## Section: New Results

### Representations and Prior Knowledge for Evolutionary Computation

Participants : Nicolas Bredèche, Alexandre Devert, Cédric Hartland, Fei Jiang, Miguel Nicolau, Marc Schoenauer.

One key issue in Evolutionary Computation is to design a representation and the associated variation operators, crossover and mutation, best suited to the problem at hand. In order to do so, the use of prior knowledge is highly recommended in practice. Resuming early work devoted to Structural Optimisation, the research done in TAO focuses on the design of scalable and modular representations. A promising direction in this respect is that of developmental representations.

Specifically in the domain of combinatorial optimization, all reported successes of EAs are based on the use of prior knowledge and domain-specific heuristics. An application in temporal planning have witnessed this, and further demonstrated the need for some characterisation of problem instances in order to facilitate the choice of the hyper-parameters.

#### Scalable and modular representations

Incorporating domain knowledge in Evolutionary Algorithms is mandatory after the No Free Lunch Theorem in boolean settings (and is a good idea in any other setting); the choice of the representation (and the associated variation operators, e.g. crossover and mutation) is the very first place where this can be done.

Marc Schoenauer's early work on Evolutionary Design included an original representation based on Voronoi diagrams
(H. Hamda and M. Schoenauer. Topological Optimum Design with Evolutionary Algorithms.
*Journal of Convex Analysis* , 9, pp 503–517, 2002). This work led to a collaboration with EZCT Design and Architecture Research. A first application was to design chairs, and the results were exposed in different contemporary architecture exhibitions
(P. Morel, H. Hamda, and M. Schoenauer. Computational chair design using genetic algorithms.
*Concept* , 71(3):95–99, 2005.), including the Beaubourg modern art museum
[Oops!] .

However, this approach has many drawbacks: its lack of flexibility makes it almost impossible to address the constructibility issue. An original representation directly handling construction plans of Lego-like structures was proposed in Alexandre Devert's PhD in 2006 (A. Devert, N. Bredèche, and M. Schoenauer. Blindbuilder : a new encoding to evolve lego-like structures. In Proc. EuroGP'06, pp 61–72, Springer Verlag LNCS 3905, 2006.). Despite its efficiency and modularity, this representation nevertheless scales up poorly with the number of elements used to build the structure. An embryogenic approach has hence recently been proposed. The idea is to evolve local rules for some “cells” that will exchange “chemicals”, and the steady-state of those chemicals will describe the target structure. Preliminary experiments on evolving 2D images have shown its robustness compared to previous approaches, explained as it automatically adjusts the stopping criterion for the developmental stage [Oops!] .

The core of this developmental approach is a Neural Network, duplicated in all the 'cells' of the underlying substrata. Whereas the first work above uses standard NN evolution of topology (K. O. Stanley and R. Miikkulainen. Evolving Neural Networks through augmenting topologies. Evolutionary Computation 10(2):99-127, 2002.), the design of an original procedure to evolve Echo State Networks (ESNs) proved to greatly increase the speed of evolution [Oops!] . Note that ESNs have also been used in TAO as models for robot controllers [Oops!] – see section 6.4.2 .

An on-going collaboration within the MIT-France program aims at further extending developmental systems in the context of architectural design. Ongoing work focus on applying this approach in the domain of truss structure design (phd of A. Devert) as well as evolving a developing multi-cellular system in a continuous substrate (work of N. Bredeche).

#### Toward developmental representations

Gradually shifting toward complex system modelling, we investigated, in collaboration with the Alchemy INRIA project-team, the influence of the topology of large Neural Networks on their computational ability, with the co-supervised PhD thesis of Fei Jiang. First studies investigated the influence of topology of SOM networks on their classification performances [Oops!] . On-going work is concerned with Echo State Networks and their use in Engineering and Control problems.

In the meantime, on-going study on Gene Regulatory Networks (GRNs) provides yet another source of diversity for representation of (Neural) Networks: within the GENNETEC project, and starting from Banzhaf's model of GRN
(W. Banzhaf, Artificial Regulatory Networks and Genetic Programming, Chapter 4 in Rick L. Riolo and Bill Worzel, Eds,
*Genetic Programming Theory and Practice* , pp 43–62, Kluwer, 2003.), Miguel Nicolau investigates the links of GRN models with Complex Neural Networks, related to both developmental representations and the abovementioned network topology studies.

#### Representations for combinatorial optimisation

The representation issue also arises for combinatorial optimisation problems, as witnessed by the new paradigm for Evolutionary Temporal Planning developped in TAO.

This original representation, based on a sequential splicing of the problem in the state space, was designed during a collaboration with Thalès [Oops!] . The idea is to use a deterministic constaint programming solver (CPT (V. Vidal, H. Geffner, Branching and Pruning: An Optimal Temporal POCL Planner based on Constraint Programming, Artificial Intelligence 170 (3), pp. 298-335, 2006.)was chosen here) to solve the (hopefully) small problems between two states of the spliced sequence. This approach allowed us to solve yet unsolved instances of well-known benchmarks of the IPC suite in Jacques Bibai's Master thesis, now continuing with a Cifre PhD: one research direction, here again, is to be able to assess the difficulty of a sub-problem a priori, i.e. without having to run the deterministic solver.