Neural Networks without Training for Optimization - Neural Networks: Methodology and Applications - page 449

• The modelling of processes with memory gave rise to the so-called tabu

search. The specificity of that approach stems from the fact that it stores
in memory the recent past of the search, and possibly parts of the faraway
past.

• The modelling of the nervous system gave rise to neural algorithms. Being

massively parallel and allowing hardware implementations (analog, digital,
optical), they are particularly attractive to solve problems requiring very
short resolution time.

• The modelling of genetics initiated the development of genetic or evolution-

ary algorithms, in which potential solutions are considered as individuals
evolving inside a population.

• The modelling of the learning process gave rise to reinforcement learning

methods (see also Chap. 5). The corresponding algorithms can be distrib-
uted over a network of calculators, each of them learning how to react
optimally (in a stationary environment), from the knowledge of an evalu-
ation of its decisions by its neighbors. Those approaches are particularly
suitable for solving dynamic problems in non-stationary environments.

Finally, it is important to emphasize that there exist hybrid methods that
couple some metaheuristics, or metaheuristics and conventional approaches.
Before considering neural networks to solve optimisation problems, we
present the most closely related metaheuristics: simulated annealing.

8.5 Techniques Derived from Statistical Physics

It is possible to devise an analogy between combinatorial optimisation prob-
lems and the modelling of complex systems by statistical physics methods. A
complex physical system has a multitude of possible states; among them, an
equilibrium state is a state for which a quantity that depends on the system
state (e.g., its free energy) is minimum. The search for an equilibrium state
of a system simulated on a computer amounts to searching the minimum
of a function that depends on the system state, which might be defined by
a huge number of variables (such as the positions of the particles of the sys-
tem). Therefore, the simulation of macroscopic properties of a physical system
amounts to the search for a minimum of thermodynamical quantities such as
the free energy. By establishing an analogy between thermodynamical quan-
tities and the cost functions of an optimisation problem, it becomes possible
to find a minimum of the cost function, hence a solution to the optimisation
problem, by taking advantage of simulation techniques derived from statistical
physics.

Remark. To this end, the optimisation problem is assimilated to a system of
interacting particles, whose states code for the values of the variables. The op-
timal solution is then considered as a fundamental state (state with minimum