### State-of-the-Art
The crossover operator recombines the elements (\"genes\") of two parent solution for generating a new (\"offspring\") solution. One-point and two-point crossover which are standard for many other genetic algorithms have been proved to present drawbacks when applied to problems such as k-means and p-median problems [69] due to generating the offspring solutions too far from their parents. The GAs with the greedy agglomerative crossover operator demonstrates better results [58; 70; 71]. In this crossover operator, as well as in the IBC algorithms [53; 54], the number of centers is successively reduced down to the desired number p. Being originally developed for the network p-median problems, they were adapted for continuous p-median and k-means problems [72]. Metaheuristic approaches, such as genetic algorithms [73], are aimed at finding the global optimum. However, in large-scale instances, such approaches require very significant computational costs, especially if they are adapted to solving continuous problems [58]. The greedy agglomerative procedure is a computationally expensive algorithm, especially in the case of continuous problems when it includes multiple execution of a local search algorithm. However, this procedure allows us to find solutions that are difficult to improve by other methods without significantly increasing the calculation time. The concept of the usage of greedy agglomerative procedures as the crossover operator in genetic algorithms is as follows. First, for two selected parent solutions (sets of medians) \(S_{1}\) and \(S_{2}\), the algorithm constructs an intermediate solution \(S^{\prime}\) adding \(r\) randomly selected medians (centers) from the second parent solution \(S_{2}\) to the first solution \(S_{1}\): \(S^{\prime}=S_{1}\cup~{}S_{2}^{\prime\prime}\). Here, \(S_{2}^{\prime\prime}\) is a randomly chosen subset of \(S_{2}\), \(\mid S_{2}\mid=r\). Integer parameter \(r\) can be given in advance (often, \(r=1\) or \(r=p\)). After improving this new intermediate solution with the ALA or local search algorithm, one or more excessive medians are removed until \(\mid S^{\prime}\mid=p\). At each iteration, the greedy agglomerative procedure removes such a median that its elimination results in the least significant increase of the objective Function (1). In [74], the authors systematized approaches to constructing algorithms for searching in neighborhoods (denoted as GREEDY\({}_{\rm r}\)) formed using greedy algorithmic procedures for the k-means problem. Searching in SWAP and GREEDY\({}_{\rm r}\) neighborhoods has advantages over the simplest Lloyd's procedure [75; 76]. However, the results strongly depend on the parameter of the greedy agglomerative procedures, and the optimal values of these parameters differ significantly for test problems. However, the GREEDY\({}_{\rm r}\) search outperforms the SWAP search in terms of accuracy. Moreover, such algorithms often outperform more complex genetic algorithms. Embedding the computationally expensive greedy agglomerative procedures into metaheuristics is even more computationally expensive, which limits the application of such a combination of algorithms to large problems. Nevertheless, the development of massively parallel systems expands the capabilities of such algorithmic combinations [74; 77]. The \((1+1)\)-evolutionary algorithms or \((1+1)\)-EAs are similar with the local search and VNS algorithms but they have no clearly defined neighborhood; therefore, they can reach in one single step any point in the search space [78]. Unlike genetic algorithms, in \((1+1)\)-EAs, there is no true population of solutions, and usually, they successively improve a single current solution with the application of the mutation operator to it. In an \((1+1)\)-evolutionary algorithm [78] for pseudo-Boolean optimization problems, the bitwise mutation operator flips each bit independently of the others with some probability \({\rm p}_{\rm m}\) that depends on the length of the bit string.