Even the shortest flight through unknown, cluttered environments requires reliable local path planning algorithms to avoid unforeseen obstacles. The algorithm must evaluate alternative flight paths and identify the best path if an obstacle blocks its way. Commonly, weighted sums are used here. This work shows that weighted Chebyshev distances and factorial achievement scalarising functions are suitable alternatives to weighted sums if combined with the 3DVFH* local path planning algorithm. Both methods considerably reduce the failure probability of simulated flights in various environments. The standard 3DVFH* uses a weighted sum and has a failure probability of 50% in the test environments. A factorial achievement scalarising function, which minimises the worst combination of two out of four objective functions, reaches a failure probability of 26%; A weighted Chebyshev distance, which optimises the worst objective, has a failure probability of 30%. These results show promise for further enhancements and to support broader applicability.

Body posture determination methods have many applications, including product design, ergonomic workplace design, human body simulation, virtual reality, and animation industry. Initiated in robotics, inverse kinematic (IK) method has been widely applied to proactive human body posture estimation. The analytic inverse kinematic (AIK) method is a convenient and time-saving type of IK methods. It is also indicated that, based on AIK methods, a specific body posture can be determined by the optimization of an arbitrary objective function. The objective of this paper is to predict the postures of human arms during reaching tasks. In this research, a human body model is established in MATLAB, where the middle rotation axis analytic kinematic method is accomplished, based on this model. The joint displacement function and joint discomfort function are selected to be initially applied in this AIK method. Results show that neither the joint displacement function nor the joint discomfort function predicts postures that are close enough to natural upper limb postures of human being, during reaching tasks. Therefore, a bi-criterion objective function is proposed by integrating the joint displacement function and joint discomfort function. The accuracy of the arm postures, predicted by the proposed objective function, is the most satisfactory, while the optimal value of the coefficient, in the proposed objective function, is determined by golden section search.

In this paper, we introduce a class of nonsmooth nonconvex optimization problems, and we propose to use a local iterative minimization-majorization (MM) algorithm to find an optimal solution for the optimization problem. The cost functions in our optimization problems are an extension of convex functions with MC separable penalty, which were previously introduced by Ivan Selesnick. These functions are not convex; therefore, convex optimization methods cannot be applied here to prove the existence of optimal minimum point for these functions. For our purpose, we use convex analysis tools to first construct a class of convex majorizers, which approximate the value of non-convex cost function locally, then use the MM algorithm to prove the existence of local minimum. The convergence of the algorithm is guaranteed when the iterative points $x^{(k)}$ are obtained in a ball centred at $x^{(k-1)}$ with small radius. We prove that the algorithm converges to a stationary point (local minimum) of cost function when the surregators are strongly convex.

We investigated whether diversification and/or structural change would improve Norwegian agriculture. Using a flexible technology approach to account for different technologies, we assessed economies of scope and scale of dairy and cropping farms, including regional differences. We fitted translog cost functions to farm-level panel data for the period 1991–2014. We found both economies of scope and scale on the farms. Dairy farms have an economic incentive to integrate dairying with cropping in all regions of Norway, and vice versa. Thus, policy makers should eschew interventions that inhibit diversification or structural change and that increase the costs of food production.

The current paper presents a path planning method based on probability maps and uses a new genetic algorithm for a group of UAVs. The probability map consists of cells that display the probability which the UAV will not encounter a hostile threat. The probability map is defined by three events. The obstacles are modeled in the probability map, as well. The cost function is defined such that all cells are surveyed in the path track. The simple formula based on the unique vector is presented to find this cell position. Generally, the cost function is formed by two parts; one part for optimizing the path of each UAV and the other for preventing UAVs from collision. The first part is a combination of safety and length of path and the second part is formed by an exponential function. Then, the optimal paths of each UAV are obtained by the genetic algorithm in a parallel form. According to the dimensions of path planning, genetic encoding has two or three indices. A new genetic operator is introduced to select an appropriate pair of chromosome for crossover operation. The effectiveness of the method is shown by several simulations.

Burn-in is a procedure used for eliminating weak components in a mixed population. In this paper we focus on general mixed populations. Three types of results are established. First, it is shown that any mixed population displays a type of monotonicity property which is appropriate for burn-in. Second, it is shown that if, asymptotically, components have constant failure rates, then the mixed population will also asymptotically have a constant failure rate and this will correspond to the rate of the strongest subpopulation of the mixture. Finally, it is shown for a reasonable cost function, that if one mixture distribution dominates another in a strong sense, the resulting mixture of the dominant distribution will have larger optimal burn-in time.