In this paper we propose a forward-backward improvement heuristic for the variant of resource-constrained project scheduling problem aiming to maximise the net present value of a project. It relies on the Lagrangian relaxation method to generate an initial set of schedules which are then improved by the iterative forward/backward scheduling technique. It greatly improves the performance of the ...

A cross-layer network optimization problem is considered. It involves network and transport layers, treating both routing and flows as decision variables. Due to the nonconvexity of the capacity constraints, when using Lagrangian relaxation method a duality gap causes numerical instability. It is shown that the rescue preserving separability of the problem may be the application of the augmente...

Given a network modeled as a graph G with each link associated with a cost and k weights, the Constrained Shortest Path (CSP(k)) problem asks for computing a minimum cost path from a source node s to a target node t satisfying pre-specified bounds on path weights. This problem is NP-hard. In this paper we propose a new approximation algorithm called GEN-LARAC for CSP(k) problem based on Lagrang...

In this research, Lagrangian relaxation algorithms are proposed for Hybrid Flow-Shop (HFS) scheduling problems. Conventional HFS consists of a series of production stages, each of which has several identical parallel machines and no buffer spaces are considered. Jobs are processed through all stages in the same direction. In the previous researches, they are assumed that the capacity of buffer ...

The constrained shortest path (CSP) problem requires the determination of a minimum cost s-t path with delay at most a nonzero integer T. In this paper, we first point out the equivalence of certain algorithms, simply called the LARAC (Lagrangian Relaxation Based Aggregated Cost) algorithm presented independently in some earlier works. The LARAC algorithm solves the integer relaxation of the CS...

There can be different approaches to the management of resources within the context of multiproject scheduling problems. In general, approaches to multi-project scheduling problems consider the resources as a pool shared by all projects. On the other hand, when projects are distributed geographically or sharing resources between projects is not preferred, then this resource sharing policy may n...

This thesis deals with a heuristic approach based on Lagrangian relaxation to the string barcoding (SB) problem, a close cousin to the well-known combinatorial set cover (SC) problem. It has recently been proven to be NP-hard and has many real-world applications, particularly in the fields of medicine and biology. Given a set of sequences over some alphabet, DNA for instance, we aim at finding ...

Lagrangian relaxation has been pursued as a pertinent methodology for many hard scheduling problems. From standard duality theory, the method is known to provide good-quality bounds to the performance of the optimal solutions of these problems, and in certain cases, the optimal Lagrange multipliers can function as a starting point for the construction good suboptimal solutions for the original ...

The clique partitioning problem is an NP-hard combinatorial optimization problem with applications to data analysis such as clustering. Though a binary integer linear programming formulation has been known for years, one needs to deal with a huge number of variables and constraints when solving a large instance. In this paper, we propose a size reduction algorithm which is based on the Lagrangi...

This paper considers the hydrothermal unit commitment problem of power systems with high proportion of hydraulic generation. In this sense, a large-scale mixed-integer nonlinear programming problem for the two day cost-optimal generation of system is developed. The model involves a large number of mixed-integer decision variables and constraints linking time periods and operation units. A Lagra...