César Rego

A Parallel Tabu Search Algorithm Using Ejection Chains for the Vehicle Routing Problem

In this paper we describe a Parallel Tabu Search algorithm for the vehicle routing problem under capacity and distance restrictions. In the neighborhood search, the algorithm uses compound moves generated by an ejection chain process. Parallel processing is used to explore the solution space more extensively and different parallel techniques are used to accelerate the search process. Tests were carried out on a network of SUNSparc workstations and computational results for a set of benchmark problems prove the efficiency of the algorithm proposed.

A cooperative parallel tabu search algorithm for the quadratic assignment problem

In this study, we introduce a cooperative parallel tabu search algorithm (CPTS) for the quadratic assignment problem (QAP). The QAP is an NP-hard combinatorial optimization problem that is widely acknowledged to be computationally demanding. These characteristics make the QAP an ideal candidate for parallel solution techniques. CPTS is a cooperative parallel algorithm in which the processors exchange information throughout the run of the algorithm as opposed to independent concurrent search strategies that aggregate data only at the end of execution. CPTS accomplishes this cooperation by maintaining a global reference set which uses the information exchange to promote both intensification and strategic diversification in a parallel environment. This study demonstrates the benefits that may be obtained from parallel computing in terms of solution quality, computational time and algorithmic flexibility. A set of 41 test problems obtained from QAPLIB were used to analyze the quality of the CPTS algorithm. Additionally, we report results for 60 difficult new test instances. The CPTS algorithm is shown to provide good solution quality for all problems in acceptable computational times. Out of the 41 test instances obtained from QAPLIB, CPTS is shown to meet or exceed the average solution quality of many of the best sequential and parallel approaches from the literature on all but six problems, whereas no other leading method exhibits a performance that is superior to this.

Traveling salesman problem heuristics: Leading methods, implementations and latest advances

Heuristics for the traveling salesman problem (TSP) have made remarkable advances in recent years. We survey the leading methods and the special components responsible for their successful implementations, together with an experimental analysis of computational tests on a challenging and diverse set of symmetric and asymmetric TSP benchmark problems. The foremost algorithms are represented by two families, deriving from the Lin-Kernighan (LK) method and the stem-and-cycle (S&C) method. We show how these families can be conveniently viewed within a common ejection chain framework which sheds light on their similarities and differences, and gives clues about the nature of potential enhancements to todays best methods that may provide additional gains in solving large and difficult TSPs.

Multistart Tabu Search and Diversification Strategies for the Quadratic Assignment Problem

The quadratic assignment problem (QAP) is a well-known combinatorial optimization problem with a wide variety of applications, prominently including the facility location problem. The acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this paper, we show the benefit of utilizing strategic diversification within the tabu search (TS) framework for the QAP, by incorporating several diversification and multistart TS variants. Computational results for an extensive and challenging set of QAP benchmark test problems demonstrate the ability of our TS variants to improve on a classic TS approach that is one of the principal and most extensively used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate the classic TS method as a subroutine.

A unified modeling and solution framework for combinatorial optimization problems

Abstract.Combinatorial optimization problems are often too complex to be solved within reasonable time limits by exact methods, in spite of the theoretical guarantee that such methods will ultimately obtain an optimal solution. Instead, heuristic methods, which do not offer a convergence guarantee, but which have greater flexibility to take advantage of special properties of the search space, are commonly a preferred alternative. The standard procedure is to craft a heuristic method to suit the particular characteristics of the problem at hand, exploiting to the extent possible the structure available. Such tailored methods, however, typically have limited usefulness in other problems domains.An alternative to this problem specific solution approach is a more general methodology that recasts a given problem into a common modeling format, permitting solutions to be derived by a common, rather than tailor-made, heuristic method. Because such general purpose heuristic approaches forego the opportunity to capitalize on domain-specific knowledge, they are characteristically unable to provide the effectiveness or efficiency of special purpose approaches. Indeed, they are typically regarded to have little value except for dealing with small or simple problems.This paper reports on recent work that calls this commonly held view into question. We describe how a particular unified modeling framework, coupled with latest advances in heuristic search methods, makes it possible to solve problems from a wide range of important model classes.

