Neural Networks without Training for Optimization - Neural Networks: Methodology and Applications - page 484

poorly fitted, by means of genetic operators of mutation and crossover .After
some generations, the population is made of well-fitted individuals, in other
words of supposedly good solutions to the problem. The main difference with
simulated annealing and tabu search is that genetic algorithms manipulate
populations of solutions, instead of manipulating a single solution, which is
improved statistically in an iterative way. Genetic algorithms can be consid-
ered as generalized local search algorithms.
At present, genetic algorithms have important limitations, mainly due to
a very di cult tuning (coding of the solutions, types of genetic operators, size
of the initial population, required number of generations, percentage of muta-
tions, of crossovers, etc.). Moreover those algorithms are slow and can require
large memory storage for the individuals of several generations. In terms of
theoretical results, at the present time, there are far less solid theoretical re-
sults than with other metaheuristics such as methods derived from statistical
physics.

8.9 Towards Hybrid Approaches

At present, in order to solve hard combinatorial problems encountered in
real applications, an tendency emerges, aimed at building complex methods
incorporating knowledge and techniques coming from various horizons (linear
programming, branch and bound, simulated annealing, tabu search, neural
networks, etc.).
For instance, to solve a 0/1 linear programming problem with tens of
thousands variables and constraints, associated with a real stock management
problem, a metaheuristics was developed around a core based on simulated
annealing, with the following specific features [Privault et al. 1998b]:

• The initial solution is derived from a binarization of the solution of the

continuous problem, obtained with the simplex algorithm.

• During the search, some intensification and diversification mechanisms de-

rived from tabu search are used.

• Since it is di cult to find valid solutions, as soon as a new linear constraint

is satisfied, that constraint is no more violated afterwards.

Another way to combine e ciently different concepts encountered in the meta-
heuristics is presented for the TSP in [Charon et al. 1996].

8.10 Conclusion

8.10.1 The Choice of a Technique

The points developed in the previous sections allow making some choices as
a function of the particularities of the problem to solve: