## 2 Methods
### CUDA Implementation of Greedy Agglomerative Procedures
Nevertheless, obtaining the most accurate results for solving problems, in addition to being of immediate practical importance in the case of a high cost of error, solves the problem of obtaining reference solutions with which the results of other, less computationally expensive algorithms can be compared. As in the case of the k-means problem [74], the most complex dependence of the greedy procedure efficiency on its parameter \(r\) and important advantage of our new algorithm is detected for the largest tested problems (IHEPC dataset) as well as for the problems of \"geographic\" location (Mopsi datasets) with the sets of demand points formed under the influence of natural factors, as well as factors associated with the development of urban infrastructure. For the majority of test problems, our computational experiments demonstrate the advantage of our new algorithm or its approximately equal effectiveness in comparison with known algorithms. For large-scale problem, the effect of our new algorithm is more significant. Nevertheless, even with equal results in comparison with known algorithms, our new Aggl-EA algorithm is a more versatile tool due to its ability of adjusting its parameter in accordance with its behavior. Sometimes, our new algorithm demonstrates less stable results (higher standard deviation of the objective function) which may limit its scope or demands running in multi-start mode. Thus, further study of the causes and factors leading to the instability of the result is required. We considered the use of the self-adjusted agglomerative procedures as the mutation operator of the simplest evolutionary algorithm with no true population of solutions. The efficiency of embedding similar mutation operators (without any self-adjustment) was shown in the paper [96]. Thus, the investigation of the self-adjustment features of other evolutionary operators (first of all, crossover operator of genetic algorithms) is a promising direction for the further research. ## 5 Conclusions

In this article, we introduced the concept of the AGGL\({}_{r}\) neighborhood based on the application of the agglomerative procedure, and investigate the search efficiency in such a neighborhood depending on the parameter \(r\). Using the similarities between local search algorithms and \((1+1)\)-evolutionary algorithms, as well as the ability of the latter to adapt their search parameters, we introduced our new Aggl-EA () algorithm with an embedded greedy agglomerative procedure with the automatically tuned parameter \(r\). Our computational experiments on large-scale and medium-scale problems demonstrate the advantages of the new algorithm in comparison with known algorithms including the algorithms based on greedy agglomerative procedures. Our computational experiments confirmed the proposed working hypotheses and led to the following conclusions:

The agglomerative mutation operator, when used as part of an evolutionary algorithm, is not only able to improve its solutions, moreover, it can also be efficiently used as the only evolutionary operator in the \((1+1)\)-evolutionary algorithm with results outperforming more complex genetic algorithms. Therefore, self-adjustment capability of other evolutionary operators based on agglomerative procedures is a promising direction for the further research. The algorithm with the adjustment of the parameter \(r\) (the number of excess centers to be removed) of the agglomerative procedure shows the most impressive results in the case of solving large problems, as well as problems of a \"geographic\" nature, where many points of demand have a complex structure, formed under the influence of natural factors. Such algorithms, implemented for massively parallel systems, despite the high computational complexity of the embedded agglomerative procedure, ALA-algorithm and Weiszfeld procedure, are capable of solving problems with several million demand points in a reasonable time. Conceptualization, L.K. ; methodology, L.K. and I.R. ; software, L.K. ; validation, I.R. ; formal analysis, L.K. and G.S.