A Parallel GRASP Implementation for the Quadratic Assignment Problem

A greedy randomized adaptive search procedure for maximum independent set. A greedy randomized adaptive search procedure for the quadratic assignment problem. subroutines for approximate solution of dense quadratic assignment problems using GRASP. Table 2: grasp-parallel-sparse empty permutation, and local search is applied to the constructed solution for further improvement. The best solution over all iterations is kept as the output. In the construction phase of the heuristic, a complete solution is constructed by adding one element at a time in a greedy adaptive randomized fashion. In order to exploit the sparsity of the input data, an additional procedure is incorporated in the construction phase of the heuristic, which reduces the computational eeort depending on the magnitude of the sparsity. Due to the nature of the heuristic, its parallel implementation on an MIMD parallel computer is very eecient. The iterations are partitioned over m-processors, with each processor having its copy of the instance data and an independent random number sequence. The heuristic was implemented on a KSR-1 parallel computer utilizing 64 processors, and the computational results indicate an almost linear average speedup. In comparison with the sequential implementation on instances from a collection of quadratic assignment test problems, the parallel implementation performed on average about 62 times faster and on one instance over 221 times faster. The grasp heuristic and its parallel implementation can be applied to more general nonlinear assignment problems. Acknowledgment The authors would like to thank the Cornell Theory Center for making available the KSR-1 parallel computer for the computational experiments.