LTLGC: a multi strategy enhanced Logistic-Gauss circle algorithm for UAV path planning

Abstract

As path planning tasks for UAVs in complex three dimensional environments place increasingly higher demands on solution accuracy, convergence robustness and dimensional scalability, the standard Logistic-Gauss Circle optimiser (LGC) struggles to effectively handle multi constraint optimisation problems due to limitations such as uneven random initialisation distributions, the tendency of single chaotic modes to become trapped in local optima during the exploitation phase, and the rapid decline in population diversity during high dimensional searches.To address these limitations, this paper proposes an improved Logistic-Gauss Circle algorithm (LTLGC), which reconstructs the algorithm’s optimisation chain through three core strategies: Firstly, a chaotic opposition based learning initialisation mechanism is introduced. By utilising a composite Logistic-Tent chaotic mapping, an initial population with good ergodicity is generated. Combined with elite opposition based learning to produce opposite solutions for selection, this significantly enhances the quality and spatial coverage of the initial population; Secondly, a Circle-Tent alternating exploitation strategy is designed, executing the Circle and Tent chaotic mappings alternately with a 50% probability. By leveraging the piecewise linear characteristics of the Tent mapping, this enriches local search behaviour and enhances the convergence accuracy towards optimal solutions in complex terrain; Thirdly, an adaptive differential evolution and Cauchy perturbation strategy is proposed. By monitoring population diversity in real time, the probability of differential mutation is dynamically adjusted, whilst the introduction of a Cauchy distribution enables long range jumps from the current optimal solution, effectively maintaining population vitality and preventing premature convergence.Performance experiments and qualitative analyses were conducted on CEC2005; multi dimensional comparisons were performed on CEC2017 (Dim = 10/30/50/100); and comparisons with seven benchmark algorithms, including LGC, WMA and RFO, were carried out on CEC2022 (Dim = 10/20). LTLGC demonstrates excellent optimisation accuracy and convergence stability, with its overall optimisation performance improving as the dimension increases.LTLGC was further applied to three dimensional mountainous UAV path planning, establishing a cost model that comprehensively considers path length, threat avoidance, flight altitude and kinematic smoothness. Experimental results indicate that the average path cost generated by LTLGC is 11.13% lower than that of the original LGC, with the average altitude cost reduced by 75.87%. Furthermore, the trajectories are collision free and exhibit excellent smoothness, providing an efficient and reliable optimisation solution for UAV path planning in complex environments.