1. Introduction
In recent years, with the development of satellite remote sensing technology, the quantity and quality of remote sensing satellites have increased significantly. It gives users higher requirements in the range and frequency of satellite observation. Regarding the observation range, it has been extended from small target imaging, such as target reconnaissance or emergency imaging [
1], to large-scale regional imaging in cities, provinces, or even a country [
2]. Regarding the observation frequency, it has also developed from long-term single-frequency production to annual, quarterly, and even monthly production [
3]. One of the most important reasons is that the regional surveying and mapping products obtained by satellite remote sensing play essential roles in many aspects, for example, national defense security [
4], natural resource management [
5], environmental protection [
6], emergency management [
7], and other fields [
8,
9,
10].
However, the current imaging satellite task planning technology is mainly used for target reconnaissance and emergency imaging and is rarely used for surveying and mapping regional products [
11]. In addition, most of the remote sensing satellites adopt the imaging method of ‘imaging wherever there is no image’ for regional products, which lacks scientific and efficient planning methods. With the continuous increase in the number of satellites, the expansion of regional imaging product application fields, and the increasing demand for regional product timeliness, it is increasingly urgent to fully utilize existing satellite resources and efficiently obtain regional remote sensing images.
Imaging satellite task planning is a technology that scientifically arranges imaging tasks for satellites based on user needs. It maximizes comprehensive imaging income by arranging each satellite to image each sub-region at the appropriate time and attitude based on user needs, satellite attribute information, and related constraints, such as energy constraints, maneuverability constraints, storage constraints, etc. [
12,
13]. For regional mapping, the efficient utilization of satellite resources and the rapid completion of regional imaging tasks are the most important and commonly used imaging benefits. Mathematical modeling and optimization algorithm solving are two core steps in imaging satellite mission planning. Because the different needs of imaging satellite mission planning are often contradictory for mathematical modeling, it is often established as a model with multiple objective functions, known as multi-objective imaging satellite task planning. Correspondingly, multi-objective optimization algorithms (MOEAs) [
14,
15] are used to solve multi-objective task planning models.
Point targets and small area targets were commonly imaged in the past imaging satellite mission planning. General MOEAs, such as NSGA-II [
16] and MOPSO [
17], can find good solutions because the number of their imaging strips is small. That is, the scale of the planning problem is small. However, when the observation range is extensive, it is difficult for general MOEAs to obtain good solutions. This is because the larger the observation area, the more imaging strips are required, which means that there are more decision variables for the regional task planning model. The search space of the solution increases the exponential growth with the increase in decision variables, that is, the dimensional disaster. This leads to a decrease in the performance of existing MOEAs in solving large-scale multi-objective task planning problems, making it difficult to obtain the optimal solution for large-scale regional imaging task planning. Some scholars have attempted to obtain a reliable solution by increasing the population size and extending the iterations of MOEAs that can effectively solve small decision variables. However, these operations greatly increase computational consumption, decrease search efficiency, and still make obtaining a globally optimal solution difficult.
For multi-objective imaging satellite task planning problems with large-scale decision variables, in the past decade, there has been some research on large-scale MOEAs that can solve these problems. In summary, there are currently three main categories: MOEAs based on decision variable grouping, MOEAs based on decision space reduction, and MOEAs based on new search strategies.
MOEAs based on decision variable grouping are the earliest MOEAs for solving large-scale problems. This method adopts the divide-and-conquer strategy. It divides many decision variables into different groups based on different strategies and then optimizes each group alternately. Common grouping strategies include random grouping, differential grouping, and decision variable analysis grouping. In [
18], the decision variables were randomly grouped, and then the operational decomposition technique was added to the non-dominated sorting genetic algorithm NSGA-III. The proposed OD-NSGA effectively improved the performance of NSGA-III without increasing computational consumption. Li [
19] divided decision variables into different groups using differential grouping and proposed a cooperative co-evolutionary large-scale MOEA called CCLSM. Bin [
20] proposed a multi-objective graph-based differential grouping with the shift method to decompose decision variables, called mogDG-shift. The mogDG-shift was combined with MOEA/D and NSGA-II, achieving better performance. MOEA/D (s & ns) [
21] decomposed decision variables into two basic groups based on their separability and inseparability characteristics and then judged whether to divide each group based on population size. Zhang [
22] proposed LMEA by decomposing decision variables into convergence-related variables and diversity-related variables based on their control information. An angle-based clustering analysis was used to analyze the attributes of decision variables. Liu [
23] proposed a large-scale MOEA framework based on variable importance-based differential evolution called LVIDE. In LVIDE, decision variables are grouped based on their importance to the objective function. To solve sparse large-scale multi-objective optimization problems (LSMOPs), Zhang [
24] improved SparseEA [
25] through decision variable grouping technology and proposed SparseEA2. The performance of SparseEA2 was improved because the variable grouping enhanced the connection between the real variables and binary variables.
