Tractable algorithms for chance-constrained combinatorial problems

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0-1 problems. Furthermore, its tractability is highlighted. Then, an optimization … Read more

Separation Algorithms for 0-1 Knapsack Polytopes

Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To use such inequalities effectively, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We show that the separation problems for the so-called extended cover and weight inequalities can be solved exactly in O(nb) … Read more

A Computational Study of Exact Knapsack Separation for the Generalized Assignment Problem

The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs a set of jobs to a set of machines satisfying capacity constraints. Most of the existing algorithms are based on Branch-and-Price, with lower bounds computed by Dantzig-Wolfe reformulation and column generation. In this paper we propose a … Read more

Sequence independent lifting for 0-1 knapsack problems with disjoint cardinality constraints

In this paper, we study the set of 0-1 integer solutions to a single knapsack constraint and a set of non-overlapping cardinality constraints (MCKP). This set is a generalization of the traditional 0-1 knapsack polytope and the 0-1 knapsack polytope with generalized upper bounds. We derive strong valid inequalities for the convex hull of its … Read more

MW: A Software Framework for Combinatorial Optimization on Computational Grids

Our goal in this paper is to demonstrate that branch-and-bound algorithms for combinatorial optimization can be effectively implemented on a relatively new type of multiprocessor platform known as a computational grid. We will argue that to easily and effectively harness the power of computational grids for branch-and-bound algorithms, the master-worker paradigm should be used to … Read more

A GRASP algorithm for the multi-objective knapsack problem

In this article, we propose a Greedy Randomized Adaptive Search Procedure (GRASP) to generate a good approximation of the efficient or Pareto optimal set of a multi-objective combinatorial optimization problem. The algorithm is applied for the 0/1 knapsack problem with r objective functions. This problem is formulated as r classic 0/1 knapsack problems. n items, … Read more

Facets of a polyhedron closely related to the integer knapsack-cover problem

We investigate the polyhedral structure of an integer program with a single functional constraint: the integer capacity-cover polyhedron. Such constraints arise in telecommunications planning and facility location applications, and feature the use of general integer (rather than just binary) variables. We derive a large class of facet-defining inequalities by using an augmenting technique that builds … Read more

A Polyhedral Study of the Cardinality Cosntrained Knapsack Problem

A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. This structure occurs, for example, in areas as finance, location, and scheduling. Traditionally, cardinality constraints are modeled by introducing auxiliary 0-1 variables and additional constraints that relate the continuous … Read more