CONCLUSION

The conclusion of this work is that it is possible to develop a problem-solving method providing evolutionary computational support to general problem formulations within some important areas of formal expression. These areas include both first-order logic and high-order modes of expression. This makes possible to apply a problem-independent evolutionary solution-procedure to a large class of problems having an accurate and potentially sophisticated formal statement. The problem-solving method can be implemented by a computer language integrated in a programming environment having a built-in evolutionary computational system. GENETICA has been developed as a prototype version of such a language. Data-generation scenarios in GENETICA can be viewed as interpretations of genotypes evolved according to the computational system. As a consequence, a higher-level problem, represented as a GENETICA program, can be reduced to a lower-level one, which is the evolution of genotypes. In a similar way, problems represented in higher-level domain-specific languages can be reduced to problems represented in GENETICA. This route connecting the lowest with the highest level of expression could offer some benefits concerning the relation between specialization and generality.

For instance, the hotel application presented here is a highly specialized one. Specialized applications are usually effective but not general, while the development cost is usually high. However, the hotel application is an instance of the class of the applications that can be developed in G-CAD. G-CAD provides both generality, within a specific domain of architectural design, and tools for the development of problem specific applications within this domain. G-CAD is a domain-specific language having itself a high cost of development. However, it is an instance of the class of languages that can be developed in GENETICA. GENETICA provides both generality, within the domain of evolutionary problem-solving, and tools for the development of domain-specific languages within this domain.

In the context of the proposed approach, integration of AI expressive power with the computational efficiency of evolutionary methods could be investigated. Development of creative design applications, having complex confirmation and optimization goals, could be based on domain-specific evolutionary tools.

DISCUSSION

A common argument against the combination of evolutionary methods with formal knowledge representation concerns the concept of "creativity": it has been said that if knowledge specifies the basic features of a solution then evolution has nothing really new to discover. On the other hand it is known that if evolution is allowed to discover virtually anything then probably will discover nothing really creative due to complexity limitations.

Both arguments are sound but also pose the limits of their validity. The first one refers to the usual but rather restrictive case where the problem representation depends on (or is contained in) the solution representation. The second one assumes a problem representation exclusively defined by the desirable properties of a solution. Of course some compromise between "creativity" and "efficiency" is inevitable: evolution should not be over-constrained, because this could cause an unnecessary decline of creativity, but also should not be allowed to discover what we already know about the problem, because this could cause an unnecessary decline of efficiency. Evolution should work exactly within our "limits of ignorance" which have to be effectively defined. This is a matter of problem representation.

Under the most abstract and general context of formal expression, which is examined in this work, there is no assumption about the specific features of the problem representation. As a consequence, this work does not concern the aforementioned debate. It aims to the full exploitation of the potential of formal expression (viewed in its most abstract and general form) in problem representation, regardless of the specific features which could bias the latter to the one or the other extreme of the creativity-efficiency compromise. Hopefully, this will make possible to achieve flexible accurate problem representations resulting in applications both creative and effective.