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In this paper, a whale optimization algorithm based on Levy flight and memory (WOALFM) is proposed to solve the curvature discontinuity problem in the global path planning of unmanned vehicles. Levy flight and chaotic mapping are introduced to disturb the solutions of each generation and enhance the diversity of solutions. A memory strategy based on fractional-order expansion is presented to remember the influence of the positions of individuals in previous generations on the positions of current generation. This strategy based on Levey flight and memory can enhance searching ability and avoid falling into local optimum. Furthermore, the ratio of global searching to local searching can be adjusted to achieve desired results in WOALFM algorithm. The proposed WOALFM algorithm is tested and compared with five algorithms including whale optimization algorithm (WOA), Moth-Flame Optimization (MFO), particle swarm optimization (PSO), Fractional-Order Velocity based Particle Swarm Optimization (FOPSO) and Grey Wolf Optimizer (GWO) on 23 standard benchmark functions. The experimental results show the effectiveness of WOALFM. The proposed algorithm is applied to smooth path planning problem of unmanned vehicles. Three factors, including the length, curvature and curvature derivative of a path are considered in order to obtain the shortest smooth path without collisions. The experimental results show that more collision-free paths can be obtained in lower computational cost by the presented method.

A new method to set up the static magnetic field of the targeted magnetic fluid hyperthermia is presented, and a new particle swarm optimization algorithm with Levy flight (LF-PSO) is proposed. Magnetic field generating system consists of 18 coils, deployed in the lesions of the peripheral symmetric space, the main principle is to heat magnetic nanoparticles by high frequency alternating magnetic field to kill the cancer cells, while building a static magnetic field in the periphery of the tumor region to protect healthy tissue from harm. Tumor location information may be shifted, so each treatment needs to reconfigure the static magnetic field. The set of magnetic heating coil currently adopted this new LF-PSO algorithm, in the reason of the particle swarm optimization algorithm with Levy flight mechanism is characterized by good robustness, high precision of optimal search and it is easy to jump out of local optimum. Experimental results show that by building a new objective function, and comparing with the FEM algorithm, the LF-PSO algorithm has advantages of fast solving speed and high accuracy.

The max–min ant system (MMAS) is a modified ant colony optimization (ACO) algorithm. Its convergence speed is effectively improved by setting the upper and lower bounds of the pheromone and updating it in the optimal path. However, MMAS still has drawbacks, such as long search time and local extremums. In this paper, the hybrid max–min ant system (HMMAS) is proposed to deal with the shortcomings of MMAS. Employing Levy flight strategy, HMMAS can dynamically adjust the parameters to increase the diversity of solutions and expand the search range. Besides, HMMAS uses the OBL strategy to generate opposite solutions in the early stage. In this way, the convergence is accelerated. When HMMAS falls into a local extremum, the path reorganization strategy is utilized. With its help, HMMAS can redistribute the pheromone in each path and achieve global optimum. To verify the effectiveness, HMMAS is first compared with the three conventional ACO algorithms of AS, ACS, and MMAS in 20 sets of experiments. The results indicate that the average results of HMMAS in the 19 sets of TSP instances are better than the other three algorithms, and the standard deviation in the 14 sets of calculation instances is the smallest. Then, HMMAS is compared with some state-of-the-art algorithms, and the results show that HMMAS is better than other comparison algorithms, either by the minimum or the average value.

Due to the increasing number of applications for various purposes, including commercial, scientific, environmental, and military ones, Underwater Wireless Sensor Networks (UWSNs) have recently attracted substantial attention from academia and enterprises in research and development. Monitoring pollutants, tactical surveillance, tsunami alerts, and offshore drilling are some important applications. Due to acoustic transmission disruptions brought on by extreme noise, extraordinarily lengthy propagation delays, a high bit error rate, a constrained bandwidth, and interference, efficient sensor communication in UWSNs is a difficult challenge. Therefore, designing efficient communication among sensors and sinks is one of the fundamental research themes in UWSNs. This paper proposes an energy-efficient optimal cluster head (CH)-based routing in UWSNs. The proposed methodology consists of three stages namely, cluster formation, CH selection, and priority-based routing. In this study, initially, the clusters are formed using a k-means clustering algorithm. Then, the CHs are selected using the Adaptive Honey Badger optimization (AHBO) algorithm, which is used to reduce energy consumption and delay. AHBO is a combination of a honey badger, Levy flight, and genetic algorithm operators. After the CH selection process, data packets are transferred toward the base station through autonomous underwater vehicles (AUVs). The efficiency of the proposed approach is analyzed based on different metrics and performance compared with the different methods.

A new analytical solution is developed for the one- and two- dimensional generalized discrete time random walk with discrete and finite length of jumping. It is shown that the ensemble average of the mean square displacement has a linear relation with time. This result is general and independent of mathematical form of distribution function but magnitude of diffusion coefficient depends on the distribution function. This result confirms our previous numerical work. The truncated Levy flight is studied as a special case and the diffusion coefficient for different maximum length of jump is calculated numerically. The obtained results are in good agreement with the analytical solution.