronomy. Specifically, before each observation, the greedy algorithm calculates a new metric or score for each possible target, selects the target with the highest current value for observation, and then repeats this process. The optimizer based on the greedy algorithm is easy to implement, can easily handle changes in observation plans and conditions, and can run in an automated manner. Furthermore, such a greedy scheduler was implemented using the astroplan library.

[0157] The method of this application and the greedy algorithm based on observation quality were applied to the sky survey scheduling problem with 5 telescopes and 100 sky areas. The performance of the two algorithms was compared by comparing their performance in terms of time slice utilization, uniformity of observation times, and uniformity of observation time intervals. The specific comparison results are shown in Figures 5(a), 5(b), and 5(c).

[0158] Figure 5(a) shows the performance of the proposed method and the greedy algorithm in terms of time slice utilization across seven experiments. The data reveals that the proposed method consistently outperforms the greedy algorithm in time slice utilization across all seven experiments, achieving an average utilization of 72.45%, higher than the greedy algorithm's average of 60.36%, representing a 20.03% improvement in time slice utilization. Furthermore, the variation range of the proposed method's time slice utilization is only 1.92%, less than the greedy algorithm's 3.01%, indicating that its performance varies less in the experiments compared to the greedy algorithm.

[0159] Figure 5(b) shows the performance of the proposed method and the greedy algorithm in terms of observation uniformity across 7 experiments. It can be seen that the proposed method performs better in terms of observation uniformity compared to the greedy algorithm. The average observation uniformity of the proposed method is 10.37, while the average of the greedy algorithm is 41.41, representing a 74.96% improvement in observation uniformity. Furthermore, it can be observed that the variation in the observation uniformity value of the proposed method is relatively small across the 7 experiments, indicating a certain degree of stability in its observation uniformity performance across multiple experiments.

[0160] Figure 5(c) shows the performance of the proposed method and the greedy algorithm in terms of observation time interval uniformity across seven experiments. It can be seen that the proposed method performs significantly better than the greedy algorithm in this regard. The average uniformity of the proposed method is 129.26, while the average for the greedy algorithm is 160.46. This indicates that the proposed method provides more consistent uniformity across different experiments, representing a 19.44% improvement in survey time interval uniformity compared to the greedy algorithm. Furthermore, the variation range of the proposed method's uniformity across the seven experiments is relatively small, indicating less performance variation across different experiments. Overall, these results demonstrate that the proposed method is more consistent and reliable in terms of observation time interval uniformity compared to the greedy algorithm.

[0161] In summary, while the greedy algorithm is simple to implement and runs quickly, it performs poorly in scheduling observations for time-domain survey telescope arrays in practical experiments. Specifically, it performs poorly in terms of time slice utilization, uniformity of observation counts, and uniformity of observation time intervals. Considering the limited telescope usage time and high observation costs, it is essential to adopt a more efficient scheduling algorithm. Furthermore, astronomers generally believe that local optimizers (such as the greedy algorithm) cannot provide global optimization, which is consistent with the experimental results presented in this application.

[0162] In summary, the time-domain survey telescope array observation scheduling method based on multi-objective genetic algorithm proposed in this application solves the time-domain survey telescope array observation scheduling problem. By abstracting and formalizing the constraints and objectives of the time-domain survey telescope array observation scheduling problem, it models it as a standard multi-objective constrained optimization problem. Furthermore, it improves the NSGA-II algorithm to address the problem that the NSGA-II algorithm may get stuck in local optima when dealing with certain complex problems. This method efficiently achieves the goal of obtaining the optimal time-domain survey telescope array observation sequence, ensuring not only high time utilization but also a stable survey frequency.

