A redistricting problem applied to meter reading in power distribution networks

The mixed capacitated arc routing problem with non-overlapping routes

“…In the last one, only the partitioning problem is solved. In some cases, the partitioning is solved keeping in mind that the application is an arc routing problem (Muyldermans et al, 2002(Muyldermans et al, , 2003Perrier et al, 2008;Assis et al, 2014) and in others that the application is on a node routing problem (Mourgaya and Vanderbeck, 2007;Lin and Kao, 2008;Ríos-Mercado and Fernández, 2009;Gonzalez-Ramírez et al, 2011;Jarrah and Bard, 2012;Lei et al, 2012;Salazar-Aguilar et al, 2012).…”

“…Furthermore, the meaning of compactness slightly differs from author to author, being, for instance, associated with: i) zones shapes as close as possible to circles, squares or rectangles (Lin and Kao, 2008;Gonzalez-Ramírez et al, 2011;Jarrah and Bard, 2012); ii) geographically or visually compact zones (Perrier et al, 2008;Lei et al, 2012); or iii) the proximity between the demand entities in the same zone (Poot et al, 2002;Muyldermans et al, 2003;Kim et al, 2006;Tang and Miller-Hooks, 2006;Ríos-Mercado and Fernández, 2009;Salazar-Aguilar et al, 2012;Assis et al, 2014).…”

“…We may find measures based on maximum travel times (Mourão et al, 2009;Gonzalez-Ramírez et al, 2011); on maximum Euclidean distances (Ríos-Mercado and Fernández, 2009;Assis et al, 2014); on the sum of the Euclidean distances (Kim et al, 2006;Mourgaya and Vanderbeck, 2007;Salazar-Aguilar et al, 2012); on the averages and standard deviations of distances, or travel times between customers, or to a reference point in a zone (Poot et al, 2002;Tang and Miller-Hooks, 2006;Mourão et al, 2009); on the perimeters of the zones (Lei et al, 2012); or even perimeters and areas of the zones (Lin and Kao, 2008). Jarrah and Bard (2012) define clusters of clients in the plane in such a way that the ratio of the difference between the maximum and the minimum x coordinate and the difference of the maximum and the minimum y coordinate lies within a given interval.…”

“…In some cases, these evaluation compactness measures are also embedded in the heuristic processes (Kim et al, 2006;Tang and Miller-Hooks, 2006;Ríos-Mercado and Fernández, 2009;Gonzalez-Ramírez et al, 2011;Lei et al, 2012;Salazar-Aguilar et al, 2012;Assis et al, 2014). In other cases, authors devise compactness indicators only embedded in the solution methods (Mourgaya and Vanderbeck, 2007;Lin and Kao, 2008).…”

“…Zones contiguity is generally related to the connectivity between all of its demand entities (Muyldermans et al, 2003;Perrier et al, 2008;Assis et al, 2014) or the possibility to reach all of them within the zone (Ríos-Mercado and Fernández, 2009;Salazar-Aguilar et al, 2012).…”