A matheuristic for the cell formation problem

In this paper we propose a GRASP matheuristic coupled with an Integer Programming refinement based on Set Partitioning to solve the Cell Formation Problem. We use the grouping efficacy measure to evaluate the solutions. As this measure is nonlinear, we propose a fractional Set Partitioning approach and its linearization. Our method is validated on a set of 35 instances from the literature. The experiments found four unknown solutions. For all instances with known optima, our method is able to determine the optimum solutions.     

Grasp Embedded Scatter Search for the Multicommodity Capacitated Network Design Problem

A GRASP embedded Scatter Search is developed for the multicommodity capacitated network design problem. Difficulty for this problem arises from the fact that selection of the optimal network design is an NP-complete combinatorial problem. There exist no polynomial exact algorithms which can solve this problem in a reasonable period of time for realistically sized instances. In such cases, heuristic procedures are commonly used. Two strategies were designed for GRASP: a traditional approach and a memory based technique. As for Scatter Search, 5 different strategies were used to update the reference set. Computational results on a large set of randomly generated instances show the convenience of the proposed procedures.     

A GRASP and Path Relinking Heuristic for Rural Road Network Development

This paper presents a model for rural road network design that involves two objectives: maximize all season road connectivity among villages in a region and maximize route efficiency, while allocating a fix budget among a number of possible road projects. The problem is modeled as a bicriterion optimization problem and solved heuristically through a greedy randomized adaptive search procedure (GRASP) in conjunction with a path relinking procedure. The implementation of GRASP and path relinking includes two novel modifications, a new form of reactive GRASP and a new form of path relinking. Overall, the heuristic approach is streamlined through the incorporation of advanced network flow reoptimization techniques. Results indicate that this implementation outperforms both GRASP as well as a straightforward form of GRASP with path relinking. For small problem instances, for which optimality could be verified, this new, modified form of GRASP with path relinking solved all but one known instance optimally.     

Multiobjective GRASP with Path Relinking

In this paper we review and propose different adaptations of the GRASP metaheuristic to solve multiobjective combinatorial optimization problems. In particular, we describe several alternatives to specialize the construction and improvement components of GRASP when two or more objectives are considered. GRASP has been successfully coupled with Path Relinking for single-objective optimization. Moreover, we propose different hybridizations of GRASP and Path Relinking for multiobjective optimization. We apply the proposed GRASP with Path Relinking variants to two combinatorial optimization problems, the biobjective orienteering problem and the biobjective path dissimilarity problem. We report on empirical tests with 70 instances and 30 algorithms, that show that the proposed heuristics are competitive with the state-of-the-art methods for these problems.     

A hybrid heuristic approach for the multi-commodity one-to-one pickup-and-delivery traveling salesman problem

This paper addresses an extension of the Traveling Salesman Problem where a vehicle with a limited capacity must transport commodities. Each commodity has a weight, and exactly one origin and one destination. The objective is to find a minimum length Hamiltonian tour satisfying all the transportation requests without ever violating the capacity constraint. We propose for this problem a hybrid heuristic approach that combines the GRASP and VND metaheuristic techniques. Two variants of the method are presented, one of them using a mathematical programming based local search. We conduct computational experiments to compare the developed algorithms. The experiments show that they improve the best known solutions for a set of instances from the literature, and are able to cope with instances with up to 300 customers and 600 commodities in a reasonable amount of computation time.     

Grasp with memory-based mechanisms for minimizing total tardiness in single machine scheduling with setup times

This paper addresses the problem of scheduling jobs in a single machine with sequence dependent setup times in order to minimize the total tardiness with respect to job due dates. We propose variants of the GRASP metaheuristic that incorporate memory-based mechanisms for solving this problem. There are two mechanisms proposed in the literature that utilize a long-term memory composed of an elite set of high quality and sufficiently distant solutions. The first mechanism consists of extracting attributes from the elite solutions in order to influence the construction of an initial solution. The second one makes use of path relinking to connect a GRASP local minimum with a solution of the elite set, and also to connect solutions from the elite set. Reactive GRASP, which probabilistically determines the degree of randomness in the GRASP construction throughout the iterations, is also investigated. Computational tests for instances involving up to 150 jobs are reported, and the proposed method is compared with heuristic and exact methods from the literature.     

A hybrid algorithm for the manufacturing cell formation problem

In this paper we compare different heuristic methods for the manufacturing cell formation problem considering part process sequence: a GRASP algorithm, a reactive GRASP algorithm and a hybrid algorithm which combines reactive GRASP and tabu search. All algorithms are tested with a set of instances from the literature. The results from the GRASP algorithm are compared to those of the reactive GRASP in order to evaluate the advantages of automatically adjusting the parameter value within the randomized greedy procedure. Also the reactive GRASP results are compared to those of the hybrid algorithm to evaluate the contribution to solution quality of replacing the local search phase of the GRASP algorithm with tabu search.     