Many complex influence relationships exist between individual variables and between variables and objective functions in mathematical models for practical application problems. Therefore, MOEAs based on decision variable grouping inevitably divide the mutually influencing decision variables into different groups, resulting in the global optimal solution being missed. In addition, differential grouping and decision variable analysis grouping require significant computational costs to calculate the correlation between the variables.
MOEAs based on decision space reduction adopt the idea of data compression in digital image processing. They compress high-dimensional decision variables into low-dimensional decision variables through some image processing methods and then restore them to the original high-dimensional space. Zille [
26] proposed a weighted optimization framework (WOF) by optimizing a weight vector to replace decision variables. In WOF, the original large-scale multi-objective optimization problem was transformed into a small-scale multi-objective optimization problem, achieving dimensionality reduction. Later, a large-scale MOF framework (LSMOF) [
27] and a weighted optimization framework with random dynamic grouping were proposed [
28]. To balance the computational cost and convergence speed of large-scale MOEAs, Liu [
29] proposed a self-guided problem transformation optimization algorithm (SPTEA). The self-guiding solution transformed the optimization of large-scale decision variables into the optimization of small-scale weights. In [
30], Liu proposed a large-scale MOEA based on principal component analysis (PCA-MOEA). In PCA-MOEA, the percentage of variance was used to control the number of compressed decision variables. In [
31], a large-scale multi-objective nature computation based on dimension reduction and clustering strategy was proposed, namely DRC-LMNC. In DRC-LMNC, the dimensionality of the decision variables was reduced via locally linear embedding. In [
32], a surrogate-assisted evolutionary algorithm based on multi-stage dimension reduction, MDR-SAEA, was proposed to solve the expensive sparse LSMOPs. The dimensions of the decision variables were reduced through feature selection and the determination of the non-zero decision variables. Tian [
33] proposed a Pareto-optimal subspace learning-based evolutionary algorithm (MOEA/PSL) to solve sparse LSMOPs. MOEA/PSL learned the sparse distribution and compact representation of decision variables using two unsupervised networks: a constrained Boltzmann machine and a denoising autoencoder.
In summary, there are two main methods based on decision space reduction: problem transformation and dimensionality reduction. However, different decision variables are given the same weight for problem transformation, and for dimensionality reduction, the decision variables are overly compressed or difficult to compress. Therefore, although both can quickly capture local optimal solutions, obtaining the global optimal solution is difficult.
MOEAs based on a new search strategy directly search for the global optimal solution in the original high-dimensional decision variable space by designing a new search strategy. It mainly includes two types: MOEAs based on the probability model and MOEAs based on the novel reproduction operator. MOEAs based on the probability model utilize probability models to generate offspring rather than evolutionary operators. Cheng [
34] proposed a direction-guided adaptive offspring generation method. Two kinds of direction vectors were used to generate convergence-related offspring and diversity-related offspring, respectively. Liang [
35] and He [
36] used distributional adversarial networks (DANs) and generative adversarial networks (GANs) instead of evolutionary operators to generate offspring, respectively. MOEAs based on novel reproduction operators design new evolutionary operators that directly act on large-scale decision variables to generate offspring. To solve sparse LOMOPs, Kropp [
37] designed a novel set of evolutionary operators, including varied striped sparse population sampling, sparse simulated binary crossover, and sparse polynomial mutation. Then, S-NSGA-II was proposed by combining these operators with NSGA-II. Ding [
38] proposed a multi-stage knowledge-guided evolutionary algorithm, MSKEA. At different stages of MSKEA, different knowledge fusions were used to guide evolution. Thus, the evolutionary efficiency of MSKEA was improved. Zhang [
39] proposed an enhanced MOEA/D using information feedback models. The feedback information model uses previous population information to guide evolution. Thus, the proposed MOEA/D-IFM performed well in large-scale optimization problems. In [
40], a multi-objective conjugate gradient and differential evolution (MOCGDE) algorithm was proposed. In MOCGDE, conjugate gradients and differential evolution were used to keep convergence and diversity performance when solving LOMOPs, respectively. Based on the competitive swarm optimizer (CSO) [
41], Tian [
42] proposed a large-scale multi-objective CSO algorithm (LMOCSO) by further improving the convergence speed of loser individuals to winner individuals. LMOCSO designs a better particle search strategy to search for LOMOPs effectively.
