Simone L. Martins

Experimental and Efficient Algorithms

The multiprocessor scheduling problem consists in scheduling a set of tasks with known processing times into a set of identical processors so as to minimize their makespan, i.e., the maximum processing time over all processors. We propose a new heuristic for solving the multiprocessor scheduling problem, based on a hybrid heuristic to the bin packing problem. Computational results illustrating the effectiveness of this approach are reported and compared with those obtained by other heuristics.

Strategies for the Parallel Implementation of Metaheuristics

Parallel implementations of metaheuristics appear quite naturally as an effective alternative to speed up the search for approximate solutions of combinatorial optimization problems. They not only allow solving larger problems or finding improved solutions with respect to their sequential counterparts, but also lead to more robust algorithms. We review some trends in parallel computing and report recent results about linear speedups that can be obtained with parallel implementations using multiple independent processors. Parallel implementations of tabu search, GRASP, genetic algorithms, simulated annealing, and ant colonies are reviewed and discussed to illustrate the main strategies used in the parallelization of different metaheuristics and their hybrids.

A Parallel Grasp for the Steiner Tree Problem in Graphs Using a Hybrid Local Search Strategy

In this paper, we present a parallel greedy randomized adaptive search procedure (GRASP) for the Steiner problem in graphs. GRASP is a two-phase metaheuristic. In the first phase, solutions are constructed using a greedy randomized procedure. Local search is applied in the second phase, leading to a local minimum with respect to a specified neighborhood. In the Steiner problem in graphs, feasible solutions can be characterized by their non-terminal nodes (Steiner nodes) or by their key-paths. According to this characterization, two GRASP procedures are described using different local search strategies. Both use an identical construction procedure. The first uses a node-based neighborhood for local search, while the second uses a path-based neighborhood. Computational results comparing the two procedures show that while the node-based variant produces better quality solutions, the path-based variant is about twice as fast. A hybrid GRASP procedure combining the two neighborhood search strategies is then proposed. Computational experiments with a parallel implementation of the hybrid procedure are reported, showing that the algorithm found optimal solutions for 45 out of 60 benchmark instances and was never off by more than 4% of the optimal solution value. The average speedup results observed for the test problems show that increasing the number of processors reduces elapsed times with increasing speedups. Moreover, the main contribution of the parallel algorithm concerns the fact that larger speedups of the same order of the number of processors are obtained exactly for the most difficult problems.

A Parallel GRASP for the Steiner Problem in Graphs

A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. Given an undirected graph with weights associated with its nodes, the Steiner tree problem consists in finding a minimum weight subgraph spanning a given subset of (terminal) nodes of the original graph. In this paper, we describe a parallel GRASP for the Steiner problem in graphs. We review basic concepts of GRASP: construction and local search algorithms. The implementation of a sequential GRASP for the Steiner problem in graphs is described in detail. Feasible solutions are characterized by their non-terminal nodes. A randomized version of Kruskals algorithm for the minimum spanning tree problem is used in the construction phase. Local search is based on insertions and eliminations of nodes to/from the current solution. Parallelization is done through the distribution of the GRASP iterations among the processors on a demand-driven basis, in order to improve load balancing. The parallel procedure was implemented using the Message Passing Interface library on an IBM SP2 machine. Computational experiments on benchmark problems are reported.

Experimental Comparison of Greedy Randomized Adaptive Search Procedures for the Maximum Diversity Problem

The maximum diversity problem (MDP) consists of identifying optimally diverse subsets of elements from some larger collection. The selection of elements is based on the diversity of their characteristics, calculated by a function applied on their attributes. This problem belongs to the class of NP-hard problems. This paper presents new GRASP heuristics for this problem, using different construction and local search procedures. Computational experiments and performance comparisons between GRASP heuristics from literature and the proposed heuristics are provided and the results are analyzed. The tests show that the new GRASP heuristics are quite robust and find good solutions to this problem.

Metaheuristics for optimization problems in computer communications

Recent years have witnessed huge advances in computer technology and communication networks, entailing hard optimization problems in areas such as network design and routing. Metaheuristics are general high-level procedures that coordinate simple heuristics and rules to find good approximate solutions to computationally difficult combinatorial optimization problems. They are among the most effective solution strategies for solving optimization problems in practice and have been applied to a very large variety of problems in telecommunications, computer communications, and network design and routing. In this paper, we review the principles associated with some of the main metaheuristics and we give templates for basic implementations of them: simulated annealing, tabu search, GRASP, VNS, genetic algorithms, and path-relinking. The main strategies underlying the development of parallel implementations of metaheuristics are also reviewed. Finally, we present an account of some successful applications of metaheuristics to optimization problems in telecommunications, computer communications, and network design and routing.

Hybridization of GRASP Metaheuristic with Data Mining Techniques

In this work, we propose a hybridization of GRASP metaheuristic that incorporates a data mining process. We believe that patterns obtained from a set of sub-optimal solutions, by using data mining techniques, can be used to guide the search for better solutions in metaheuristics procedures. In this hybrid GRASP proposal, after executing a significant number of GRASP iterations, the data mining process extracts patterns from an elite set of solutions which will guide the following iterations. To validate this proposal we have worked on the Set Packing Problem as a case study. Computational experiments, comparing traditional GRASP and different hybrid approaches, show that employing frequent patterns mined from an elite set of solutions conducted to better results. Besides, additional performed experiments evidence that data mining strategies accelerate the process of finding good solutions.

Applications of the DM‐GRASP heuristic: a survey

Recent research has shown that the hybridization of metaheuristics is a powerful mechanism to develop more robust and efficient methods to solve hard optimization problems. The combination of different techniques and concepts behind metaheuristics, if well designed, has the potential to exploit their advantages while diminishing their drawbacks, which results in methods suited to a more diverse set of real problems. The DM-GRASP heuristic is one such hybrid method that has achieved promising results. It is a hybrid version of the GRASP metaheuristic that incorporates a data-mining process. In this work, we review how this hybridization was designed and survey the results of its practical applications evaluated until now.

New heuristics for the maximum diversity problem

Abstract The maximum diversity problem (MDP) consists of identifying, in a population, a subset of elements, characterized by a set of attributes, that present the most diverse characteristics among the elements of the subset. The identification of such solution is an NP-hard problem. Some heuristics are available to obtain approximate solutions for this problem. In this paper, we propose different GRASP heuristics for the MDP, using distinct construction procedures and including a path-relinking technique. Performance comparison among related work and the proposed heuristics is provided. Experimental results show that the new GRASP heuristics are quite robust and are able to find high-quality solutions in reasonable computational times.

A hybrid GRASP with data mining for the maximum diversity problem

The maximum diversity problem (MDP) consists in identifying, in a population, a subset of elements, characterized by a set of attributes, that present the most diverse characteristics among themselves. The identification of such solution is an NP-hard problem. In this work, we propose a hybrid GRASP metaheuristic for the MDP that incorporates a data mining process. Data mining refers to the extraction of new and potentially useful knowledge from datasets in terms of patterns and rules. We believe that data mining techniques can be used to extract patterns that represent characteristics of sub-optimal solutions of a combinatorial optimization problem. Therefore these patterns can be used to guide the search for better solutions in metaheuristics procedures. Performance comparison between related work and the proposed hybrid heuristics is provided. Experimental results show that the new hybrid GRASP is quite robust and, mainly, this strategy is able to find high-quality solutions in less computational time.