Minimizing total tardiness in parallel machine scheduling with setup times: An adaptive memory-based GRASP approach

This paper deals with the problem of scheduling jobs in uniform parallel machines with sequence-dependent setup times in order to minimize the total tardiness relative to job due dates. We propose GRASP versions that incorporate adaptive memory principles for solving this problem. Long-term memory is used in the construction of an initial solution and in a post-optimization procedure which connects high quality local optima by means of path relinking. Computational tests are carried out on a set of benchmark instances and the proposed GRASP versions are compared with heuristic methods from the literature.     

A novel GRASP solution approach for the Orienteering Problem

The Orienteering Problem (OP) is a well-known variant of the Traveling Salesman Problem. In this paper, a novel Greedy Randomized Adaptive Search Procedure (GRASP) solution is proposed to solve the OP. The proposed method is shown to outperform state-of-the-art heuristics for the OP in producing high quality solutions. In comparison with the best known solutions of standard benchmark instances, the method can find the optimal or the best known solution of about 70 % of the instances in a reasonable time, which is about 17 % better than the best known approach in the literature. Moreover, a significant improvement is achieved on the solution of two standard benchmark instances.     

Crossdocking— Just in Time scheduling: an alternative solution approach

In this paper, a scheduling problem which allows a warehouse to function as a crossdock where transit storage time for cargo is minimized according to Just in Time scheduling is studied. A model that uses the machine scheduling notation to describe the problem is written. As the problem is NP-hard, a solution approach based on a combination of two metaheuristics, Reactive GRASP and Tabu Search (RGTS), is provided. Experiments are carried out to determine the usefulness of this approach. The results obtained from the exact method that uses the ILOG CPLEX 9.1 solver for 16 problem instances and the results obtained from the RGTS metaheuristic scheduling algorithm and two other algorithms proposed by other authors for the same problem instances are discussed. Analysis and comparisons are made.     

GRASP with path relinking for the orienteering problem

In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adaptive Search Procedure (GRASP) and the Path Relinking methodologies—for finding approximate solutions to this optimization problem. We explore different constructive methods and combine two neighbourhoods in the local search of GRASP. Our experimentation with 196 previously reported instances shows that the proposed procedure obtains high-quality solutions employing short computing times.     

A GRASP heuristic for the manufacturing cell formation problem

In this work, we address the Manufacturing Cell Formation Problem (MCFP). Cellular Manufacturing is a production strategy that has emerged to reduce materials handling and set up times in order to reduce lead times in production systems and to improve customer??s service levels while reducing costs. We propose a GRASP heuristic to obtain lower bounds for the optimal solution of the problem. To evaluate the performance of the proposed method, we test the heuristic with different instances from the literature and compare the results obtained with those provided by other heuristic methods from the literature. According to the obtained results, the proposed GRASP procedure provides good quality lower bounds with reasonable computational effort.     

Computing Approximate Solutions of the Maximum Covering Problem with GRASP

We consider the maximum covering problem, a combinatorial optimization problem that arises in many facility location problems. In this problem, a potential facility site covers a set of demand points. With each demand point, we associate a nonnegative weight. The task is to select a subset of p > 0 sites from the set of potential facility sites, such that the sum of weights of the covered demand points is maximized. We describe a greedy randomized adaptive search procedure (GRASP) for the maximum covering problem that finds good, though not necessarily optimum, placement configurations. We describe a well-known upper bound on the maximum coverage which can be computed by solving a linear program and show that on large instances, the GRASP can produce facility placements that are nearly optimal.     

An effective solution for a real cutting stock problem in manufacturing plastic rolls

We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferences, and then propose a heuristic solution based on a GRASP algorithm. The generation phase of this algorithm solves a simplified version which is rather similar to the conventional one dimensional cutting stock. To do that, we propose a Sequential Heuristic Randomized Procedure (SHRP). Then in the repairing phase, the solution of the simplified problem is transformed into a solution to the real problem. For experimental study we have chosen a set of problem instances of com-mon use to compare SHRP with another recent approach. Also, we show by means of examples, how our approach works over instances taken from the real production process. All authors are supported by MEC-FEDER Grant TIN2007-67466-C02-01 and by contract CN-05-127 of the University of Oviedo and the company ERVISA, and by FICYT under grant BP04-021.     

