What is Ambiguous Grammar

Evolutionary computation (EC) is the study of computational systems that borrow ideas from and are inspired by natural evolution and adaptation (Yao & Xu, 2006, pp. 1-18). EC covers a number of techniques based on evolutionary processes and natural selection: evolutionary strategies, genetic algorithms and genetic programming (Keedwell & Narayanan, 2005). Evolutionary strategies are an approach for efficiently solving certain continuous problems, yielding good results for some parametric problems in real domains. Compared with genetic algorithms, evolutionary strategies run more exploratory searches and are a good option when applied to relatively unknown parametric problems. Genetic algorithms emulate the evolutionary process that takes place in nature. Individuals compete for survival by adapting as best they can to the environmental conditions. Crossovers between individuals, mutations and deaths are all part of this process of adaptation. By substituting the natural environment for the problem to be solved, we get a computationally cheap method that is capable of dealing with any problem, provided we know how to determine individuals’ fitness (Manrique, 2001). Genetic programming is an extension of genetic algorithms (Couchet, Manrique, Ríos & Rodríguez- Patón, 2006). Its aim is to build computer programs that are not expressly designed and programmed by a human being. It can be said to be an optimization technique whose search space is composed of all possible computer programs for solving a particular problem. Genetic programming’s key advantage over genetic algorithms is that it can handle individuals (computer programs) of different lengths. Grammar-guided genetic programming (GGGP) is an extension of traditional GP systems (Whigham, 1995, pp. 33-41). The difference lies in the fact that they employ context-free grammars (CFG) that generate all the possible solutions to a given problem as sentences, establishing this way the formal definition of the syntactic problem constraints, and use the derivation trees for each sentence to encode these solutions (Dounias, Tsakonas, Jantzen, Axer, Bjerregard & von Keyserlingk, D. 2002, pp. 494-500). The use of this type of syntactic formalisms helps to solve the so-called closure problem (Whigham, 1996). To achieve closure valid individuals (points that belong to the search space) should always be generated. As the generation of invalid individuals slows down convergence speed a great deal, solving this problem will very much improve the GP search capability. The basic operator directly affecting the closure problem is crossover: crossing two (or any) valid individuals should generate a valid offspring. Similarly, this is the operator that has the biggest impact on the process of convergence towards the optimum solution. Therefore, this article reviews the most important crossover operators employed in GP and GGGP, highlighting the weaknesses existing nowadays in this area of research. We also propose a GGGP system. This system incorporates the original idea of employing ambiguous CFG to overcome these weaknesses, thereby increasing convergence speed and reducing the likelihood of trapping in local optima. Comparative results are shown to empirically corroborate our claims.