Nonlinear optimization simplified by hypersurface deformation

Journal Article · Thu Sep 01 00:00:00 EDT 1988 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01011658· OSTI ID:6139817

Stillinger, F H; Weber, T A

A general strategy is advanced for simplifying nonlinear optimization problems, the ant-lion method. This approach exploits shape modifications of the cost-function hypersurface which distend basins surrounding low-lying minima (including global minima). By intertwining hypersurface deformations with steepest-descent displacements, the search is concentrated on a small relevant subset of all minima. Specific calculations demonstrating the value of this method are reported for the partitioning of two classes of irregular but nonrandom graphs, the prime-factor graphs and the pi graphs. We also indicate how this approach can be applied to the traveling salesman problem and to design layout optimization, and that it may be useful in combination with simulated annealing strategies.

• Research Organization: AT and T Bell Lab., Murray Hill, NJ (USA)
• OSTI ID: 6139817
• Journal Information: J. Stat. Phys.; (United States), Vol. 52:5-6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
NONLINEAR PROBLEMS
MATHEMATICAL MANIFOLDS
COMPUTER-AIDED DESIGN
DEFORMATION
GRAPHS
MATRICES
OPTIMIZATION
RANDOMNESS
STATISTICAL MECHANICS
TRANSPORT THEORY
VERTEX FUNCTIONS
FUNCTIONS
MECHANICS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics