This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned ...This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.展开更多
In this paper, we consider the planar multi-facility Weber problem with restricted zones and non-Euclidean distances, propose an algorithm based on the probability changing method (special kind of genetic algorithms) ...In this paper, we consider the planar multi-facility Weber problem with restricted zones and non-Euclidean distances, propose an algorithm based on the probability changing method (special kind of genetic algorithms) and prove its efficiency for approximate solving this problem by replacing the continuous coordinate values by discrete ones. Version of the algorithm for multiprocessor systems is proposed. Experimental results for a high-performance cluster are given.展开更多
文摘This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.
文摘In this paper, we consider the planar multi-facility Weber problem with restricted zones and non-Euclidean distances, propose an algorithm based on the probability changing method (special kind of genetic algorithms) and prove its efficiency for approximate solving this problem by replacing the continuous coordinate values by discrete ones. Version of the algorithm for multiprocessor systems is proposed. Experimental results for a high-performance cluster are given.