[0163] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm, characterized in that, The steps are as follows: S1. Determine the constraints and objectives of the time-domain survey telescope array observation scheduling problem. The constraints include: the observable range of the telescope, the influence of air masses, the effective observation period, the sky background conditions, and the lunar phase. The objectives include: maximizing observation quality and priority; maintaining a uniform number of observations for each sky region; and maximizing telescope utilization. S2. Based on the constraints and objectives determined in step S1, the time-domain survey telescope array observation scheduling problem is constructed as a multi-objective optimization model, the steps of which are as follows: S201, Based on observations from a time-domain survey telescope array, N o One area of ​​sky to be observed. One available telescope, N t If there is a time window, then: 1) Define set O as the set of all celestial regions, O = {o i , i=1, 2, 3,…, N0}; 2) Define set T as the set of all available time windows, T = {t i , i=1, 2, 3,…, N t }; 3) Define set M as the set of all available telescopes, M = {m i , i=1, 2, 3,…, N m }; 4) Define variable Q otm Let represent the observation quality of each sky region within each time window, where 'o' represents the i-th sky region, 't' represents the i-th time window, and 'm' represents the i-th telescope; where Based on the observations of the i-th telescope o on the i-th sky region m in the i-th time window t, the observation quality The calculation method is as follows: i) When telescope o can effectively observe the sky region m, then =1; otherwise, =0; ii) By adopting a standardization method that maps values ​​in the range [1,2] to values ​​in the range [0,1], the size of the air mass between telescope o and sky region m is converted into a standardized value in the range [0,1]. ; iii) When the time window t falls within the effective observation period, then =1; otherwise, =0; iv) When the moon's brightness within time window t is less than or equal to the set brightness, then =1; otherwise, =0; v) If the angle between the right ascension and declination of the center point of region m and the center point of the moon is greater than or equal to the set angle, then... =1; otherwise, =0; vi) Calculate variable Q otm Result: Q otm = × × × × ; 5) Define variable p ot Let represent the observation priority of the i-th observation target o in the i-th time window t, with a value range of (0,1]. Before each round of scheduling, the observation priorities of all observation targets o are adjusted based on the time of their most recent observation: Step 1) Set all observation targets o to have the same observation priority at the initial time, and their observation priority p ot The value of each is 1; Step 2) Obtain the difference e between the most recent observation time and the current time for each observation target o. o And sum all the differences to get the sum of the differences ∑e o Step 3) Based on the difference e between the most recent observation time and the current time for each observation target o o and the sum of the differences ∑e o The observation priority adjustment coefficient λ for each observation target o is obtained: λ = e o / ∑e o Step 4) Based on the current observation priority p of each observation target o ot Update the observation priority of each observation target o to λ×p ot ; 6) Define variable a pqm And set when a pqm =1 indicates that telescope m observes these two sky regions consecutively, with sky region p first and sky region q second, when a pqm A value of 0 indicates that the aforementioned situation does not exist; S202. Construct a mathematical model for sky survey scheduling, including: The first objective function is expressed as follows: ， In the formula, d d is the decision variable. ∈{0,1}, o∈O,t∈T,m∈M; For observation quality; Priority of the observed target o within time window t; The second objective function is expressed as follows: ； The third objective function is expressed as follows: ， in, The total idle time is expressed as: ， In the formula, length_of_timeslot is the length of the time window; slewTime is the rotation time taken for telescope m to turn from target p to target q, and its expression is: ， Each telescope can observe at most one area of ​​the sky per time window (i.e., observe one area of ​​the sky or remain idle), and its expression is: ， In the formula, ; S3. Using a multi-objective genetic algorithm, solve the multi-objective optimization model for the observation scheduling of the time-domain survey telescope array to obtain the observation sequence of the time-domain survey telescope array; wherein, in the multi-objective genetic algorithm, the population consists of several chromosomes, and is based on One telescope, N t A time window and N o For each observation area, the number of genes on one chromosome is set to... ×N t ×N o Each gene has a value of 0 or 1, meaning that one chromosome composition represents one observation scheme. At the same time, during the truncation selection operation, the new population sorts all individuals according to the subdominance ranking value and the crowding degree. The subdominance ranking value is obtained by adding the nondominance rank value of each individual to the number of all individuals that dominate that individual.

2. The time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm according to claim 1, characterized in that, The specific implementation steps of step S3 are as follows: S301, Set the encoding scheme, the number of individuals in the population, and the number of iterations for the algorithm; S302, Adaptive crossover and mutation operations: Two chromosomes to be crossed are arranged according to the crossover probability p. c The crossover operation is performed, and the chromosomes to be mutated are selected according to the mutation probability p. m Perform mutation operation; where p c and The value is adaptively adjusted based on the number of iterations and the individual fitness, and its calculation formula is as follows: ， ， ， In the formula, gen is the current iteration number, gen_max is the total iteration number, pop_size is the population size, and a is the proportion of individual fitness to the total fitness. S303. Calculate the non-dominated ordination value based on the binding density. The specific steps are as follows: S3031. Calculate the non-dominated rank value for each individual, that is, in the population P, the non-dominated rank of each individual on the Pareto optimal front is 1; S3032. Remove individuals with a non-dominance level of 1 on the Pareto optimal front, and form a new population P' with the remaining individuals; at this time, the non-dominance level of each individual on the Pareto optimal front is 2; and so on, calculate the non-dominance level of all remaining individuals. S3033. Add the number of all individuals that dominate that individual to the non-dominance rank value of each individual to obtain the non-dominance ranking value of that individual. S304. Crowding Degree Calculation: Crowding degree is represented by crowding distance, which is the sum of the differences between all objective function values ​​of the (i-1)th individual and the (i+1)th individual; S305, Truncated Selection Operation: Merge the parent population and child population into a new population; sort all individuals in the new population according to the non-dominated ranking value and crowding degree, and truncate them according to the set population size. S306, increment the population iteration count by 1, and determine whether the number of iterations set in step S301 is satisfied: if satisfied, end the iteration, and the parent population obtained in step S305 is the optimal solution for the population, i.e., the observation sequence of the survey telescope array; otherwise, return to step S302 and start a new round of iteration. S307. End the algorithm iteration process and output the population optimal solution and the corresponding observation sequence.

3. The time-domain survey telescope array observation scheduling method based on a multi-objective genetic algorithm according to claim 2, characterized in that, In step S301, the population size is set to 100, and the number of algorithm iterations is set to 1000.

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