Intelligent mission planning of sky survey based on the NSGA-III algorithm

In recent years, China has been scheduled to launch an all-sky survey telescope for celestial observation. The meticulous arrangement of observation sequences for this telescope is of paramount importance, given the myriad challenges and constraints inherent to such astronomical survey missions. These challenges encompass factors such as spatial limitations, stray light contamination, as well as constraints related to data storage and energy consumption. This undertaking presents a quintessential NP-hard optimization problem. To address this complexity and enhance in-orbit observation efficiency, this study closely adheres to practical engineering considerations. A comprehensive evaluation of diverse constraints is conducted, culminating in the establishment of an optimization model for systematic planning of sky survey missions. The primary optimization objectives encompass maximizing in-orbit observation duration, augmenting the count of observable celestial points, and minimizing maneuvering angles. To tackle this multifaceted problem, a mission planning algorithm is devised based on NSGA-III, a multi-objective optimization technique. The experimental results indicate that the sky survey planning algorithm proposed in this paper can effectively accomplish sky survey observation tasks, achieving the scientific objective of no fewer than 350 daily observation points. It holds the potential to provide algorithmic support for the sky survey telescope mission on the Chinese space station.


Introduction
China is planning to deploy the Chinese Space Station Telescope (CSST) for all-sky astronomical observation.With a diameter of two meters, the CSST boasts exceptional attributes such as a wide field of view and high image quality.It is designed for conducting all-encompassing surveys with high angular resolution, covering extensive celestial regions.By harnessing the extensive data from billions of stars, and galaxies, as well as terahertz spectral line information, the CSST aims to investigate mechanisms underlying the cosmic acceleration expansion, such as the nature of dark energy.This involves precisely determining fundamental cosmological parameters, testing cosmological models, gravitational theories, and theories of large-scale structure formation and evolution.The telescope will also measure neutrino mass, explore properties of dark matter particles, reconstruct initial density fluctuations of the universe, unveil the three-dimensional structure and formation history of the Milky Way galaxy, and reveal the patterns governing the formation and evolution of various celestial bodies including stars, planets, black holes, galaxies, and quasars.These pursuits aim to provide critical clues to breakthroughs in cutting-edge fields of astronomy and physics, potentially leading to revolutionary 2 discoveries.
The CSST is dedicated to advancing both physics and astronomy research.One of its scientific missions involves achieving seamless spectral surveys across 17, 500 targets.However, during actual observations, the telescope will be subject to various constraints, such as contamination from sources like sunlight, moonlight, and atmospheric effects.Energy and thermal constraints, as well as restrictions related to data storage and mode switching, further impact the telescope's operation.Therefore, to accommodate these multifaceted constraints and enhance observation efficiency, optimization of the telescope's observation sequence becomes imperative to maximize its scientific yield.

Models and algorithm
Hu et al. [1] developed a task-planning model for a survey telescope.Their optimization objectives focused on maximizing the observation weight of sky regions while minimizing maneuver angles.They introduced a multi-stage algorithm and particle swarm optimization method, enabling the completion of seamless spectral surveys covering 15, 000 square degrees and deep-field surveys spanning 400 degrees ahead of schedule by three years.Liu and Liu [2] investigated the survey scanning observation pattern of the HXMT astronomical satellite.Using real-world requirements, they formulated an intelligent planning model for celestial point trajectory.The primary aim was to achieve extensive sky coverage with minimal energy consumption and attitude adjustments.They devised a multi-objective genetic algorithm to address energy shortage issues.Huang et al. [3] analyzed the optimization objectives and constraints of long-term mission planning for HXMT.They established a mathematical model and proposed a hybrid solution method merging greedy and genetic algorithms.The model prioritized maximizing observation efficiency and task ranking, accounting for observation and time window constraints.Their experiments and simulations validated the approach.Ren et al. [4] focused on the unique characteristics of the LAMOST telescope and established an algorithmic model for static constraints.These constraints encompassed factors such as daily observable time, lunar phases, zenith passages, and guiding stars, each assigned observation priority.Through simulation experiments, they evaluated the impact of various static constraints.Hao et al. [5] designed a dynamic target selection algorithm based on priority strategies tailored to LAMOST's features.This approach prioritized selection based on maximum unobserved density and uniform distribution criteria.It effectively considered previous selections and current observation conditions, overcoming the limitations of static target selection.Simulation results demonstrated a notable increase in observation efficiency.Wu [6] proposed a dynamic replanning algorithm involving pausing and then resuming satellite observation missions in response to the impacts of Target of Opportunity (ToO) observations.Solar et al. [7], based on the ALMA mission, introduced a mixed-integer programming-based approach.

