To solve the problems of low efficiency, not to consider collision and poor applicability of the current robot path planning method for spraying entities with complex structure, a discrete grey wolf optimizer algorithm for solving multilayer decision problems was proposed and applied to the above path planning problem. In order to transfer the grey wolf optimizer algorithm with continuous domain to discrete grey wolf optimizer algorithm for solving multilayer decision problems, the matrix coding method was used to solve the coding problem of multilayer decision problem, a hybrid initialization method based on prior knowledge and random selection was proposed to improve the solving efficiency and precision of the algorithm, the crossover operator and the two-level mutation operator were used to define the population update strategy of the discrete grey wolf optimizer algorithm. In addition, the path planning problem of spraying robot was simplified to the generalized traveling salesman problem by the graph theory, and the shortest path model and path collision model of this problem were established. In the path planning experiment, compared with particle swarm optimization algorithm, genetic algorithm and ant colony optimization algorithm, the proposed algorithm has the average planned path length decreased by 5.0%, 5.5% and 6.6%, has the collision time reduced to 0, and has smoother paths. Experimental results show that the proposed algorithm can effectively improve the spraying efficiency of spraying robot as well as the safety and applicability of the spraying path.

A mathematical analysis was carried out theoretically to reveal the fact that the Firefly Algorithm (FA) gets the risk of premature convergence and being trapped in local optimum. A hybrid Memetic algorithm based on simulated annealing was proposed. In the hybrid algorithm, the FA was employed to keep the diversity of firefly population and global exploration ability of the proposed algorithm. And then, the simulated annealing operator was incorporated to get rid of local optimum, which was utilized to carry out local search with partial firefly individuals by accepting bad solutions with some probability, and the proposed algorithm conducted simultaneously the attracting process and the annealing process to reduce the complexity. Finally, the performance of the proposed algorithm and other comparison algorithms were tested on ten standard functions, respectively. The experimental results show that the proposed algorithm can find the optimal solutions in six functions, outperform firefly algorithm, particle swarm optimization, etc, in terms of optimal value, mean value and standard deviation, and find better solutions than firefly algorithm in four functions.