SIGMA - A Stochastic-Integration Global Minimization Algorithm.
Abstract
The paper gives a detailed description of a FORTRAN IV program based on a new method of finding a global (or absolute ) minimizer of a function of N real variables, i.e. the point x in N-dimensional space (or possibly one of the points) such that not only the function increases if one moves away from x in any direction, ( local or relative minimum), but also such that no other point exists where f has a lower value. The method, which was first proposed by the present authors in a paper which is to appear in the Journal of Optimization Theory and Applications, is based on ideas from statistical mechanics, and looks for a point of global minimum by following the solution trajectories of a stochastic differential equation representing the motion of particle (in N-space) under the action of a potential field and of a random perturbing force. The tests were performed by running the program on an extensive set of carefully selected tests were performed by running the program on an extensive set of carefully selected test problems of varying difficulty, and the performance was remarkably successful, even on very hard problems (e.g. problems with a single point of global minimum and up to about 10 to the 10th power points of non-global minimum). Keywords include: Algorithms; Global Optimization, Stochastic Differential Equations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1985
- Accession Number
- ADA154878
Entities
People
- F. Aluffi-pentini
- F. Zirilli
- V. Parisi
Organizations
- University of Wisconsin–Madison