Mauro Dell'Amico

Applying tabu search to the job-shop scheduling problem

In this paper, we apply the tabu-search technique to the job-shop scheduling problem, a notoriously difficult problem in combinatorial optimization. We show that our implementation of this method dominates both a previous approach with tabu search and the other heuristics based on iterative improvements.

Assignment Problems: Revised Reprint

This book provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. The authors have organized the book into 10 self-contained chapters to make it easy for readers to use the specific chapters of interest to them without having to read the book linearly. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems, and many variations of these problems. Exercises in the form of numerical examples provide readers with a method of self-study or students with homework problems, and an associated webpage offers applets that readers can use to execute some of the basic algorithms as well as links to computer codes that are available online. Audience: Assignment Problems is a useful tool for researchers, practitioners, and graduate students. Researchers will benefit from the detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its many variations. Practitioners will learn about practical applications of the methods, the performance of exact and heuristic algorithms, and software options. This book also can serve as a text for advanced courses in discrete mathematics, integer programming, combinatorial optimization, and algorithmic computer science. Contents: Preface; Chapter 1: Introduction; Chapter 2: Theoretical Foundations; Chapter 3: Bipartite Matching Algorithms; Chapter 4: Linear Sum Assignment Problem; Chapter 5: Further Results on the Linear Sum Assignment Problem; Chapter 6: Other Types of Linear Assignment Problems; Chapter 7: Quadratic Assignment Problems: Formulations and Bounds; Chapter 8: Quadratic Assignment Problems: Algorithms; Chapter 9: Other Types of Quadratic Assignment Problems; Chapter 10: Multi-index Assignment Problems; Bibliography; Author Index; Subject Index

Exact solution of large-scale, asymmetric traveling salesman problems

A lowest-first, branch-and-bound algorithm for the <italic>Asymmetric Traveling Salesman Problem</italic> is presented. The method is based on the <italic>Assignment Problem relaxation</italic> and on a <italic>subtour elimination branching scheme</italic>. The effectiveness of the algorithm derives from reduction procedures and parametric solution of the relaxed problems associated with the nodes of the branch-decision tree. Large-size, uniformly, randomly generated instances of complete digraphs with up to 2000 vertices are solved on a DECstation 5000/240 computer in less than 3 minutes of CPU time. In addition, we solved on a PC 486/33 <italic>no wait flow shop</italic> problems with up to 1000 jobs in less than 11 minutes and real-world <italic>stacker crane</italic> problems with up to 443 movements in less than 6 seconds.

A branch and bound algorithm for the multiple depot Vehicle Scheduling Problem

This article describes analyses carried out to solve the scheduling problem for freight vehicles assigned to various different depots. The vehicle scheduling problem concerns the assigning of a set of time-tabled trips to vehicles so as to minimize a given cost function. We consider the np-hard multiple depot case in which, in addition, one has to assign vehicles to depots. Different lower bounds based on assignment relaxation and on connectivity constraints are presented and combined in an effective bounding procedure. A strong dominance procedure derived from new dominance criteria is also described. A branch and bound algorithm is finally proposed. Computational results are given.

Algorithms and codes for dense assignment problems: the state of the art

The paper considers the classic linear assignment problem with a min-sum objective function, and the most efficient and easily available codes for its solution. We first give a survey describing the different approaches in the literature, presenting their implementations, and pointing out similarities and differences. Then we select eight codes and we introduce a wide set of dense instances containing both randomly generated and benchmark problems. Finally we discuss the results of extensive computational experiments obtained by solving the above instances with the eight codes, both on a workstation with Unix operating system and on a personal computer running under Windows 95.

The Capacitated m-Ring-Star Problem

The Capacitated m-Ring-Star Problem (CmRSP) is the problem of designing a set of rings that pass through a central depot and through some transition points and/or customers, and then assigning each nonvisited customer to a visited point or customer. The number of customers visited and assigned to a ring is bounded by an upper limit: the capacity of the ring. The objective is to minimize the total routing cost plus assignment costs. The problem has practical applications in the design of urban optical telecommunication networks. This paper presents and discusses two integer programming formulations for the CmRSP. Valid inequalities are proposed to strengthen the linear programming relaxation and are used as cutting planes in a branch-and-cut approach. The procedure is implemented and tested on a large family of instances, including real-world instances, and the good performance of the proposed approach is demonstrated.

Shop Problems with two Machines and Time-Lags

We consider Job-Shop and Flow-Shop scheduling problems with two machines, no more than two operations per job, and Time Lags, i.e., a minimum time interval between the completion time of the first operation and the starting time of the second one. We give complexity results for the preemptive and nonpreemptive cases and study the relationship between the two problems. For the Flow-Shop problem we give lower bounds and upper bounds and analyze their worst-case performances. Finally we define a Tabu Search algorithm and prove the effectiveness of the proposed bounds through extensive computational results.

On prize-collecting tours and the asymmetric travelling salesman problem

We consider a variant of the Travelling Salesman Problem which is to determine a tour visiting each vertex in the graph at most at one time; if a vertex is left unrouted a given penalty has to be paid. The objective function is to find a balance between these penalities and the cost of the tour. We call this problem the Profitable Tour Problem (PTP). If, in addition, each vertex is associated with a prize and there is a knapsack constraint which guarantees that a sufficiently large prize is collected, we have the well-known Prize-collecting Travelling Salesman Problem (PCTSP). In this paper we summarize the main results presented in the literature, then we give lower bounds for the asymmetric version of PTP and PCTSP. Moreover, we show, through computational experiments, that large size instances of the asymmetric PTP can be solved exactly.

The k -cardinality assignment problem

Abstract We consider a generalization of the assignment problem in which an integer k is given and one wants to assign k rows to k columns so that the sum of the corresponding costs is a minimum. The problem can be seen as a 2-matroid intersection, hence is solvable in polynomial time; immediate algorithms for it can be obtained from transformation to min-cost flow or from classical shortest augmenting path techniques. We introduce original preprocessing techniques for finding optimal solutions in which g ⩽ k rows are assigned, for determining rows and columns which must be assigned in an optimal solution and for reducing the cost matrix. A specialized primal algorithm is finally presented. The average computational efficiency of the different approaches is evaluated through computational experiments.

A lower bound for the non-oriented two-dimensional bin packing problem

Given a set of rectangular items, and an unlimited number of identical rectangular bins, we consider the problem of allocating, without overlapping, all the items to the minimum number of bins. We assume that the items may be rotated by 90°. The problem is strongly NP-hard, and has several industrial applications. No specific lower bound is known for it. We present a lower bound which explicitly takes into account the possible item rotation. The bound is embedded into an exact branch-and-bound algorithm. The average performance is evaluated through computational experiments.