Resumen de Neural linear programming Neuro-LP

Luis Biondi Neto, F. Hideo Fukuda, Vicenzo Roberto Junior, Luis Chiganer, M. Estellita Lins, A.E. Restum

• This article presents a method of resolution of Linear Programming Problems (LPP) by using similar philosophy adopted in Artificial Neural Networks (ANN). It intends to show that architectures of ANN, when used in conjunction with numeric algorithms, can be more adequate to solve a LPP.

  The main motivation in realize this research is based on a possibility of to build dedicated Electronic Integrated Circuits (VLSI for example), by using the model Neuro-LP proposed in this article and bringing the following immediate benefits: very high speed convergence;

  possibility to incorporate the optimization module in any electronic equipment of interest.

  The model introduced here was implemented like cells such as sums, integrators, and amplifiers. This implementation was easy using VLSI technology or any other large-scale integration technique.

  Initially will be introduced the model of artificial neuron and after the learning algorithm by using the quadratic error minimization on network output across of the gradient decent method. The resulted of the iterative cost function minimization that modeling the problem allows synaptic weights upgrade and converge for a value that reflective the knowledge acquired by ANN. In the investigated case the ANN was used in the execution phase (after trained), so the synaptic weights that would be obtained by training, received the values of the own constraints and of objective function coefficient that modeling the problem. The neural network is an unconventional architecture.

  In the next step the LPP, composed of an objective function and of a set of constraints, is transformed into an optimization problem without constraints. Therefore was adopted a function called pseudo-cost function where was added a term of penalty, by causing high cost every time that one of the constraints was broken.

  The best solution for the optimization problem without constraints is an ANN. We transform the problem into a differential equations system and by using a not traditional neural architecture, was possible solved numerically from gradient method.

  The model Neuro-LP proposed is a kind of two layers unconventional ANN, working in the execution phase and with feedback. The first layer calculates the value of the constraints and if there be a case violation of some of them layers is applied the penalty process. The second layer works processing the output of the first layer. So, the second layer integrates theses results and returns the decision variables values proposed in the PLL.

  Finally we show a case study to verify and to validate the method proposed in this paper.