Mathematical Programming

, Volume 46, Issue 1, pp 1–29

Concurrent stochastic methods for global optimization


  • Richard H. Byrd
    • Department of Computer ScienceUniversity of Colorado
  • Cornelius L. Dert
    • Department of Computer ScienceUniversity of Colorado
    • Econometric InstituteErasmus University Rotterdam
  • Alexander H. G. Rinnooy Kan
    • Econometric InstituteErasmus University Rotterdam
  • Robert B. Schnabel
    • Department of Computer ScienceUniversity of Colorado

DOI: 10.1007/BF01585724

Cite this article as:
Byrd, R.H., Dert, C.L., Rinnooy Kan, A.H.G. et al. Mathematical Programming (1990) 46: 1. doi:10.1007/BF01585724


The global optimization problem, finding the lowest minimizer of a nonlinear function of several variables that has multiple local minimizers, appears well suited to concurrent computation. This paper presents a new parallel algorithm for the global optimization problem. The algorithm is a stochastic method related to the multi-level single-linkage methods of Rinnooy Kan and Timmer for sequential computers. Concurrency is achieved by partitioning the work of each of the three main parts of the algorithm, sampling, local minimization start point selection, and multiple local minimizations, among the processors. This parallelism is of a coarse grain type and is especially well suited to a local memory multiprocessing environment. The paper presents test results of a distributed implementation of this algorithm on a local area network of computer workstations. It also summarizes the theoretical properties of the algorithm.

Key words

Global optimizationconcurrentparallelstochasticnetwork of computers
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© North-Holland 1990