# Large-Scale Multi-Objective Imaging Satellite Task Planning Algorithm for Vast Area Mapping
###### Abstract
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], [PERSON] [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 LMOPs 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.