a b s t r a c tBloat is one of the most widely studied phenomena in Genetic Programming (GP), it is normally defined as the increase in mean program size without a corresponding improvement in fitness. Several theories have been proposed in the specialized GP literature that explain why bloat occurs. In particular, the Crossover-Bias Theory states that the cause of bloat is that the distribution of program sizes during evolution is skewed in a way that encourages bloat to appear, by punishing small individuals and favoring larger ones. Therefore, several bloat control methods have been proposed that attempt to explicitly control the size distribution of programs within the evolving population. This work proposes a new bloat control method called neat-GP, that implicitly shapes the program size distribution during a GP run. neat-GP is based on two key elements: (a) the NeuroEvolution of Augmenting Topologies algorithm (NEAT), a robust heuristic that was originally developed to evolve neural networks; and (b) the Flat Operator Equalization bloat control method, that explicitly shapes the program size distributions toward a uniform or flat shape. Experimental results are encouraging in two domains, symbolic regression and classification of real-world data. neat-GP can curtail the effects of bloat without sacrificing performance, outperforming both standard GP and the Flat-OE method, without incurring in the computational overhead reported by some state-of-the-art bloat control methods. L. Trujillo et al. / Information Sciences 333 (2016) 21-43 problem but also provide insights into the problem domain. Secondly, GP uses a variable length encoding scheme, where the set of candidate solutions contains programs of different size and shape.EC literature contains many examples of the problem solving abilities of GP, that illustrate the flexibility of the search paradigm [8]. Indeed, GP can be understood as a hyper-heuristic, an algorithmic approach for the automatic synthesis of heuristic approaches, a view that has strong theoretical background and real-world applicability [19]. Despite its success, GP is still not used as an off-the-shelf methodology [16], in the way that, for example, Support Vector Machines or Linear Regression are used. This lack of wider acceptance stems from some important pragmatic limitations of the GP approach.In particular, syntactic search can be inefficient, due to its poor local structure and ill-defined fitness landscape (refer to [18] and [22] where the authors reviewed some of the main open issues in GP). Among them, one of the most studied problems is the bloat phenomenon, which occurs when program trees tend to grow unnecessarily large, without a corresponding increase in fitness [21,25]. In some sense, bloat seems to be an unavoidable consequence of the nature of the search space in GP and fitness driven search [11,12]. Moreover, bloat causes several undesirable side effects, since evaluating large programs is more time consuming, and large solutions are more difficult to interpre...
Multidimensional Multiclass Genetic Programming with Multidimensional Populations (M3GP) was originally proposed as a wrapper approach for supervised classification. M3GP searches for transformations of the form k : R p → R d , where p is the number of dimensions of the problem data, and d is the dimensionality of the transformed data, as determined by the search. This work extends M3GP to symbolic regression, building models that are linear in the parameters using the transformed data. The proposal implements a sequential memetic structure with Lamarckian inheritance, combining two local search methods: a greedy pruning algorithm and least squares parameter estimation. Experimental results show that M3GP outperforms several standard and state-of-the-art regression techniques, as well as other GP approaches. Using several synthetic and realworld problems, M3GP outperforms most methods in terms
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