## 1 Introduction  
With continuous energy shortages, accurate exploration of underground energy has become the mainstream of international research [1]. Electromagnetic tomography (EMT) has particular advantages over other exploration methods, such as drilling methods, 3-D seismic exploration, and channel wave tomography, as it can realize high imaging resolution, has convenient construction, and is non-hazardous [2; 3; 4; 5]. EMT has been widely used in the exploration of coal, oil, natural gas, and other mineral resources [6; 7; 8]. However, in the process of exploration, the ray coverage angle in the observation system is limited by field detection conditions, and the electromagnetic wave projection data obtained are always incomplete. Therefore, the most challenging task of EMT is solving for a large, sparse, and ill-conditioned tomographic inversion model.  
In the current study, various random global search iterative methods that have attracted greater attention because of their decreased dependence on the initial model have been introduced to deal with the above problems. The simple genetic algorithm (SGA) is a highly parallel, random, and adaptive global optimization probability search algorithm developed from natural selection and evolutionary mechanisms in the biological world [9]. Since it does not depend on gradients in optimization, it hasstrong robustness and global search ability. Therefore, SGA is widely used in machine learning, pattern recognition, mathematical programming, and other fields [10; 11; 12; 13; 14; 15]. At the same time, SGA has also been employed as the solution of geophysical tomographic inversion problems [16; 17; 18; 19]. However, many shortcomings have also been exposed by the wide application of SGA and deeper research. In the evolution of SGA, the choice of crossover probability and mutation probability often determines the balance of global and local search ability of the algorithm. The values of crossover and mutation probability in SGA are always fixed, so there are risks of premature convergence and poor local searchability [20; 21].  
To make full use of the global evolutionary characteristics of SGA and restrain its shortcomings of premature convergence and poor local search ability in the inversion process of EMT, an adaptive multi-population parallel genetic algorithm (AMPGA) with constraints is proposed in this paper. On the basis of SGA, global and local search capabilities are improved by multi-group parallel evolution with different genetic parameters. Then, the crossover and mutation probabilities are adaptively acquired according to the fitness value of each individual in each population, which further improves the local search ability and reduces the possibility of premature convergence. Finally, the tomographic resolution is further improved by adding the constraint with prior information.  
In this research, the proposed algorithm of AMPGA with constraints has been developed combined with a numerical experiment and field test to find a better solution for the tomographic inversion model with incomplete projections. The root mean square error (\(RMSE\)) between the computed and the picked attenuation coefficient is set as the fitness reference in the optimized calculation. By repeating experiments on the algorithms, the variation characteristics of the \(RMSE\) curve and the average value of the \(RMSE\) are used to verify the accuracy and stability of the algorithms. The results show that the accuracy and stability of image reconstruction of the proposed algorithm in the EMT is significantly improved compared with the SGA, and it has important guiding significance for accurate energy exploration and mining.