We present an algorithm to compute a complete set of efficient solutions for the biobjective integer minimum cost flow problem. We use the two phase method with a parametric network simplex algorithm in phase 1 to compute all supported non-dominated extreme points. In phase 2, the remaining nondominated points (non-extreme supported and non-supported) are computed using a k best flow algorithm ...

Finding wirelength optimal packings of rectangles is a well known problem in VLSI design. We propose a branch and bound algorithm for this problem that is based on the rectangle packing algorithm of Moffitt and Pollack. It makes use of a very efficient implementation of an incremental network simplex algorithm. Our algorithm allows for the first time to find optimum solutions of three instances...

In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes. 

this paper proposes an efficient network architecture to improve energy consumption in wireless sensor networks (wsn). the proposed architecture uses a mobile data collector to a partitioned network. the mobile data collector moves to center of each logical partition after each decision period. the mobile data collector must declare its new location by packet broadcasting to all sensor nodes. h...

transmission network expansion planning (tnep) is an important component of power system planning. itdetermines the characteristics and performance of the future electric power network and influences the powersystem operation directly. different methods have been proposed for the solution of the static transmissionnetwork expansion planning (stnep) problem till now. but in all of them, stnep pr...

In this paper, a scheduling problem for automated guided vehicles in container terminals is defined and formulated as a Minimum Cost Flow model. This problem is then solved by a novel algorithm, NSA+, which extended the standard Network Simplex Algorithm (NSA). Like NSA, NSA+ is a complete algorithm, which means that it guarantees optimality of the solution if it finds one within the time avail...

An interactive approach for Bicriteria Transportation Problems, allowing for non-integer solutions, is presented. The decision-maker (DM) conducts the search by introducing upper bounds on the values of one or both criteria, adding one/two additional constraints to the original problem structure. So, usual algorithms for solving transportation problems cannot be used. Two extensions of the netw...

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Lö...

We present a column generation algorithm for solving the bi-objective multicommodity minimum cost flow problem. This method is based on the biobjective simplex method and Dantzig-Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using DantzigWolfe decomposition. Then, sim...