A tactical maintenance optimization model for multiple interconnected energy production systems

Multiple interconnected energy production systems are a common solution to satisfy the energy demand of industrial processes. Such energy demand is usually the combination of various energy types such as heat and electricity. This implies the installation of different technologies able to produce one or multiple energy types, to satisfy all energy needs. However, multiple … Read more

Delay and disruption management at ATM: technical details

Most of the local public transit companies have vehicle monitoring systems able to collect huge quantities of data in real-time. Typically, these data are used to measure the performance of the transportation system, and rarely they are fully exploited to improve it and to tackle disruptions. In this report we take into consideration the case … Read more

The Quadratic Shortest Path Problem: Complexity, Approximability, and Solution Methods

We consider the problem of finding a shortest path in a directed graph with a quadratic objective function (the QSPP). We show that the QSPP cannot be approximated unless P=NP. For the case of a convex objective function, an n-approximation algorithm is presented, where n is the number of nodes in the graph, and APX-hardness … Read more

On the Quadratic Shortest Path Problem

Finding the shortest path in a directed graph is one of the most important combinatorial optimization problems, having applications in a wide range of fields. In its basic version, however, the problem fails to represent situations in which the value of the objective function is determined not only by the choice of each single arc, … Read more

Lower bounding procedure for the Asymmetric Quadratic Traveling Salesman Problem

In this paper we consider the Asymmetric Quadratic Traveling Salesman Problem. Given a directed graph and a function that maps every pair of consecutive arcs to a cost, the problem consists in finding a cycle that visits every vertex exactly once and such that the sum of the costs is minimum. We propose an extended … Read more

A Tight Lower Bound for the Adjacent Quadratic Assignment Problem

In this paper we address the Adjacent Quadratic Assignment Problem (AQAP) which is a variant of the QAP where the cost coefficient matrix has a particular structure. Motivated by strong lower bounds obtained by applying Reformulation Linearization Technique (RLT) to the classical QAP, we propose two special RLT representations for the problem. The first is … Read more

Lower Bounds for the Quadratic Minimum Spanning Tree Problem Based on Reduced Cost Computation

The Minimum Spanning Tree Problem (MSTP) is one of the most known combinatorial optimization problems. It concerns the determination of a minimum edge-cost subgraph spanning all the vertices of a given connected graph. The Quadratic Minimum Spanning Tree Problem (QMSTP) is a variant of the MST whose cost considers also the interaction between every pair … Read more

Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation

We consider two approaches for solving the classical minimum vertex coloring problem�that is, the problem of coloring the vertices of a graph so that adjacent vertices have different colors and minimizing the number of used colors, namely, constraint programming and column generation. Constraint programming is able to solve very efficiently many of the benchmarks but … Read more

A simple branching scheme for Vertex Coloring Problems

We present a branching scheme for some Vertex Coloring Problems based on a new graph operator called extension. The extension operator is used to generalize the branching scheme proposed by Zykov for the basic problem to a broad class of coloring problems, such as the graph multicoloring, where each vertex requires a multiplicity of colors, … Read more