A cooperative parallel rollout algorithm for the sequential ordering problem (original) (raw)

An Efficient CGM-Based Parallel Algorithm Solving the Matrix Chain Ordering Problem

International Journal of Grid and High Performance Computing, 2014

This study focuses on the parallel resolution of the matrix chain ordering problem and the optimal convex polygon triangulation problem on the Coarse grain multicomputer model (CGM for short). There has been intensive work on the parallelization of these dynamic programming problems in PRAM, including the use of systolic arrays, but a BSP/CGM solution is necessary for ease of implementation and portability. Our CGM algorithm is based on Yao's sequential solution running in O(n2) time and O(n2) space. This CGM algorithm uses p processors, each with O(n/p) local memory. It requires at most O(S/p×n2) running time with S communication rounds and with S/p<1. Our algorithm performs better than the algorithm proposed in 2012 by Dilson and Marco when S is less than n/p. We offer several ways of partitioning the problem to solve and study the impact of each partitioning algorithm performance. A CGM solution exists based on Yao's algorithm, but the subdivision of tasks is defined a...

Scalable parallel algorithms for difficult combinatorial problems: A case study in optimization

A novel combination of emergent algorithmic meth- ods, powerful computational platforms and support- ing infrastructure is described. These complementary tools and technologies are used to launch systematic attacks on combinatorial problems of significance. As a case study, optimal solutions to very large in- stances of the NP-hard vertex cover problem are computed. To accomplish this, an efficient sequen- tial algorithm and two forms of parallel algorithms are implemented. The importance of maintaining a balanced decomposition of the search space is shown to be critical to achieving scalability. With the syn- ergistic combination of techniques detailed here, it is now possible to solve problem instances that before were widely viewed as hopelessly out of reach. Tar- get problems need only be amenable to reduction and decomposition. Applications are also discussed.

Local search procedures for improving feasible solutions to the sequential ordering problem

Annals of Operations Research, 1993

Given a digraphG=(V, A), a weight for each node inV and a weight for each arc inA, the Sequential Ordering Problem (SOP) consists of finding a Hamiltonian path, such that a release date and a deadline for each node and precedence relationships among nodes are satisfied and a linear function is minimized. In our case, the objective function is the

A Parallel Approach for Solving a Large-Scale Traveling Salesman Problem

A parallel approach for solving a large-scale Euclidean Traveling Salesman Problem (TSP) is presented. The approach consists of the following stages: partitioning the input data set into clusters, solving the TSP for each cluster to get partial solutions, merging the partial solutions to form a complete solution, and optimizing the complete solution. Lin-Kernighan-Helsgaun (LKH) algorithm is used to solve TSP in each cluster. Rings are used to form a complete solution. Several optimization strategies are presented to improve the quality of the complete solution. The approach minimizes the run time of the overall solution. The quality loss of the solution obtained with this approach is negligible when compared to the best known solutions. Keywords: parallel approach, combinatorial optimization, decomposition, clustering, TSP.

An ordered heuristic for the allocation of resources in unrelated parallel-machines

Global competition pressures have forced manufactures to adapt their productive capabilities. In order to satisfy the ever-changing market demands many organizations adopted flexible resources capable of executing several products with different performance criteria. The unrelated parallel-machines makespan minimization problem (Rm||Cmax) is known to be NPhard or too complex to be solved exactly. In the heuristics used for this problem, the MCT (Minimum Completion Time), which is the base for several others, allocates tasks in a random like order to the minimum completion time machine. This paper proposes an ordered approach to the MCT heuristic. MOMCT (Modified Ordered Minimum Completion Time) will order tasks in accordance to the MS index, which represents the mean difference of the completion time on each machine and the one on the minimum completion time machine. The computational study demonstrates the improved performance of MOMCT over the MCT heuristic.