Isabel Rosseti

Efficient parallel cooperative implementations of GRASP heuristics

We propose a parallel cooperative strategy for the implementation of the GRASP metaheuristic and we illustrate it with a GRASP with path-relinking heuristic for the 2-path network design problem. Numerical results illustrating the effectiveness of the approach are reported. We comment in detail the implementation strategies that take most advantage of the algorithm structure. Computational experiments show linear speedups on a Linux cluster with 32 machines.

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.

Exploiting run time distributions to compare sequential and parallel stochastic local search algorithms

Run time distributions or time-to-target plots are very useful tools to characterize the running times of stochastic algorithms for combinatorial optimization. We further explore run time distributions and describe a new tool to compare two algorithms based on stochastic local search. For the case where the running times of both algorithms fit exponential distributions, we derive a closed form index that gives the probability that one of them finds a solution at least as good as a given target value in a smaller computation time than the other. This result is extended to the case of general run time distributions and a numerical iterative procedure is described for the computation of the above probability value. Numerical examples illustrate the application of this tool in the comparison of different sequential and parallel algorithms for a number of distinct problems.

A parallel GRASP heuristic for the 2-path network design problem

We propose a parallel GRASP heuristic with path-relinking for the 2-path network design problem. A parallel strategy for its implementation is described. Computational results illustrating the effectiveness of the new heuristic are reported. The parallel implementation obtains linear speedups on a cluster with 32 machines.

New benchmark instances for the Steiner problem in graphs

We propose in this work 50 new test instances for the Steiner problem in graphs. These instances are characterized by large integrality gaps (between the optimal integer solution and that of the linear programming relaxation) and symmetry aspects which make them harder to both exact methods and heuristics than the test instances currently in use for the evaluation and comparison of existing and newly developed algorithms. Our computational results indicate that these new instances are not amenable to reductions by current preprocessing techniques and that not only do the linear programming lower bounds show large gaps, but they are also hard to be computed. State-of-the-art heuristics, which found optimal solutions for almost all test instances currently in use, faced much more difficulties for the new instances. Fewer optimal solutions were found and the numerical results are more discriminant, allowing a better assessment of the effectiveness and the relative behavior of different heuristics.

On the Use of Run Time Distributions to Evaluate and Compare Stochastic Local Search Algorithms

Run time distributions or time-to-target plots are very useful tools to characterize the running times of stochastic algorithms for combinatorial optimization. We further explore run time distributions and describe a new tool to compare two algorithms based on stochastic local search. For the case where the running times of both algorithms fit exponential distributions, we derive a closed form index that gives the probability that one of them finds a solution at least as good as a given target value in a smaller computation time than the other. This result is extended to the case of general run time distributions and a numerical iterative procedure is described for the computation of the above probability value. Numerical examples illustrate the application of this tool in the comparison of different algorithms for three different problems.

A hybrid data mining GRASP with path-relinking

The exploration of hybrid metaheuristics-combination of metaheuristics with concepts and processes from other research areas-has been an important trend in combinatorial optimization research. An instance of this study is the hybrid version of the GRASP metaheuristic that incorporates a data mining process. Traditional GRASP is an iterative metaheuristic which returns the best solution reached over all iterations. In the hybrid GRASP proposal, after executing a significant 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 GRASP iterations in the search through the combinatorial solution space. The hybrid data mining GRASP has been successfully applied for different combinatorial problems: the set packing problem, the maximum diversity problem, the server replication for reliable multicast problem and the p-median problem. In this work, we show that, not only the traditional GRASP, but also GRASP improved with the path-relinking heuristic-a memory-based intensification strategy-could benefit from exploring a data mining procedure. Computational experiments, comparing traditional GRASP with path-relinking and different path-relinking hybrid proposals, showed that employing the combination of path-relinking and data mining made the GRASP find better results in less computational time. Another contribution of this work is the application of the path-relinking hybrid proposal for the 2-path network design problem, which improved the state-of-the-art solutions for this problem.

Applications and Parallel Implementations of Metaheuristics in Network Design and Routing

Successful applications of metaheuristics in telecommunications and network design and routing are reviewed, illustrating the major role played by the use of these techniques in the solution of many optimization problems arising in these areas. The main issues involved in the parallelization of metaheuristics are discussed. The 2-path network design problem is used to illustrate the development of robust and efficient parallel cooperative implementations of metaheuristics. Computational results on Linux clusters are reported.

Effective probabilistic stopping rules for randomized metaheuristics: GRASP implementations

The main drawback of most metaheuristics is the absence of effective stopping criteria. Most implementations stop after performing a given maximum number of iterations or a given maximum number of consecutive iterations without improvement in the best known solution value, or after the stabilization of the set of elite solutions found along the search. We propose probabilistic stopping rules for randomized metaheuristics such as GRASP and VNS. We first show experimentally that the solution values obtained by GRASP fit a Normal distribution. Next, we use this approximation to obtain an online estimation of the number of solutions that might be at least as good as the best known at the time of the current iteration. This estimation is used to implement effective stopping rules based on the trade off between solution quality and the time needed to find a solution that might improve the best found to date. This strategy is illustrated and validated by a computational study reporting results obtained with some GRASP heuristics.

tttplots-compare: a perl program to compare time-to-target plots or general runtime distributions of randomized algorithms

Run time distributions or time-to-target plots display on the ordinate axis the probability that an algorithm will find a solution at least as good as a given target value within a given running time, shown on the abscissa axis. Given a pair of different randomized algorithms