# Large-Scale Multi-Objective Imaging Satellite Task Planning Algorithm for Vast Area Mapping
###### Abstract
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. [PERSON] [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, [PERSON] [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], [PERSON] 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. [PERSON] [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. [PERSON] [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. [PERSON] [35] and [PERSON] [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, [PERSON] [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. [PERSON] [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. [PERSON] [39] proposed an enhanced MOEA/D using information feedback models.