# Local Crossover: A New Genetic Operator for Grammatical Evolution
## 1 Introduction  
Genetic algorithms are stochastic optimization algorithms originated in the work of [PERSON] [1]. They belong to a wide area of optimization algorithms called evolutionary techniques [2]. Genetic algorithms initiate by formulating candidate solutions of the objective problem. These solutions are evolved through a series of processes that mimic natural evolution, such as selection, crossover and mutation [3; 4; 5]. The genetic algorithms were incorporated in a variety of problems, such as networking problems [6], problems arising in robotics [7; 8], energy problems [9; 10], medicine problems [11; 12], agriculture problems [13], etc. Grammatical Evolution [14] is an integer-based genetic algorithm, where each chromosome represents a series of production rules derived from a Backus-Naur form (BNF) grammar [15]. Grammatical Evolution can be utilized to produce programs in the provided programming language. This method was used in a series of cases derived from real-world problems, such as data fitting [16; 17], credit classification [18], detection of network attacks [19], solving differential equations [20], monitoring the quality of drinking water [21], construction of optimization methods [22], application in trigonometric problems [23], composition of music [24], constructing neural networks [25; 26], computer games [27; 28], problems regarding energy demand [29], combinatorial optimization [30], security topics [31], automatic construction of decision trees [32], circuit design [33], discovering taxonomies in Wikipedia [34], trading algorithms [35], bioinformatics [36], modeling glycemia in humans [37], etc. Grammatical Evolution has been extended by many researchers in the recent bibliography. Among these extensions there are works, such as the Weighted HierarchicalGrammatical Evolution [38], which proposed a novel technique to map genotypes to phenotypes, or the method of Structured Grammatical Evolution [39; 40]. Also, [PERSON] et al. suggested the usage of shape grammars in the Grammatical Evolution for evolutionary design [41]. Also, the \(\pi\)Grammatical Evolution method [42] was suggested as a modification of the Grammatical Evolution, where a position-independent mapping was proposed. Another interesting work was the incorporation of Particle Swarm Optimization (PSO) [43] to create expressions in Grammatical Evolution. This method was named Grammatical Swarm [44; 45] in the relevant literature. Moreover, the method of Probabilistic Grammatical Evolution [46] has been introduced recently, where a stochastic procedure was used as a mapping mechanism. Recently, the optimization method of the Fireworks algorithm [47] was applied as a learning algorithm for the Grammatical Evolution procedure [48]. [PERSON] et al. suggested the combination of Grammatical Evolution and some ideas from interval analysis to solve problems with uncertainty [49]. Grammatical evolution has also been extended using programming techniques [50; 51] or Christiansen grammars [52]. Additionally, many researchers have developed and published open source software for Grammatical Evolution, such as the graphical user interface (GUI) application of Grammatical Evolution in Java (GEVA) [53], a Java implementation called jGE [54], an R implementation of Grammatical Evolution under the name gramEvol [55], the GRAPE software version 1.0 that implemented Grammatical Evolution in Python [56], the GeLab [57] software that suggested a Matlab toolbox for Grammatical Evolution, a software which produced classification programs with Grammatical Evolution called GenClass [58], the QFc software version 1.0 [59] was incorporated for feature construction, etc. In this work, a new genetic operator for Grammatical Evolution is introduced, which is derived from the one crossover technique. The new genetic operator is stochastically applied to the genetic population, randomly selecting a set of chromosomes on which to apply it.