Lagrangean decomposition has been recognized as a promising approach for solving large-scale optimization problems. However, Lagrangean decomposition is critically dependent on the method of updating the Lagrangean multipliers used to decompose the original model. This paper presents a Lagrangean decomposition approach based on Nelder–Mead optimization algorithm to update the Lagrangean multipl...

In this work, we apply a decomposition technique to address the multiperiod heat exchanger network synthesis. Each period corresponds to changes in operating conditions, i.e. inlet temperatures and heat capacity flowrates. The problem size grows quickly with the number of streams and the number of periods resulting in a large scale problem to solve. In order to reduce the problem to a manageabl...

The supply chain optimization of continuous process networks is essential for most chemical companies. The dynamic nature of this problem leads to systems that involve types of chemicals as well as multiple time periods, and ultimately many complex and large combinatorial optimization models. These models become very difficult to solve, and sometimes not even solvable. Hence, such models requir...

We describe a decomposition algorithm that combines Benders and scenariobased Lagrangean decomposition for two-stage stochastic programming investment planning problems with complete recourse, where the first-stage variables are mixedinteger and the second-stage variables are continuous. The algorithm is based on the cross-decomposition scheme and fully integrates primal and dual information in...

The point-feature cartographic label placement problem (PFCLP) consists in placing text labels adjacent to point features on a map. This paper proposes a 0-1 integer linear programming model for the PFCLP defined as the maximum number of free labels placed where all points must be labeled. We also present a Lagrangean decomposition technique based on graph partitioning where the PFCLP is repres...

This work presents Lagrangean/surrogate relaxation to the problem of maximum pro®t assignment of n tasks to m agents (n > m), such that each task is assigned to only one agent subject to capacity constraints on the agents. The Lagrangean/surrogate relaxation combines usual Lagrangean and surrogate relaxations relaxing ®rst a set of constraints in the surrogate way. Then, the Lagrangean relaxati...

The paper addresses a multi-item, multi-plant lot-sizing problem with transfer costs and capacity constraints. The problem is reformulated according to a multi-commodity flow formalism, and decomposed, through Lagrangean relaxation, into a master facility location problem and a slave minimal cost multi-commodity flow problem. The decomposition framework gives rise in a natural way to the design...

We present a scenario decomposition framework based on Lagrangean decomposition for the multi-product, multi-period, supply investment planning problem considering network design and discrete capacity expansion under demand uncertainty. We also consider a risk measure that allows us to reduce the probability of incurring in high costs while preserving the decomposable structure of the problem. ...