Compared to methods based on decision variable grouping and decision space reduction, MOEAs based on new search strategies have three advantages. First, without a large amount of decision variable analysis (i.e., a large amount of computational consumption), it can efficiently balance exploitation and exploration in high-dimensional decision variable space and search for LSMOPs. Second, it can effectively reserve the global optimal solution without grouping, compressing, or transforming the decision variables. The imaging satellite task planning calculation involves regional target information, satellite orbit information, complex geometric imaging, etc. For the entire process, the calculation is complex (i.e., the cost of decision variable analysis is high), the correlation between the decision variables is strong (i.e., the decision variables are difficult to group), and the satellite resources are precious (i.e., there is a need to obtain a global optimal solution). Third, most new strategies are independent of evolutionary algorithms, making them easier to use for other MOEAs. Therefore, from a comprehensive perspective, an MOEA based on new search strategies is the best choice for large-scale imaging satellite mission planning problems.
To better solve the problem of large-scale imaging satellite task planning for vast area mapping, a large-scale multi-objective optimization algorithm based on efficient competition learning and improved non-dominated sorting (ECL-INS-LMOA) is proposed. Specifically, the main contributions of this article are as follows:
(1) An efficient competition learning particle update strategy (ECLUS) is proposed. ECLUS is the core part of ECL-INS-LMOA. Its goal is to accelerate the proposed ECL-INS-LMOA convergence by three aspects: One is to improve the particle update strategy in LMOCSO to make it converge faster. The second is to introduce flight time to avoid the oscillation convergence that particle swarm optimization (PSO) algorithms are prone to. The third is to propose the BCSO to update binary decision variables.
(2) A large-scale multi-objective optimization algorithm called ECL-INS-LMOA is proposed based on efficient competition learning and improved non-dominated sorting. ECL-INS-LMOA adopts the idea of evolution in two stages. In the early stage, the proposed ECLUS and the improved non-dominated sorting NSGA-II are run alternately. In the later stage, only the improved non-dominated sorting NSGA-II is run. ECL-INS-LMOA focuses on fast convergence in the early stage while also considering global optimization and focuses on global optimization in the later stage while also considering convergence. By doing so, ECL-INS-LMOA keeps a fast global optimization ability throughout the entire evolutionary process, thereby enabling rapid acquisition of high-quality imaging solutions for large regional mapping.
(3) To verify the effectiveness of the proposed ECL-INS-LMOA, this paper uses GF3 as an imaging satellite and selects five expansive regions from around the world, namely the Congo (K), India, Australia, the United States, and Antarctica, as the imaging regions for the simulation imaging experiments. The proposed ECL-INS-LMOA is compared with three multi-objective optimization algorithms: NSGA-II, LMOCSO, and LMEA. The effectiveness of ECL-INS-LMOA in solving large-scale regional mapping task planning problems is experimentally verified. The proposed method provides a reference for imaging satellite task planning for surveying and mapping product production in the future.
The rest of this paper is organized as follows:
Section 2 briefly introduces some work related to the proposed method, including the multi-objective task planning model, ECL-INS-LMOA, to solve and the particle update strategy in LSOCSO;
Section 3 introduces the principles and procedures of ECLUS and ECL-INS-LMOA in detail;
Section 4 presents the experiments and analysis;
Section 5 discusses the experimental results obtained. Finally, the conclusion is drawn in
Section 6.
