Computational testing of exact mixed knapsack separation for MIP problems

In this paper we study an exact separation algorithm for mixed knapsack sets with the aim of evaluating its effectiveness in a cutting plane algorithm for Mixed-Integer Programming. First proposed by Boyd in the 90’s, exact knapsack separation has recently found a renewed interest. In this paper we present a “lightweight” exact separation procedure for … Read more

Computational experience with general cutting planes for the Set Covering problem

In this paper we present a cutting plane algorithm for the Set Covering problem. Cutting planes are generated by a “general” (i.e. not based on the “template paradigm”) separation algorithm based on the following idea: i) identify a suitably small subproblem defined by a subset of the constraints of the formulation; ii) run an exact … 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

Computational study of a cutting plane algorithm for University Course Timetabling

In this paper we describe a successful case-study where a Branch-and-Cut algorithm yields the \lq\lq optimal” solution of a real-world timetabling problem of University courses \emph{(University Course Timetabling problem)}. The problem is formulated as a \emph{Set Packing problem} with side constraints. To tighten the initial formulation, we utilize well-known valid inequalities of the Set Packing … Read more

Computational study of large-scale p-Median problems

Given a directed graph G(V,A), the p-Median problem consists of determining p nodes (the median nodes) minimizing the total distance from the other nodes of the graph. We present a Branch-and-Cut algorithm yielding provably good solutions for instances up to 3795 nodes (14,402,025 variables). Key ingredients of our approach are: lagrangian relaxation, a simple procedure … Read more

Near-optimal solutions of large-scale Single Machine Scheduling Problems

We present a lagrangean heuristic based on the time-indexed formulation of the Single Machine Scheduling Problem with Release Dates. We observe that lagrangian relaxation of job constraints leads to a Weighted Stable Set problem on an Interval Graph. The problem is polynomially solvable by a dynamic programming algorithm. Computational experience is reported on instances up … Read more