A Parallel GRASP Heuristic for the 2-Path Network Design Problem (original) (raw)

Efficient parallel cooperative implementations of GRASP heuristics

Parallel Computing, 2007

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.

A reactive GRASP with path relinking for capacitated clustering

This paper presents a greedy randomized adaptive search procedure (GRASP) coupled with path relinking (PR) to solve the problem of clustering n nodes in a graph into p clusters. The objective is to maximize the sum of the edge weights within each cluster such that the sum of the corresponding node weights does not exceed a fixed capacity. In phase I, both a heaviest weight edge (HWE) algorithm and a constrained minimum cut algorithm are used to select seeds for initializing the p clusters. Feasible solutions are obtained with the help of a self-adjusting restricted candidate list that sequentially guides the assignment of the remaining nodes. At each major GRASP iteration, the list length is randomly set based on a probability density function that is updated dynamically to reflect the solution quality realized in past iterations. In phase II, three neighborhoods, each defined by common edge and node swaps, are explored to attain local optimality. The following exploration strategies are investigated: cyclic neighborhood search, variable neighborhood descent, and randomized variable neighborhood descent (RVND). The best solutions found are stored in an elite pool.

Restart strategies for GRASP with path-relinking heuristics

Optimization Letters, 2011

GRASP with path-relinking is a hybrid metaheuristic, or stochastic local search (Monte Carlo) method, for combinatorial optimization. A restart strategy in GRASP with path-relinking heuristics is a set of iterations {i1, i2,. . .} on which the heuristic is restarted from scratch using a new seed for the random number generator. Restart strategies have been shown to speed up stochastic local search algorithms. In this paper, we propose a new restart strategy for GRASP with path-relinking heuristics. We illustrate the speedup obtained with our restart strategy on GRASP with path-relinking heuristics for the maximum cut problem, the maximum weighted satisfiability problem, and the private virtual circuit routing problem.

A GRASP heuristic using path-relinking and restarts for the Steiner traveling salesman problem

International Transactions in Operational Research, 2017

The traveling salesman problem (TSP) is one of the most studied problems in combinatorial optimization. Given a set of nodes and the distances between them, it consists in finding the shortest route that visits each node exactly once and returns to the first. Nevertheless, more flexible and applicable formulations of this problem exist and can be considered. The Steiner TSP (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by the shortest route, eventually visiting some nodes and edges more than once. In this paper, we adapt some classical TSP constructive heuristics and neighborhood structures to the STSP variant. In particular, we propose a reduced 2-opt neighborhood and we show that it leads to better results in smaller computation times. Computational results with an implementation of a GRASP heuristic using path-relinking and restarts are reported. In addition, ten large test instances are generated. All instances and their best-known solutions are made available for download and benchmarking purposes.

A hybrid GRASP with perturbations and adaptive path-relinking for the Steiner problem in graphs

2001

We propose and describe a hybrid GRASP with weight perturbations and adaptive path-relinking heuristic (HGP-PR) for the Steiner problem in graphs. In this multi-start approach, the greedy randomized construction phase of a GRASP is replaced by the combination of several construction heuristics with a weight perturbation strategy that combines intensification and diversification elements, as in a strategic oscillation approach. The improvement phase circularly explores two different local search strategies: the first uses a node-based neighborhood for local search, while the second uses a key-path-based neighborhood. An adaptive path-relinking technique is applied to a set of elite solutions as a post-optimization strategy. Computational experiments on a large set of benchmark problems of three different classes are reported. We first illustrate the effectiveness of preprocessing procedures for several classes of test problems. Next, we present computational results illustrating the contribution of each algorithmic feature to the robustness of the complete algorithm. Finally, we show that our algorithm outperforms other heuristics in the literature, obtaining consistently better or comparably good solutions for all classes of test problems.

GRASP with path relinking heuristics for the antibandwidth problem

Networks, 2011

This paper proposes a linear integer programming formulation and several heuristics based on GRASP and path relinking for the antibandwidth problem. In the antibandwidth problem, one is given an undirected graph with n nodes and must label the nodes in a way that each node receives a unique label from the set {1, 2, . . . , n}, such that, among all adjacent node pairs, the minimum difference between the node labels is maximized. Computational results show that only small instances of this problem can be solved exactly (to optimality) with a commercial integer programming solver and that the heuristics find high-quality solutions in much less time than the commercial solver.

A Parallel GRASP for the Steiner Problem in Graphs

1998

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 Kruskal's 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.

GRASP with evolutionary path-relinking for the capacitated arc routing problem

Computers & Operations Research, 2013

The Capacitated Arc Routing Problem (CARP) is a well-known NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours servicing a subset of required edges under vehicle capacity constraints. There are numerous applications for the CARP, such as street sweeping, garbage collection, mail delivery, school bus routing, and meter reading. A Greedy Randomized Adaptive Search Procedure (GRASP) with Path-Relinking (PR) is proposed and compared with other successful CARP metaheuristics. Some features of this GRASP with PR are (i) reactive parameter tuning, where the parameter value is stochastically selected biased in favor of those values which historically produced the best solutions in average; (ii) a statistical filter, which discard initial solutions if they are unlikely to improve the incumbent best solution; (iii) infeasible local search, where high-quality solutions, though infeasible, are used to explore the feasible/ infeasible boundaries of the solution space; (iv) evolutionary PR, a recent trend where the pool of elite solutions is progressively improved by successive relinking of pairs of elite solutions. Computational tests were conducted using a set of 81 instances, and results reveal that the GRASP is very competitive, achieving the best overall deviation from lower bounds and the highest number of best solutions found.

GRASP with Path-Relinking: Recent Advances and Applications

Metaheuristics: Progress as Real Problem Solvers

Path-relinking is a major enhancement to the basic greedy randomized adaptive search procedure (GRASP), leading to significant improvements in solution time and quality. Path-relinking adds a memory mechanism to GRASP by providing an intensification strategy that explores trajectories connecting GRASP solutions and the best elite solutions previously produced during the search. This paper reviews recent advances and applications of GRASP with path-relinking. A brief review of GRASP is given. This is followed by a description of path-relinking and how it is incorporated into GRASP. Several recent applications of GRASP with path-relinking are reviewed. The paper concludes with a discussion of extensions to this strategy, concerning in particular parallel implementations and applications of path-relinking with other metaheuristics.