A dynamic model for road protection against flooding

This paper focuses on the problem of identifying optimal protection strategies to reduce the impact of flooding on a road network. We propose a dynamic mixed-integer programming model that extends the classic concept of road network protection by shifting away from single-arc fortifications to a more general and realistic approach involving protection plans that cover multiple components. We also consider multiple disruption scenarios of varying magnitude. To efficiently solve large problem instances, we introduce a customised GRASP heuristic. Finally, we provide some analysis and insights from a case study of the Hertfordshire road network in the East of England. Results show that optimal protection strategies mainly involve safeguarding against flooding events that are small and likely to occur, whereas implementing higher protection standards are not considered cost-effective.     

A Bus Driver Scheduling Problem: a?new mathematical model and a GRASP approximate solution

This paper addresses the problem of determining the best scheduling for Bus Drivers, a $\mathcal{NP}$ -hard problem consisting of finding the minimum number of drivers to cover a set of Pieces-Of-Work (POWs) subject to a variety of rules and regulations that must be enforced such as spreadover and working time. This problem is known in literature as Crew Scheduling Problem and, in particular in public transportation, it is designated as Bus Driver Scheduling Problem. We propose a new mathematical formulation of a Bus Driver Scheduling Problem under special constraints imposed by Italian transportation rules. Unfortunately, this model can only be usefully applied to small or medium size problem instances. For large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. Results are reported for a set of real-word problems and comparison is made with an exact method. Moreover, we report a comparison of the computational results obtained with our GRASP procedure with the results obtained by Huisman et al. (Transp. Sci. 39(4):491?C502, 2005).     

A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems

This paper presents a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional non-guillotine cutting problem, the problem of cutting the rectangular pieces from a large rectangle so as to maximize the value of the pieces cut. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures.     

Bayesian Stopping Rules for Greedy Randomized Procedures

A greedy randomized adaptive search procedure (GRASP) is proposed for the approximate solution of general mixed binary programming problems (MBP). Examples are provided of practical applications that can be formulated as MBP requiring the solution of a large number of problem instances. This justifies, from both a practical and a theoretical perspective, the development of stopping rules aimed at controlling the number of iterations in a GRASP. To this end, a bayesian framework is laid down, two different prior distributions are proposed and stopping conditions are explicitly derived in analytical form. Numerical evidence shows that the stopping rules lead to an optimal trade-off between accuracy and computational effort, saving from unneeded iterations and still achieving good approximations.     

Expanding Neighborhood GRASP for the Traveling Salesman Problem

In this paper, we present the application of a modified version of the well known Greedy Randomized Adaptive Search Procedure (GRASP) to the TSP. The proposed GRASP algorithm has two phases: In the first phase the algorithm finds an initial solution of the problem and in the second phase a local search procedure is utilized for the improvement of the initial solution. The local search procedure employs two different local search strategies based on 2-opt and 3-opt methods. The algorithm was tested on numerous benchmark problems from TSPLIB. The results were very satisfactory and for the majority of the instances the results were equal to the best known solution. The algorithm is also compared to the algorithms presented and tested in the DIMACS Implementation Challenge that was organized by David Johnson.     

Adaptive and multi-mining versions of the DM-GRASP hybrid metaheuristic

Metaheuristics represent an important class of techniques to solve, approximately, hard combinatorial optimization problems for which the use of exact methods is impractical. Some researches have been combining machine learning techniques with metaheuristics to adaptively guide and improve the search for near optimal solutions. An example of such development is the DM-GRASP, a hybrid version of the Greedy Randomized Adaptative Search Procedures (GRASP) metaheuristic which incorporates a data mining process. In this hybrid proposal, after executing half of the total number of iterations, the data mining process extracts patterns from an elite set of sub-optimal solutions for the optimization problem. These patterns present characteristics of near optimal solutions and can be used to guide the following half GRASP iterations in the search through the solution space. In this work, we explore new versions of the DM-GRASP metaheuristic to experiment, not a single activation, but multiple and adaptive executions of the data mining process during the metaheuristic execution. We also applied the data mining technique into a reactive GRASP to show that a more sophisticated and not memoryless GRASP approach can also benefit from the use of this technique. In order to evaluate these new proposals, we adopted the server replication for reliable multicast problem since the best known results for this problem were obtained by GRASP and DM-GRASP implementations. The computational experiments, comparing traditional GRASP, DM-GRASP, and the new proposals, showed that multiple and adaptive executions of the data mining process can improve the results obtained by the DM-GRASP hybrid metaheuristic—the new proposals were able to find better results in less computational time for the reliable multicast problem.