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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.

A contra-rotating axial-flow fan is prone to stalling and motor overload at partial flow rates. Moreover, its efficiency decreases sharply at a high flow rate, which is accompanied by disparity between the shaft powers of the two impellers and the light loads of their motors. It is necessary to maintain a high fan operating efficiency and a reasonable match between the powers of the two impellers. In this study, model and simulation analyses of a mine contra-rotating axialflow fan were conducted. Different impeller rotational speeds were obtained by controlling the pole speed. The aerodynamic characteristics, namely, the total pressure rise, shaft power, and operating efficiency, were investigated with respect to the flow rate and rotational speed combination of the impellers. The pressure and velocity distributions were also determined and analyzed. The high-efficiency operating range and variation range of the total pressure rise of the fan with different speed combinations were obtained. The findings indicate that the variable speed operation of two impellers can expand the fans' stable operating range and that impeller speed combinations can be set based on the flow rate and the resistance of the pipe network. This enables the contra-rotating axial-flow fan to operate in the highefficiency operating range.

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