Lately, a lot of research has been conducted on the automatic design of artificial neural networks (ADANNs) using evolutionary algorithms, in the so-called neuro-evolutive algorithms (NEAs). Many of the presented proposals are not biologically inspired and are not able to generate modular, hierarchical and recurrent neural structures, such as those often found in living beings capable of solving intricate survival problems. Bearing in mind the idea that a nervous system's design and organization is a constructive process carried out by genetic information encoded in DNA, this paper proposes a biologically inspired NEA that evolves ANNs using these ideas as computational design techniques. In order to do this, we propose a Lindenmayer System with memory that implements the principles of organization, modularity, repetition (multiple use of the same sub-structure), hierarchy (recursive composition of sub-structures), minimizing the scalability problem of other methods. In our method, the basic neural codification is integrated to a genetic algorithm (GA) that implements the constructive approach found in the evolutionary process, making it closest to biological processes. Thus, the proposed method is a decision-making (DM) process, the fitness function of the NEA rewards economical artificial neural networks (ANNs) that are easily implemented. In other words, the penalty approach implemented through the fitness function automatically rewards the economical ANNs with stronger generalization and extrapolation capacities. Our method was initially tested on a simple, but non-trivial, XOR problem. We also submit our method to two other problems of increasing complexity: time series prediction that represents consumer price index and prediction of the effect of a new drug on breast cancer. In most cases, our NEA outperformed the other methods, delivering the most accurate classification. These superior results are attributed to the improved effectiveness and efficiency of NEA in the decision-making process. The result is an optimized neural network architecture for solving classification problems.