# Crossover Operator Inspired by the Selection Operator
###### Abstract  
This paper proposes a novel crossover operator for evolutionary algorithms in task sequencing and verifies its efficacy. Unlike the conventional blind and entirely stochastic selection of sequence fragments exchanged with the second individual, the proposed operator employs a method where the probability of fragment selection is influenced by the total cost of internal connections within the exchanged fragments. At the same time, the new operator retains its stochastic nature and is not a deterministic operator, which reduces the risk of the evolutionary algorithm getting stuck in a local minimum. The idea of the proposed crossover operator was based on the main mechanism of the evolutionary algorithm that determines the success of this type of algorithm selection. To assess its effectiveness, the new operator was compared against previously employed crossover operators using a traveling salesman problem (TSP) instance in a multidimensional space in order to map the problem of symmetric sequencing tasks described with multiparameters (e.g., a symmetric variant of production tasks sequencing). evolutionary algorithm; task sequencing; crossover operator; TSP +
Footnote †: journal: Applied  
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Footnote 1: email: _Applied_  
Footnote †: journal: Applied  
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Footnote 1: email: _Applied_  
orders) or technological reasons. Highly optimized, sophisticated algorithms dedicated to the classic TSP problem do not provide such an opportunity. Such freedom, the ability to take into account various constraints and freely define multifaceted optimization criteria, is provided by evolutionary algorithms. Therefore, despite their possibly lower efficiency (compared with the above-mentioned dedicated algorithms), they find practical applications in industrial IT systems. This justifies the search for ways to increase their effectiveness. The evolutionary algorithm consists of three basic operators: selection, crossover, and mutation [13]. In the case of chromosome-modifying operators (crossover and mutation), it should be emphasized that the methods of implementing these operators are entirely distinct in classical problems--where genes (binary, integer, or real) with fixed positions define solution parameters--and in sequencing problems, where the order of nodes is rearranged. Researchers are continually developing new variations in these operators for sequencing problems. Focusing on crossover operators, two classic methods, single-point crossover and two-point crossover [14; 15; 16], which involve creating children by cutting the parents' chromosomes in one or two randomly selected places, are still very popular. Articles [14; 17] proposed extending the commonly used crossover methods to a multipoint form, presenting methods such as N-point crossover [17] and uniform crossover [14]. The uniform crossover method was then modified by [18] to the three-parent uniform crossover version. Among the classic, general crossover operators, another noteworthy method is the arithmetic crossover [19] method, which is dedicated to encoding real numbers. Its operating principle is to define a linear combination of two parents. In addition to the above crossover methods, many methods specially dedicated to TSP problems have also been proposed. According to [20; 21], the classic and most frequently used methods from this group are partially mapped crossover, PMX [22], ordered crossover, OX [23] and cycle crossover, CX [24], which apart from randomly determining intersection points and exchanging fragments of the parent sequences, they also have built-in repair algorithms. The need for their use in TSP class problems results from damage to individuals resulting from the crossover operation. The mentioned damage consists of both missing and duplicate genes (cities) in the offspring [20].