5. Discussion
This paper focuses on the research of large-scale multi-objective imaging satellite task planning in large areas, where large areas generally refer to areas with more than 100 imaging strips. On the one hand, it is easy to solve imaging satellite task planning in small areas using existing MOEAs. On the other hand, if the large area is decomposed into several small areas for optimization, only the local optimal solution can be obtained, limiting the acquisition of the optimal solution. We should strive to explore better imaging solutions to utilize precious satellite resources and complete imaging tasks more efficiently.
The proposed ECL-INS-LMOA achieved better optimization results than the existing MOEAs. This is because, firstly, ECL-INS-LMOA performs global optimization by directly designing more efficient search strategies and better environmental selection strategies. The global optimal solution of ECL-INS-LMOA is preserved. However, the MOEAs based on the decision variable grouping method and the decision space reduction lose the global optimal solution because of the methods of processing decision variables. Secondly, the proposed ECLUS has a faster convergence speed than the strategy in LMOCSO. The particles go directly from position to position with one evolution. On the other hand, ECLUS adjusts the flight distance by introducing flight time to accelerate convergence and avoid oscillation convergence. In addition, BCSO was proposed for updating the binary decision variables. Thirdly, ECL-INS-LMOA adopts the idea of two-stage optimization. In the early stages of evolution, ECLUS and NSGA-II-SDE run alternately, which focuses on fast convergence while balancing global optimization. In the later stage of evolution, only NSGA-II-SDE runs, which focuses on global optimization while balancing fast convergence.
ECL-INS-LMOA not only provides the optimal planning solution, but also has advantages in runtime. Firstly, ECL-INS-LMOA is based on a new search strategy without the need for additional analysis and the calculation of decision variables, so the time consumption is significantly less than LMEA. Secondly, the accelerated particle update strategy, flight time, and the winner selection strategy in ECLUS are all linear, and their increased computational cost is negligible and can be ignored. Compared with ECL-INS-LMOA, only non-dominated solutions in LMOCSO are used in particle updates per generation, which results in LMOCSO having many more evolutionary generations than ECL-INS-LMOA within the same number of objective function evaluations. As a result, the environment selection strategy of LMOCSO is executed more frequently, resulting in a lower running efficiency than the proposed ECL-INS-LMOA. Thirdly, all particles in ECL-INS-LMOA participate in winner and loser selection rather than just non-dominant particles. On the one hand, it can maintain the diversity of solutions. On the other hand, ECLUS can select winner individuals by simply comparing SDEs, and then obtain new populations by only updating the losers. In contrast, NSGA-II requires a series of operations such as competitive selection, crossover, and mutation on all individuals to obtain new populations. Therefore, ECL-INS-LMOA has a higher running efficiency than NSGA-II.
In our study, based on previous research, we specifically defined the scope of a large area, which is the area with more than 100 imaging strips. And a large-scale multi-objective optimization algorithm was specifically designed to solve large-scale task planning problems efficiently. We rarely see these in other related studies [
46,
47]. Although the imaging area is large in some studies, the scale of their problems may not be large. It is believed that this paper can provide some new references for large-scale satellite mission planning problems.
In addition, although the experimental satellite in this paper is only GF3, the proposed MOEA can also be applied to multi-satellite optimization problems, for example, constellation optimization [
48], multi-satellite joint scheduling [
49], etc. For different application problems, the goal of an MOEA is always to find the best solution to the problem. In addition to the imaging satellite task planning problem for large-scale mapping studied in this paper, there are many large-scale multi-objective optimization problems in the real world, for example, feature selection in machine learning [
50,
51], neural network training [
52], drone-assisted camera network [
53], routing problems [
54,
55], etc. The proposed method can also be explored for its value in different fields.
The proposed ECL-INS-LMOA focuses on innovating new search strategies, but the environmental selection strategy adopts the methods in existing papers. In the future, the environment selection strategy will be designed to enhance the performance of MOEAs. In addition, the regional mapping we are currently researching only focuses on obtaining orthophoto images of one region. In the future, we will focus on obtaining regional stereo imaging products and multi-satellite multi-region task planning problems. In summary, we will construct different imaging satellite task planning models and design corresponding solving algorithms based on specific imaging satellite task planning problems in practical applications.