Neural Networks without Training for Optimization - Neural Networks: Methodology and Applications - page 443

8
Neural Networks without Training for
Optimization
L. Herault
Previous chapters have shown neural networks as powerful tools for mod-
elling, control, discrimination and automatic classification. In those fields,
non-linearity and training properties are used: a parameterised static or dy-
namic function is used, and the parameters are estimated through training.
This chapter will focus on another way of taking advantage of neural networks:
non-linearity and dynamics properties are also used, but the parameters of
those networks are naturally derived from the application, without training.
That approach is particularly well suited to solving optimisation problems.
What decision should to be taken? How to minimize the production costs
through an optimised tasks scheduling and an optimal management of flows
and resources? How to increase productivity? How to make the best use of
available resources to fulfil a request at a minimum cost? An optimisation
problem is the core issue behind all these questions. In fact, the optimisation
task deals with the choice between several alternatives. This choice is gov-
erned by the desire to make the best decision, which is often expressed as the
selection of a solution satisfying the problem requirements with a minimum
realization cost.
8.1 Modelling an Optimisation Problem
When facing an optimisation problem, the first step consists in reformulating
it in a mathematical way. That modelling is a crucial step and is sometimes
critical, since quantifying the quality of a solution is not that simple, and
the mathematical formulation (sometimes named coding) of a problem has an
influence on the choice of the methodology to solve it. That phase requires
a close cooperation between the optimisation experts and the application ex-
perts, who are looking for a solution. The result of that step is a mathematical
model, generally defined by