The primary objective of these procedures is to group n items into K mutually exclusive clusters so that items within each cluster are relatively homogeneous in nature while the clusters themselves are distinct. Linear and superlinear speed-ups are obtained. Thus, solutions to real-world, complex clustering problems, which could not be solved due to the lack of efficient parallel algorithms, can now be attempted. Algorithms are reviewed, classified and compared. Qualitative comparisons are based on the applicability, scope, ease of implementation, robustness and reliability of each algorithm, while quantitative comparisons are based on the computational performance of algorithmic implementations on multiprocessor systems.
Emphasis is placed on the potential of parallel algorithms to solve large-scale stochastic programs.
This paper presents a parallel computation approach for the efficient solution of very large multistage linear and nonlinear network problems with random parameters. These problems result from particular instances of models for the robust optimization of network problems with uncertainty in the values of the right-hand side and the objective function coefficients. The methodology considered here models the uncertainty using scenarios to characterize the random parameters. A scenario tree is generated and, through the use of full-recourse techniques, an implementable solution is obtained for each group of scenarios at each stage along the planning horizon. As a consequence of the size of the resulting problems, and the special structure of their constraints, these models are particularly well-suited for the application of decomposition techniques, and the solution of the corresponding subproblems in a parallel computation environment.