A Method for Solving Optimization Problems with Equality Constraints by Using the SPICE Program

Jun GUO  Tetsuo NISHI  Norikazu TAKAHASHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.9   pp.2325-2332
Publication Date: 2003/09/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Optimization and Control
Keyword: 
HNNs,  optimization problem,  equality constraints,  energy function,  SPICE program,  

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Summary: 
Analog Hopfield neural networks (HNNs) have so far been used to solve many kinds of optimization problems, in particular, combinatorial problems such as the TSP, which can be described by an objective function and some equality constraints. When we solve a minimization problem with equality constraints by using HNNs, however, the constraints are satisfied only approximately. In this paper we propose a circuit which rigorously realizes the equality constraints and whose energy function corresponds to the prescribed objective function. We use the SPICE program to solve circuit equations corresponding to the above circuits. The proposed method is applied to several kinds of optimization problems and the results are very satisfactory.