Sky survey systems
The Hubble Space Telescope (HST) was launched into Earth's orbit by the United States in 1990.Researchers have developed two categories of planning and scheduling software: HSTS (Heuristic Scheduling Testbed System) and SPIKE.HSTS [8] serves as short-term task planning and scheduling software for HST, while SPIKE is employed for long-term task planning and scheduling.The James Webb Space Telescope (JWST) integrates the Generalized Differential Evolution 3 (GDE3) algorithm [9], a generalized differential evolution method for multi-objective optimization, with the SPIKE system.GDE3 functions as the driver for the multi-objective evolutionary algorithm, while SPIKE is responsible for modeling JWST's time allocation problem.These two components collaborate, with GDE3 providing decision vectors to SPIKE, which in turn returns objective function values.The European Southern Observatory has developed the TaToo system to arrange observation plans for telescopes.Subsequently, efforts have been directed towards interface design, aiming to transform TaToo into a user-friendly, interactive, and semi-automatic system.NASA's Chandra X-ray Observatory uses a planning system known as the Offline System (OFLS) [10].This system comprehensively takes into account all relevant constraints in the Chandra mission.Depending on the evolving conditions of the Chandra mission, the planning system continuously adjusts based on these constraints.This is done to ensure the safe operation of the equipment while maximizing observation efficiency.
3 Proposed method

. Problem description
The workflow of a single observation cycle is depicted in Figure 1.Upon the completion of a given observation, the observational data is read out, and a new observation cycle is initiated.Utilizing an optimization strategy, the observation target points are selected, and the optical axis is adjusted to point toward the chosen target.Once the line of sight is accurately aligned and the data from the previous observation cycle has been retrieved, the exposure begins.In case of any interruptions, the exposure is immediately halted, and the subsequent exposure cycle commences.Following the completion of the exposure, the next observation cycle ensues.Long-term observation mission planning has already developed mature models and algorithms.In this study, the short-term, day-specific observation plan sequences are derived by integrating the outcomes of long-term observation planning.

Variable definition
Before building the model and analyzing the constraints, we define and explain some of the symbols used to facilitate the model building later.the symbols used and the specific descriptions are listed in Table 1.

Symbol Detailed Description 𝑥𝑥 𝑖𝑖,𝑗𝑗
The i-th observation point is observed in the j -th cycle t s

Start time of observation t e
End time of observation.

Decision variable
In this paper, the entire observation timeline is partitioned into discrete intervals of 200 seconds each, resulting in a total of 432 intervals per day.Each of these intervals defines a distinct temporal window within the celestial sphere, denoted as ti for the i-th interval.The ensemble of all such temporal windows is represented as t i for the i-th interval.The ensemble of all such temporal windows is represented as t={t i ,i=1,2…,M}.where M signifies the overall count of windows.Drawing upon the survey module's field of view embedded within the telescope, the overarching observational region is subdivided into numerous smaller celestial sectors.This segmentation ensures that the telescope's field of view adequately encompasses each of these smaller sectors.The nomenclature attributed to these celestial sectors adheres to a systematic numbering scheme.A celestial sector labeled as S j corresponds to the j -th numbered sector, and the aggregate collection of such sectors is denoted as S={S j ,i=1,2…,k}.Considering the constraints imposed by the on-orbit context, the determination of whether the telescope should engage in observing a specific small celestial sector during a particular time interval is transcribed into a binary decision format.This binary variable assumes a value of 1 when the telescope opts to observe S j within the temporal window t i and a value of 0 otherwise.The formulation of this decision variable is succinctly expressed by Equation (1): , denotes the binary decision variable,   represents the j-th celestial sector, and   corresponds to the i-th time interval.

