Performance aspects of a Lagrangian relaxation based heuris-tic for solving large 0-1 integer linear programs are discussed. In particular , we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, GG oteborg, Sweden, based on distributing the variables and a new sequentia...

No wait flow shop scheduling problem (NWFSP) by minimizing make-span is an NP-hard problem with various applications in the industry. In this paper a new lower bound for NWFSP is presented. For this, the MIP model of the problem is relaxed and dived into two separate problems with polynomial solution. Then by applying Lagrangian relaxation method an algorithm is present to obtain a lower-bound....

In this paper, we study nonnegative tensor data and propose an orthogonal Tucker decomposition (ONTD). We discuss some properties of ONTD develop a convex relaxation algorithm the augmented Lagrangian function to solve optimization problem. The convergence is given. employ on image sets from real world applications including face recognition, representation, hyperspectral unmixing. Numerical re...

Distribution network design (DND) attempts to integrate tactical issues such as inventory policies and/or vehicle routing decisions with strategic ones such as the problem of locating facilities and allocate customers to such facilities. When inventory policy decision making is considered the problem is also known as inventory location modelling (ILM) problem. During the last two decades, mathe...

Title: MULTIOBJECTIVE OPTIMIZATION MODELS AND SOLUTION METHODS FOR PLANNING LAND DEVELOPMENT USING MINIMUM SPANNING TREES, LAGRANGIAN RELAXATION AND DECOMPOSITION TECHNIQUES José Alberto Faria, Doctor of Philosophy, 2005 Directed By: Professor Steven A. Gabriel Department of Civil and Environmental Engineering and Applied Mathematics and Scientific Computation Program University of Maryland The...

This paper presents a distributed scheduling methodology for a two-machine flowshop problem. It is assumed that the decision authorities and information are distributed in multiple sub-production systems that must share two machines in order to satisfy their demands. The associated scheduling problems are modeled using 0/1 integer formulations, and the problem is solved using Lagrangian relaxat...

Lagrangian relaxation has been widely used in hydrothermal scheduling. Complicating constraints are relaxed by multipliers which are usually updated by a subgradient method (SGM). The SGM suffers from slow convergence caused by the non-differentiable characteristics of dual functions. This paper presents an algorithm that utilizes the Bundle Trust Region Method (BTRM) to update the multipliers ...

The Quadratic Knapsack Problem (QKP) calls for maximizing a quadratic objective function subject to a knapsack constraint, where all coeecients are assumed to be nonnegative and all variables are binary. The problem has applications in location and hydrology, and generalizes the problem of checking whether a graph contains a clique of a given size. We propose an exact branch-and-bound algorithm...