A new method for the second-order design (SOD) of geodetic networks: Improved tornado optimizer with Coriolis force (ITOC) based on traversing population sizes

Aiming at the problems that the analytical method for second-order design of geodetic networks is computationally complex and has poor convergence, while the heuristic algorithm is prone to falling into local optimization despite its unique advantages, this study proposes a multi-strategy improved tornado optimizer with Coriolis force (ITOC). ITOC combines global search with local refinement by introducing logistic chaos mapping to initialize the population, combining differential evolutionary variation strategy, and dynamically switching to Adam optimizer-based gradient descent at the late iteration stage to minimize the matrix two-norm difference between the variance-covariance matrix and the criterion matrix in order to achieve the optimization. Meanwhile, this study systematically employs a traverse population size strategy for the first time. By testing population sizes one by one within a fixed range (4-200), the probability of obtaining the optimal solution is significantly improved. Experimental analysis shows that in terms of the average number of convergence iterations, compared with 81.396 times for TOC and 93.421 times for particle swarm optimization (PSO), ITOC achieves 49.914 times, representing decreases of 38.7% and 46.5%, respectively. The average objective function value decreased from 0.66831 to 0.60367 to 0.59686, with reduction rates of 10.7% and 1.1%, respectively. Moreover, the standard deviation of the objective function value of ITOC, which is 0.0091, is also lower than 0.0372 for TOC and 0.0192 for PSO. In addition, compared with the analytical method, ITOC reduces the observation work of 2 baselines, and compared with TOC and PSO, it obtains the optimal solution with three times the probability. This research result not only provides a better algorithm choice for the second-order design of the geodetic network, but also offers an important reference for the optimization strategy of heuristic algorithms.