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The traveling salesman problem (TSP) is one of the most extensively studied problems in the combinatorial optimization area and still presents unsolved challenges due to its NP-hard attribute. Although many real-coded algorithms are available for TSP, they still have some performance challenges in the switch from continuous space to discrete space and perform at low convergence speed. This paper proposes a real-coded carnivorous plant algorithm with a heuristic decoding method (CPA-HDM) to solve the traveling salesman problem (TSP), which exhibits good convergence speed and solution accuracy. In this improved method, a new heuristic decoding method (HDM) is designed, which helps to map continuous variables to discrete ones without losing information, maintain population diversity, and enhance the solution quality after decoding. To balance the algorithm’s search capability and enhance the probability of preferable individuals generated, an adaptive attraction probability (AAP), an improved growth model of carnivorous plants (IGMOCP), and a position update method of prey (IPUMOP) are developed. Aiming to reduce the probability of premature and prevent search stagnation, an improved reproduction strategy (IRS) and an adaptive combination perturbation are reconstructed. Finally, a local search algorithm is employed to improve the exploitation capability. To verify its validation, CPA-HDM is compared with six algorithms, for solving 28 TSP instances. The simulation results and statistical analyses demonstrate the superior performance of the proposed algorithm.

When using the Cobb-Douglas (C-D) production function to measure the contribution rate of agricultural technological progress (ATP), it is necessary to estimate the output elasticity coefficient (OEC) of each input factor in C-D production function. For this purpose, it is usually necessary to take logarithm at both sides of C-D production function and convert it into a linear function, and then use regression analysis method to estimate the OECs of input factors. However, there are some problems in this method remains unsolved: first, the OECs estimated by taking logarithm of C-D production function are not the optimal estimation of the original C-D production function; second, the regression results sometimes fail to pass statistical test; third, some OECs cannot be guaranteed to be non-negative. Aiming at resolving these problems, a method for estimating OECs in C-D production function based on the Hybrid Improved Bat Optimization Algorithm (HIBA) was proposed. This method solves the problems existing in the OEC estimation methods in the existing literatures. To verify the effectiveness of the proposed method in this study, the OECs of input factors in China' Sichuan Province from 1996 to 2018 was estimated. The estimation results show that, compared with other estimation methods in the existing literatures, the proposed method can not only guarantee that it is the optimal estimation of the OECs in the original C-D production function, but also ensure that the OECs are non-negative and with high precision and good fitting effect. Finally, based on the estimation results, this study measured and analyzed the contribution rate of agricultural input factors and ATP of Sichuan Province and puts forward corresponding suggestions for the agricultural development in this region.