The Maxwell-Lame equations governing the principal components of Cauchy stress for plane deformations are well known in the context of photo-elasticity, and they form a pair of coupled first-order hyperbolic partial differential equations when the deformation geometry is known. In the present paper this theme is developed for nonlinear isotropic elastic materials by supplementing the (Lagrangea...

The cellular network design (CND) problem is formulated as a comprehensive linear mixed integer programming model integrating the base station location (BSL) problem, the frequency channel assignment (FCA) problem and the topological network design (TND) problem. A solution algorithm based on Lagrangean relaxation is proposed for solving this complex cellular network design problem. Pursuing th...

In this paper, we propose two exact algorithms for the GQAP (generalized quadratic assignment problem). In this problem, given M facilities and N locations, the facility space requirements, the location available space, the facility installation costs, the flows between facilities, and the distance costs between locations, one must assign each facility to exactly one location so that each locat...

Network design models are extensively used to represent a wide range of planning and operation management issues in transportation, telecommunications, logistics and production-distribution. In a very general sense, the problem consists of designing a network by selecting links to connect a set of nodes and to determine the amount of flow on each link such that the demand of each node for a num...

The Traveling Salesman Problem (TSP) is a classical Combinatorial Optimization problem, which has been intensively studied. The Lagrangean relaxation was first applied to the TSP in 1970. The Lagrangean relaxation limit approximates what is known today as HK (Held and Karp) bound, a very good bound (less than 1% from optimal) for a large class of symmetric instances. It became a reference bound...

Conventional Lagrangean preprocessing for the network Weight Constrained Shortest Path Problem (WCSPP), for example Beasley and Christofides [3], calculates lower bounds on the cost of using each node and edge in a feasible path using a single optimal Lagrange multiplier for the relaxation of the WCSPP. These lower bounds are used in conjunction with an upper bound to eliminate nodes and edges....