# Large-Scale Multi-Objective Imaging Satellite Task Planning Algorithm for Vast Area Mapping
###### Abstract
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 variable solution by increasing the population size and extending the 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. [PERSON] [19] divided decision variables into different groups using differential grouping and proposed a cooperative co-evolutionary large-scale MOEA called CCLSM. [PERSON] [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. [PERSON] [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. [PERSON] [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), [PERSON] [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.