We study the polyhedral structure of two primal relaxations of a class of specially structured mixed integer programming problems. This class includes the generalized capacitated plant location problem and a production scheduling problem as special cases. We show that for this class of problems two polyhedra constructed from the constraint sets in two difl‘erent primal relaxations are identical...

This paper presents a methodology based on the Variable Neighbourhood Search metaheuristic, applied to the Capacitated Vehicle Routing Problem. The presented approach uses Constraint Programming and Lagrangean Relaxation methods in order to improve algorithm’s efficiency. The complete problem is decomposed into two separated subproblems, to which the mentioned techniques are applied to obtain a...

We present an integrated methodology for optimal short-term planning of refinery-petrochemical complexes (IRPCs) and demonstrate it on a full-scale industrial case study under four realistic scenarios. The large-scale mixed-integer quadratically constrained optimization models are amenable to spatial Lagrangean decomposition through dividing the IRPC into multiple subsections, which comprise cr...

In this paper we will present class of new lower bounds for the Quadratic Semi-Assignment Problem (QSAP). These bounds are based on recent results about polynomially solvable cases, in particular we will consider the QSAP's whose quadratic cost coefficients define a reducible graph. Several lower bounds will be computationally compared, moreover we will present a method which improves these bou...

We describe a hybrid bi-level decomposition scheme that addresses the challenge of solving a large-scale two-stage stochastic programming problem with mixed-integer recourse, which results from a multi-scale capacity planning problem as described in part I of this paper series. The decomposition scheme combines bi-level decomposition with Benders decomposition, and relies on additional strength...

This paper presents a comprehensive survey of models and algorithms for multicommodity capacitated network design problems, which are mostly encountered in telecommunications and transportation network planning. These problems are important not only due to the major relevance of their applications, but also because they pose considerable modeling and algorithmic challenges. We present a general...

We address robust versions of combinatorial optimization problems, specializing on the discrete scenario case and the uncorrelated ellipsoidal uncertainty case. We present a branch and bound-algorithm for the min-max variant of these problems which uses lower bounds obtained from Lagrangean decomposition, allowing to separate the uncertainty aspect in the objective function from the combinatori...

We show that various duals that occur in optimization and constraint satisfaction can be classified as inference duals, relaxation duals, or both. We discuss linear programming, surrogate, Lagrangean, superadditive, and constraint duals, as well as duals defined by resolution and filtering algorithms. Inference duals give rise to nogood-based search methods and sensitivity analysis, while relax...

We present a new Lagrangean approach for the pooling problem, a fundamental problem in the petro-chemical industry. The relaxation targets all nonlinear constraints, resulting in a Lagrangean subproblem with a nonlinear objective function, that is reformulated as a linear mixed integer program. Besides being used to generate lower bounds, the subproblem solutions are exploited within Lagrangean...