## 2 Problem Definition and Scenario of Application
### State-of-the-Art Methodologies for the TLP  
The recent surge of the TLP during the COVID-19 pandemic has promoted the lack of scientific background in analysing the TLP. However, it is a problem that is very close to the coverage NLP. In the case of the NLP, the objective is to guarantee the coverage of a sensor network meeting the design requirements. Therefore, the solution of this problem entails the location of the sensor nodes in a determined location to ensure an effective link among the target and the sensor nodes in all the coverage range [44].  
This leads to two different optimisation problems: the location of the minimum number of nodes to assure the coverage in all the regions of interest of the sensor network or maximising the system properties for a pre-determined number of sensor nodes. These are exactly the inverse criteria of the TLP: maximising the number of tables in a particular space keeping the social distancing or maximising the distance between the tables for a pre-determined number of tables.  
In addition, the TLP must also be treated as a combinatorial non-linear discontinuous optimisation as the NLP in Non-Line-of-Sight scenarios [45]. Therefore, we can conclude that the bibliography of the NLP is optimal to address the TLP due to the absence of appropriate research at the moment and the closeness of the two problems.  
Although exact solutions to the NLP are proposed in the literature [46], the most extended methodologies are the metaheuristics, due to the huge dimension of the space of solutions. This is also the case for the TLP. The firefly algorithm [47], the grey wolf optimiser [48], GA [49, 50], simulated annealing [51], the elephant herding optimisation [52], cuckoo search [53] or MA [54, 55, 45] have been proposed for the NLP.  
In this paper, we analyse the consideration of the MA for the TLP, which has shown an excellent adaptation to large-scale global optimisation problems [56] which is especially suitable for addressing the TLP. We propose an extended and enhanced methodology for the TLP with regards to our previous research, which first stated the problem and solved it through GAs [37].  
Particularly, GA permits more flexibility for the adaptation to the TLP due to the large number of encodings and genetic operators that we studied in our previous work [37]. In addition, the GA enables a good exploration stage of the space of solutions which allows the finding of potential good locations for the tables which are later enhanced through the GBLS and also allows an optimal control pressure in the hyperparameters of the optimisation to achieve competitive performance in large-scale problems with discontinuities in the fitness function such as the TLP.  
For these reasons, a MA, containing a GA as the base algorithm of the optimisation, has been selected for the TLP instead of other hybridisations of LS with other heuristic algorithms such as particle swarm [57, 58, 59].  
The selection of a GBLS procedure is based on the local derivability of the problem, achieving an improvement of the fitness value of the GA individuals.  
We apply a GBLS procedure based on the local derivability of the problem in order to improve the fitness of the GA individuals.  
This process is applied gradually to the tables of the optimisation from the more promising candidate tables to improve their properties (i.e., minimum distance with the other tables) to the least based on the value of the gradient calculation and we control not to introduce the particular table in a conflict zone with other different tables making the LS procedure ineffective. This allows us to improve our previous results thus supposing a novelty for the TLP.