Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements.

As an intelligent search optimization technique, genetic algorithm (GA) is an important approach for non-deterministic polynomial (NP-hard) and complex nature optimization problems. GA has some internal weakness such as premature convergence and low computation efficiency, etc. Improving the performance of GA is a vital topic for complex nature optimization problems. The selection operator is a crucial strategy in GA, because it has a vital role in exploring the new areas of the search space and converges the algorithm, as well. The fitness proportional selection scheme has essence exploitation and the linear rank selection is influenced by exploration. In this article, we proposed a new selection scheme which is the optimal combination of exploration and exploitation. This eliminates the fitness scaling issue and adjusts the selection pressure throughout the selection phase. The \(\chi ^2\) goodness-of-fit test is used to measure the average accuracy, i.e., mean difference between the actual and expected number of offspring. A comparison of the performance of the proposed scheme along with some conventional selection procedures was made using TSPLIB instances. The application of this new operator gives much more effective results regarding the average and standard deviation values. In addition, a two-tailed t test is established and its values showed the significantly improved performance by the proposed scheme. Thus, the new operator is suitable and comparable to established selection for the problems related to traveling salesman problem using GA.

Genetic algorithms (GAs) are stochastic-based heuristic search techniques that incorporate three primary operators: selection, crossover, and mutation. These operators are supportive in obtaining the optimal solution for constrained optimization problems. Each operator has its own benefits, but selection of chromosomes is one of the most essential operators for optimal performance of the algorithms. In this paper, an improved genetic algorithm-based novel selection scheme, i.e., stairwise selection (SWS) is presented to handle the problems of exploration (population diversity) and exploitation (selection pressure). For its global performance, we compared with several other selection schemes by using ten well-known benchmark functions under various dimensions. For a close comparison, we also examined the significance of SWS based on the statistical results. Chi-square goodness of fit test is also used to evaluate the overall performance of the selection process, i.e., mean difference between observed and expected number of offspring. Hence, the overall empirical results along with graphical representation endorse that the SWS outperformed in terms of robustness, stability, and effectiveness other competitors through authentication of performance index (PI).

A round-robin tournament is a contest where each and every player plays with all the other players. In this study, we propose a round-robin based tournament selection operator for the genetic algorithms (GAs). At first, we divide the whole population into two equal and disjoint groups, then each individual of a group competes with all the individuals of other group. Statistical experimental results reveal that the devised selection operator has a relatively better selection pressure along with a minimal loss of population diversity. For the consisting of assigned probability distribution with sampling algorithms, we employ the Pearson’s chi-square and the empirical distribution function as goodness of fit tests for the analysis of statistical properties analysis. At the cost of a nominal increase of the complexity as compared to conventional selection approaches, it has improved the sampling accuracy. Finally, for the global performance, we considered the traveling salesman problem to measure the efficiency of the newly developed selection scheme with respect to other competing selection operators and observed an improved performance.

Selection criteria, crossover and mutation are three main operators of genetic algorithm's performance. A lot of work has been done on these operators, but the crossover operator has a vital role in the operation of genetic algorithms. In literature, multiple crossover operators already exist with varying impact on the final results. In this article, we propose two new crossover operators for the genetic algorithms. One of them is based on the natural concept of crossover i.e. the upcoming offspring takes one bit from a parent and next from other parent and continuously takes bits till last one. The other proposed scheme is the extension of two-point crossover with the concept of multiplication rule. These operators are applied for eight benchmark problems in parallel with some traditional crossover operators. Empirical studies show a remarkable performance of the proposed crossover operators.

As an intelligent search technique, genetic algorithm (GA) is a key member of optimization research methods. Motivated by the ability of GA in resolving complex and non‐deterministic polynomial (NP‐hard) problems, this research proposes a new operator namely, completely‐ mapped crossover (CMX) operator to facilitates the search of optimal solutions. Under a very general setting of the state‐of‐the‐art parameters, the performance of newly proposed method is explored with respect to five vibrant and most commonly used techniques existent in the literature. Furthermore, the generality of the applicability of contemporary techniques is maintained by considering eighteen benchmarks from the library of traveling salesman problem (TSPLIB), possessing different levels of complexity. Based on diverse performance assessment criteria, we observe that propose method outperforms the contemporary alternatives.