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This paper aims to describe two enhancements of the variable neighbourhood search (VNS) algorithm to solve efficiently the minimum interference frequency assignment problem (MI-FAP) which is a major issue in the radio networks, as well as a well-known NP-hard combinatorial optimisation problem. The challenge is to assign a frequency to each transceiver of the network with limited or no interferences at all. Indeed, considering that the number of radio networks users is ever increasing and that the radio spectrum is a scarce and expensive resource, the latter should be carefully managed to avoid any interference.

The authors suggest two new enhanced VNS variants for MI-FAP, namely, the iterated VNS (It-VNS) and the breakout VNS (BVNS). These two algorithms were designed based on the hybridising and the collaboration approaches that have emerged as two powerful means to solve hard combinatorial optimisation problems. Therefore, these two methods draw their strength from other meta-heuristics. In addition, the authors introduced a new mechanism of perturbation to enhance the performance of VNS. An extensive experiment was conducted to evaluate the performance of the proposed methods on some well-known MI-FAP datasets. Moreover, they carried out a comparative study with other metaheuristics and achieved the Friedman’s non-parametric statistical test to check the actual effect of the proposed enhancements.

The experiments showed that the two enhanced methods (It-VNS) and (BVNS) achieved better results than the VNS method. The comparative study with other meta-heuristics showed that the results are competitive and very encouraging. The Friedman’s non-parametric statistical test reveals clearly that the results of the three methods (It-VNS, BVNS and VNS) are significantly different. The authors therefore carried out the Nemenyi’s post hoc test which allowed us to identify those differences. The impact of the operated change on both the It-VNS and BVNS was thus confirmed. The proposed BVNS is competitive and able to produce good results as compared with both It-VNS and VNS for MI-FAP.

Approached methods and particularly newly designed ones may have some drawbacks that weaken the results, in particular when dealing with extensive data. These limitations should therefore be eliminated through an appropriate approach with a view to design appropriate methods in the case of large-scale data.

The authors designed and implemented two new variants of the VNS algorithm before carrying out an exhaustive experimental study. The findings highlighted the potential opportunities of these two enhanced methods which could be adapted and applied to other combinatorial optimisation problems, real world applications or academic problems.

This paper aims at enhancing the VNS algorithm through two new approaches, namely, the It-VNS and the BVNS. These two methods were applied to the MI-FAP which is a crucial problem arising in a radio network. The numerical results are interesting and demonstrate the benefits of the proposed approaches in particular BVNS for MI-FAP.

The purpose of this study is to examine herd behaviour under different market conditions, examine the potential impact of the firm size and stock characteristics on this relationship, and explore how herding affects market prices in the German market.

The authors apply a method that does not rely on theoretical models, thus eliminating the biases inherent in their application. This technique is based on the assumption that macro herding manifests itself in the synchronicity (comovement) of stock returns.

The study’s findings show that herding is more pronounced in down markets and is more pronounced when market returns reach extreme levels. Additionally, the authors have found that there is stronger herding among large companies compared to small companies, and that stock characteristics considered have no effect on the degree of macro herding. Results also suggest that the contemporaneous market-wide information drives macro herding and that macro herding facilitates the incorporation of market-wide information into prices.

The study’s results strongly support the idea of directional asymmetry, which holds that stocks react quickly to negative macroeconomic news while small stocks react slowly to positive macroeconomic news. Additionally, the study’s results suggest that the contemporaneous market-wide information drives macro herding and that macro herding facilitates the rapid incorporation of market-wide information into prices.

To the best of the researchers’ knowledge, this is the first study that examines macro herding for a major financial market using a herding measure based on the co-movement of returns that does not rely on theoretical models.