This research focuses on the long empty cutting path problem during the laser cutting process by employing an improved proximity method to establish the starting point set in complex closed graphics. Specifically, this work improves the particle swarm algorithm and proposes the Levy Flight, power function, and Singer map employed particle swarm optimization (LPSPSO) to avoid the disadvantages of the standard particle swarm optimization (PSO) algorithm. Specifically, the comprehensive prospect-regret theoretical model evaluation value is used as the fitness value to guide the algorithm's evolution and adaptively adjust the parameters in the LPSPSO algorithm, including the inertia weight power function, the learning factors, and the chaotic random number based on the Singer chaotic map. Additionally, the Levy flight is introduced to disturb the particles and prevent local optimization. This is achieved by adjusting the Levy flight threshold based on the distance between the particles to prevent the Levy flight from starting prematurely and increasing the calculation burden. To verify the performance of the LPSPSO algorithm, it was challenged against three state-of-the-art algorithms on 22 benchmark test instances and a laser cutting problem, with the results revealing that the LPSPSO algorithm has a better performance and can be used to solve the empty length of the laser cutting path problem.INDEX TERMS laser cutting path planning, improved particle swarm optimization, improved proximity method, Levy flight threshold, comprehensive prospect-regret theory, chaotic random number

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