In BA, each bat is defined by its position xit, velocity vit, frequency fi, loudness Ait, and the emission pulse rate rit in a d-dimensional search space. The new solutions xit and velocities vit at time step t are given byfi=fmin?+(fmax??fmin?)��,vit=vit?1+(xit?x?)fi,xit=xit?1+vit,(7)where �� [0, 1] selleck Pazopanib is a random vector drawn from a uniform distribution. Here x is the current global best location (solution) which is located after comparing all the solutions among all the n bats. Generally speaking, depending on the domain size of the problem of interest, the frequency f is assigned to fmin = 0 and fmax = 100 in practical implementation. Initially, each bat is randomly given a frequency which is drawn uniformly from [fmin , fmax ]. Algorithm 1Bat Algorithm.

For the local search part, once a solution is selected among the current best solutions, a new solution for each bat is generated locally using random walkxnew??=??xold??+??��At,(8)where �� [?1, 1] is a scaling factor which is a random number, while At = Ait is the average loudness of all the bats at time step t. The updates of the velocities and positions of bats have some similarity to the procedure in the standard particle swarm optimization [18] as fi in essence controls the pace and range of the movement of the swarming particles. To some degree, BA can be considered as a balanced combination of the standard particle swarm optimization and the intensive local search controlled by the loudness and pulse rate. Furthermore, the loudness Ai and the rate ri of pulse emission update accordingly as the iterations proceed as shown rit+1=ri0[1?exp?(?��t)],(9)where �� and �� are constants.

In??inAit+1=��Ait, essence, �� is similar to the cooling factor of a cooling schedule in the simulated annealing [19]. For simplicity, we set �� = �� = 0.9 in this work.3.2. Algorithm BA for UCAV Path PlanningIn BA, the standard ordinates are inconvenient to solve UCAV path planning directly. In order to apply BA to UCAV path planning, one of the key issues is to transform the original ordinate into rotation ordinate by (1).Fitness of bat i at position xi is determined by the threat cost by (4), and the smaller the threat cost, the smaller the fitness of bat i at position xi. Each bat is encoded by D-dimensional deciding variables. And then, we use BA to optimize the path planning to get the best solution that is optimal flight route for UCAV. At last, the best solution is inversely converted to the original ordinates and output. The algorithm BA for UCAV path planning is shown as Algorithm 2.Algorithm 2Algorithm of BA for UCAV path Entinostat planning.4.