# Crossover Operator Inspired by the Selection Operator
###### Abstract
The edge recombination crossover is based on the concept of neighborhood, ERX [25], generalized N-point crossover, GNX [26], tie-break crossover, TBX [27], MOX [28], Moon Crossover, MX [29; 30] proposed combining PMX and TBX operators, modification of the OX operator Non-Wrapping Order Crossover, NWOX [31], two-part chromosome crossover, TCX [32], modification of the CX Modified-Cycle Crossover Operator, CX2 [33], modifications of the classic PMX method like PMX2 [34], IMPX [35], completely mapped crossover, CMX [36]. It should be emphasized that all the crossover methods mentioned above are characterized by random selection of sequence fragments and intersection points during the crossover operation. In addition to these random methods, the literature also presents many proposals for deterministic crossover based on distances, such as Greedy Crossover, GX and Heuristic Crossover, HX [37], which select a random starting city and then select the next gene based on the distances to neighboring cities in parents. In the paper [38], the authors proposed a modification of the HX algorithm called Modified Heuristic Crossover, MHX, which introduces an improvement in the selection of the next city in the event of a loop. However, the GX method has been modified by [39] as a Very Greedy Crossover, VGX, which modifies the behavior of the original method in case the nearest neighbor found causes a loop. In such a situation, GX selects a random city and VGX tries to select additional neighbors that are located at further distances. The Neighborhood Relationship Crossover methods, NRX [28], and the sequential constructive crossover, SCX [40], which brings very good results, similarly to the previous ones, also base the selection of the next gene on the distances of the neighbors of the current city in the crossed parents. Proposed by [41], Ordered Distance Vector, ODV, uses the ODV matrix and focuses on individual initialization techniques, and its improved version of the ODV-based crossover operator, ODVX in [42] additionally uses the multiparent technique [43] and modifies and extendsthe failure reduction method described in [43]. The algorithm by [21], which uses the Crossover Neighbor algorithm, CNN, and Sequential Insertion algorithm, CSI [21], also achieves good results. The authors of [44] have developed an algorithm that stepwise compares subsequent parent sequences. As presented above, newer crossover methods for TSP are being developed. However, it is worth noting that they are mainly based on complete randomness or, on the contrary, fully deterministic selection of the best fragments of the parental sequence. However, random algorithms require a large number of iterations to find a solution. In contrast, deterministic algorithms are at risk of getting stuck in a local minimum. This paper proposes and confirms the effectiveness of a new crossover operator for evolutionary algorithms that implement task sequencing. This operator is inspired by a mutation operator previously proposed in [45]. In this mutation operator, the probability of selecting the cut site within a sequence is proportional to the cost of transition between adjacent tasks. Building on this principle, the proposed new crossover operator deviates from the usual blind and completely stochastic selection of the sequence fragment exchanged with the second individual. Instead, it employs a method where the probability of sequence selection is linked to the total cost of internal connections in the exchanged sequence fragment. Therefore, the proposed method is an intermediate solution between completely random and completely deterministic crossover. As part of the performance assessment, the new crossover method was compared with the efficient, well-known random crossover methods PMX [22], OX [23], Single-Point Crossover [14; 15] and the newer deterministic SCX method [40]. The authors of [46; 47] indicated the SCX method as one of the most effective for TSP problems.