Node-ejection chains for the vehicle routing problem: sequential and parallel algorithms

We present a Tabu search algorithm for the vehicle routing problem under capacity and distance restrictions. The neighborhood search is based on compound moves generated by a node-ejection chain process. During the course of the algorithm, two types of neighborhood structures are used and crossing infeasible solutions is allowed. Then, a parallel version of the algorithm which exploits the moves’ characteristics is described. Parallel processing is used to explore the solution space more extensively and to accelerate the search process. Tests are carried out on a SUNSparc workstation and the parallel algorithm uses a network of four of these machines. Numerical tests indicate that the sequential version of the algorithm is highly competitive with the best existing heuristics and that the parallel algorithm outperforms all of these algorithms.

Relaxed tours and path ejections for the traveling salesman problem

Abstract We describe an edge based ejection chain method to generate compound neighborhood structures for the Traveling Salesman Problem (TSP). These neighborhood structures enclose a special substructure which is not necessarily a Hamiltonian tour. Instead the neighborhood components are linked together to compose successive levels of an ejection chain, and coordinated by a suitable reference structure to generate compound moves with outstanding proprieties. More precisely, such a substructure can be viewed as a relaxed tour, which allows solution transformations to be obtained without preserving the Hamiltonian property at each step. Furthermore, in the ejection chain process, the generation of substructures produces a variety of alternating paths for the selection of subsequent ejection moves as well as for the choice of the corresponding trial moves. Finally, we propose two algorithmic variants — a Preliminary and a Full Subpath Ejection Chain Method (P-SEC and F-SEC) — based on this type of compound neighborhood design. Both variants are guided by a simple tabu search mechanism. Computational results on 67 TSPLIB problems show that both the Preliminary and the Full methods find optimal and near-optimal solutions very quickly, frequently outperforming the best heuristic procedures for the TSP. In addition, the Full method generally dominates the best alternative TSP procedures.

One-pass heuristics for large-scale unconstrained binary quadratic problems

Abstract Many significant advances have been made in recent years for solving unconstrained binary quadratic programs (UQP). As a result, the size of problem instances that can be efficiently solved has grown from a hundred or so variables a few years ago to 2000 or 3000 variables today. These advances have motivated new applications of the model which, in turn, have created the need to solve even larger problems. In response to this need, we introduce several new “one-pass” heuristics for solving very large versions of this problem. Our computational experience on problems of up to 9000 variables indicates that these methods are both efficient and effective for very large problems. The significance of problems of this size is that they not only open the door to solving a much wider array of real world problems, but also that the standard linear mixed integer formulations of the nonlinear models involve over 40,000,000 variables and three times that many constraints. Our approaches can be used as stand-alone solution methods, or they can serve as procedures for quickly generating high quality starting points for other, more sophisticated methods.

A filter-and-fan approach to the job shop scheduling problem

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new heuristic algorithm for the JSSP that effectively combines the classical shifting bottleneck procedure (SBP) with a dynamic and adaptive neighborhood search procedure. Our new search method, based on a filter-and-fan (F&F) procedure, uses the SBP as a subroutine to generate a starting solution and to enhance the best schedules produced. The F&F approach is a local search procedure that generates compound moves by a strategically abbreviated form of tree search. Computational results carried out on a standard set of 43 benchmark problems show that our F&F algorithm performs more robustly and effectively than a number of leading metaheuristic algorithms and rivals the best of these algorithms.

An Unconstrained Quadratic Binary Programming Approach to the Vertex Coloring Problem

The vertex coloring problem has been the subject of extensive research for many years. Driven by application potential as well as computational challenge, a variety of methods have been proposed for this difficult class of problems. Recent successes in the use of the unconstrained quadratic programming (UQP) model as a unified framework for modeling and solving combinatorial optimization problems have motivated a new approach to the vertex coloring problem. In this paper we present a UQP approach to this problem and illustrate its attractiveness with preliminary computational experience.