My interest in genetic algorithms grew from my search of an
algorithmic mean to reproduce the mechanisms of natural evolution. I
could not have found better!
Being rather complex, I first tried to understand how genetic algorithms work. My readings had given me the feeling that there was something mysterious going on there. However, all that was going on a mere computer, so the mystery could not stand for long. I used very simple problems and studied how population of a canonical GA evolves in these cases.
In the same time, I read much about natural selection and I was struck and fascinated by the mechanisms described there, and the dynamics I saw in GAs. Those concepts of the theory of evolution known as genetic drifts, epistasis, hitch-hiker genes, fitness landscapes, ... where happening in these simple simulations. I figured out that there was something profound here about the dynamics of systems in general, which was shared among them, regardless of their biological, or silicon nature.
I then took interest in the resolution of real problems with GAs. In particular, I turned myself towards problems of combinatorial optimization, namely, the traveling salesman problem, the job-shop scheduling problem, and the quadratic assignment problem. We designed hybrid algorithms, combining genetic algorithms, tabu search, and basic hill-climber, and used the concept of fitness landscapes to understand what the algorithms were doing, and how we could improve them.
To study the fitness landscapes, I had the idea to use hill-climbers as probes and gather information along their path in the landscape. Starting from points sampled at random (in the case of the problems under study, these were typically bad solutions), studying the length of trajectories, the increase in the quality of solutions found along the trajectories, the correlation between the solutions at the end-points of the trajectories, ... gave me many interesting information to be able to figure out what the fitness landscape looked like. It gave me a certain knowledge of the so-called massif central, that is, this region in the landscape where the global optima are located.
In the case of the traveling salesman problem, going on along this experimental approach of the study of (combinatoiral optimization problems) fitness landscapes, I generated instances with particular characteristics to test my hypotheses regarding issues like:
Finding answers to these questions leads to some sort of a spectrum of
fitness landscapes, ranging from those made of a Fujiyama sort --
that is, a single very good optimum (by "very good", we mean an
optimum which quality is much better than random solution), where
hill-climbers can easily travel starting from the large valley made of
random solutions -- to rather flat and dull landscapes with a
very large number of small local optima (by "small", we mean that the
quality of the optima are not much better than those of random
solutions). This variety of landscapes is also well-known in so-called
Nk-landscapes, introduced by S. Kauffman.
This improved knowledge on the TSP helped me figure out the landscape of other problems, namely the QAP and the JSP. All NP-hard problems being equivalent (up to a polynomial transformation), there must be some equivalence between these TSP landscapes and those of all other NP-hard problems.