Lagrangian Techniques for NP-Complete Problems with Application to ILP, Satisfiability, and TSP
Download:
|
|
by Yao-jen Chang, Chun Yuan
http://wavelet.el.cycu.edu.tw/~chang/Images/nlp.ps
Add To MetaCart
Abstract:
In this paper, we creat a continuous dual space where a dynamic system characterizing an NP complete problem evolves. The combinatorial problem, when represented in continuous variables, enables the Lagrange method to provide a trap avoidance mechanism and ensure integer solutions when equilibrium has been established. Experimental results show problems of relatively large sizes can be solved on line if run on the proposed dynamic system. Even if the special purpose architecture is not available, many problems such as a 0-1 ILP FEASIBILITY problem with 384 variables and 556 constraints have been solved faster by simulation than by the branch-and-bound method. 1
Citations
| 119 | Combinatorial Optimization – Papadimitriou, Steiglitz - 1982 |
| 13 | Lagrangian techniques for solving a class of zero-one integer linear programs – Chang, Wah - 1995 |
| 7 | Algorithms for Combinatorial Optimization in Real Time and their Automated Refinement by Genetic Programming – Chu - 1994 |
| 5 | Switched-capacitor artificial neural networks for nonlinear optimization with constraints – Cichocki, Unbehauen - 1990 |
| 1 | Constantinides, "Lagrangian programming neural networks – Zhang, G - 1992 |
| 1 | Zemlin, "Integer programming formulation and traveling salesman problems – Miller, Tucker, et al. - 1960 |