Analysis of constraints
Visibility Constraint: Space telescopes are deployed on spacecraft following specific orbits around the Earth.Due to the occlusion caused by the Earth, Moon, and other planets, there are numerous regions that remain unobservable even when the telescope's attitude is maneuvered arbitrarily.Only when the spacecraft reaches a particular position and the celestial sector can be brought within the telescope's field of view through attitude adjustments, is it possible to conduct observation activities in that region, as shown in Equation (2).
≤   ≤   ≤   (2) Solar and Lunar Stray Light Avoidance Constraint: The intrusion of solar and lunar stray light into the instrument's aperture leads to increased noise levels, thereby significantly compromising image quality.Among these sources, solar stray light poses the most substantial challenge, necessitating an assurance that the line of sight maintains a solar incidence angle greater than 50° to minimize such effects.Lunar stray light, originating from sunlight reflected off the lunar surface, is approximately five orders of magnitude weaker than direct sunlight and exhibits variations due to lunar phases.However, its impact is relatively minor.To mitigate this, it is imperative to ensure that the line of sight maintains a lunar incidence angle greater than 30°, thereby effectively managing potential stray light contamination, as shown in Equations (3)(4).
(, ) ≥ (, ) ≥  (4) Terrestrial Atmospheric Glow Impact Constraint: Operating within a low Earth orbit, the influence of terrestrial atmospheric glow, which encompasses the reflections from the Earth's surface and atmospheric scattering, becomes notably significant.To mitigate the substantial impact of terrestrial atmospheric glow, it is imperative to impose specific requirements on the angle formed between the line of sight and the tangent to the Earth's surface.Precisely, within regions exposed to direct sunlight, this angle must exceed 80° to effectively mitigate the influence of terrestrial atmospheric glow.In areas experiencing shadowed illumination, the angle is stipulated to be greater than 30° to ensure the successful avoidance of such adverse effects, as shown in Equation (5).

𝜃𝜃(𝐸𝐸𝑜𝑜𝑜𝑜𝑜𝑜ℎ, 𝑁𝑁𝑛𝑛𝑜𝑜) ≥ 𝛾𝛾
(5) South Atlantic Anomaly Constraint: Also known as the South Atlantic Anomaly (SAA), the South Atlantic Abnormal Region is characterized by the penetration of significant amounts of cosmic radiation from outer space.Space telescopes traversing this region are susceptible to instrument malfunction, communication errors, and other anomalies.Furthermore, the region gives rise to an abundance of particles, resulting in a decrease in the signal-to-noise ratio of imaging due to elevated background noise.Consequently, during survey observations passing through this area, unless specific observational imperatives exist, the survey module should halt its observations (enter standby or shutdown mode) to prevent potential adverse effects, as shown in Equation (6).
∑   = 0 ∈ (6) Spacecraft Energy Balance Constraint: Solar panels provide energy for spacecraft and telescopes, with the panels capable of single-degree-of-freedom rotation along the axis (approximately parallel to the line of sight).The incident direction of sunlight must maintain an angle of less than 25° relative to the orientation of the solar panels to ensure a continuous energy supply.Consequently, to guarantee the provision of energy, the angular relationship between the Sun and the solar panels must be maintained within the specified range in sunlit regions.Under energy balance considerations, the observable sky area in the sunlit region accounts for approximately 1/10 to 1/4 of that achievable without energy balance considerations, as shown in Equations ( 7) (8).
≥   (7) (, ) ≤  (8) Spacecraft Maneuverability Constraint: During the process of survey observation, transitioning between target celestial sectors necessitates swift spacecraft attitude adjustments.The time required for the maneuver depends on the rotation angle and the stabilization time of the camera.Hence, it becomes essential to optimize the selection of observation targets to enhance overall observation efficiency, as shown in Equation (9).
+1 −    >  ℎ (9) Data Retrieval Constraint: The time required for data retrieval defines the minimum interval between consecutive exposures.Based on existing design parameters, the combined duration of shutter operation and CCD data retrieval should not exceed 25 seconds, as shown in Equation (10).
+1 −    >   (10) Data Storage and Downlink Constraint: The imaging data generated by the telescope constitutes a substantial volume, necessitating a comprehensive consideration of limitations imposed by data downlink bandwidth and total storage capacity.Judicious observation planning is crucial to avert data accumulation and storage burdens, thereby preventing any hindrance to the expeditious analysis of scientifically time-sensitive discoveries.The storage resources available aboard the spacecraft are finite, hence the volume of data accumulated during survey observations must adhere to the spacecraft's storage capacity.Furthermore, the downlink of data is only feasible within predefined time intervals, as shown in Equation (11).

Objective functions
To assess the fitness of solution outcomes, corresponding objective functions need to be established.Generally, objective functions formulated within task planning models can be categorized into three types.Firstly, the on-orbit observation duration objective function seeks to maximize the telescope's operational status over the course of a day's observation plan.This objective incorporates the notion of observation point weighting, recognizing that distinct observation points possess varying observational significance.Consequently, observation points with higher weights ought to be prioritized for more frequent and earlier observations, thereby minimizing idle time and maneuvering rotation angles.This strategy optimally utilizes the equipment, consequently elevating observation efficiency, as is shown in Equation ( 12).(12) The second objective entails the maximization of on-orbit observations, with the aim of observing the greatest possible number of target points per day.Given the substantial quantity of observation points in survey missions, it is stipulated that the daily count of observed points should not fall below 300.Endeavoring to accomplish as many observation tasks as possible for these points expedites the completion of the survey mission, subsequently enhancing observation efficiency, as is shown in Equation (13).
2 :  = ∑    =1 (13) The third objective involves minimizing the telescope's maneuvering angles.This objective pertains to the principle that smaller rotation angles of the telescope correspond to reduced energy consumption.Therefore, achieving the lowest total energy expenditure is a target of importance.This objective can be represented by the sum of the angles of rotation required for the telescope to observe its designated targets.Employing less energy for maneuvers serves to conserve power, as is shown in Equation ( 14).
4 Design of algorithm

Calculation of time windows
Given the necessity to consider a multitude of celestial sectors for observations, in order to simplify the problem, reduce the solution space, and enhance computational speed, this study adopts an approach of considering all constraints and precomputing observable sky sectors for various time windows.The collection of observable sky sectors corresponding to each time window collectively forms a list of observable sky sectors.During the actual planning process, for each time window, the appropriate observable sky sectors are selected, forming the basis for constructing the corresponding observation plan.The fitness function for distinct observation plans is determined through comparison, leading to the identification of the optimal observation strategy.

NSGA-III algorithm
Genetic algorithms simulate the process of genetic evolution in nature to search for optimal solutions to optimization problems.In the context of population evolution, the algorithm incorporates operators akin to natural evolution, such as selection, mating, and mutation.The process of a genetic algorithm in seeking the globally optimal solution is an iterative one, continuing until the algorithm's termination criteria are met.Multi-objective genetic algorithms employ non-dominated sorting, where a higher nondominated rank implies a higher priority for gene transmission.Individuals within the same rank are selected through random sampling.The convergence of the algorithm to the highest non-dominated rank enhances the distribution uniformity of individuals on the Pareto front, thereby preserving greater diversity within the population.In this paper, a modification of the selection operation based on the NSGA-III algorithm is employed, aimed at ensuring diversity among non-dominated solutions.The algorithmic flowchart of the survey optimization algorithm based on NSGA-III is depicted in Table 2. we randowly choose n j in F m which is union to reference point F m = F m /n(j) j=j+1 P t+1 is updated t=t+1 Output: the nondominated-sorting set F 1 , the best sequence S is chosen from F 1 .

Basic information and algorithm parameters
The target time span for the planning in this study is from January 1, 2020, to January 2, 2030.The selected planning region encompasses the area within the ecliptic latitudes of [-80, -20] to [20, 80], excluding the region of low ecliptic latitudes.The total area covered by this region exceeds 20, 000 square degrees, surpassing the requirement of the survey observation task.The algorithm's pertinent parameter settings are as follows: a population size of 200, a total of 1200 iterations, a crossover rate of 0.9, and a mutation rate of 0.4.The weights assigned to the three objective functions are uniformly set at 0.33.

Analysis of simulation results
Figures 2, 3, and 4 illustrate the convergence behavior of the three objective functions.The optimization of telescope maneuver angles, observation point count, and observation duration all converge to their optimal values within the first 800 generations, maintaining a high level of stability within 1200 generations.The observation point count stabilizes at 369 points within a single day, satisfying the requirement for the telescope's daily observation needs of more than 350 points.Convergence of observed duration.Figure 5 depicts a temporal curve illustrating the telescope's energy status.When energy remains constant, it signifies that the solar panel charging capacity surpasses the maximum electrical capacity, thus maintaining a steady state.A descending trend indicates energy consumption due to telescope maneuvers, while an ascending trend signifies the fulfillment of solar panel charging constraints, thereby providing power to recharge the telescope.Figure 6 illustrates the storage status of the telescope.The maximum storage capacity of the telescope is 64 TB.To mitigate the occurrence of unforeseen circumstances, a greedy strategy is employed in this study.Data downlink is initiated when the storage capacity reaches 80% of its rated capacity.Due to the satellite's capability to simultaneously observe and downlink data, the curve shows a descending trend representing data downlink.Taking into account the telescope's maneuver angles, it becomes feasible to generate a precise timetable for the telescope's observation sequence down to the second.With the celestial sectors already segmented, specific observation latitudes and longitudes can be indexed based on the sector identifiers.The observation duration falls within the range of 150 s to 200 s.Hence, it is possible to initiate observations as early as feasible within the time window based on the starting time of observation, subsequently determining the observation's end time.Through computation of the required time for attitude transition between adjacent observation points in the sequence, accounting for the time for point transition and data storage, the starting time for the subsequent observation point can be calculated.If the next observation point's starting time precedes the earliest available observation time, it necessitates waiting until the observation requirements can be fulfilled before proceeding with the observation.Table 3 represents the timetable for the telescope's observation sequence.

Conclusion
This paper addresses the research on observation tasks conducted by the Chinese Space Station's survey telescope.By considering the practical scenarios of observation tasks and comprehensively accounting for various constraints, a complex task planning model is established, and an efficient solving algorithm is designed.Leveraging long-term planning outcomes as input, specific daily observation sequences down to the second are derived.The constraints are adequately considered, encompassing aspects such as stray light, space environment, energy, and storage.The objective functions are thoroughly considered, encompassing energy consumption, on-orbit operational duration, and other goals.The algorithm demonstrates rapid execution, robust performance, and effective planning capability.It can also be applied to the re-planning of observation tasks in emergency situations and future scenarios.Experimental results affirm that under the constraints of energy and storage, the telescope is capable of completing a daily observation task of no fewer than 350 points.It holds the potential to provide a model and algorithmic support for China's survey telescope survey mission planning.

Figure 1 .
Figure 1.The workflow of observation.
Earliest start time of the observation time window.Latest start time of the observation time window Angle between the Sun and the telescope line of sight Angle between the Moon and the telescope line of sight.Angle between the Earth and the telescope line of sight.Available energy for the telescope.Time required for telescope attitude change.Time required for telescope data storage.Telescope data storage capacity.Weight of the observation point.

Figure 5 .
Figure 5.The energy resumption.Figure6illustrates the storage status of the telescope.The maximum storage capacity of the telescope is 64 TB.To mitigate the occurrence of unforeseen circumstances, a greedy strategy is employed in this study.Data downlink is initiated when the storage capacity reaches 80% of its rated capacity.Due to the satellite's capability to simultaneously observe and downlink data, the curve shows a descending trend representing data downlink.

Figure 6 .
Figure 6.The downlink of data.

Table 2 .
NSGA-III for sky survey.∪F 2 ∪…F M-1 , and we choose L=K-|P t+1 | individuals join to P t+1 , then f 1 , f 2 , and f 3 are normalized, and r reference points R r is produced.n s is calculated, which union to the s-reference point R s , let j=1