## 5 Optimization Problems with Synchronization Issues  
Problems with synchronization have attracted much attention in research related to the behavior of complex networks. The ability of a network to synchronize depends on many factors and parameters associated with its structure [30]. There are many examples in the industry today where event synchronization plays an important role in ensuring the efficient functioning of a network or system. Generally, the application of BR-DEH algorithms targets all those problems characterized by synchronization issues. These scenarios are typically characterized by three aspects: (i) a high coefficient of dynamism; (ii) a limited number of elements or resources; and (iii) a set of events whose triggering and succeeding depend on each other. In particular, the triggering of an event can depend on the succeeding of one or more other events, and the succeeding of an event may give rise to other events not scheduled before. In these cases, the integration of DES in a biased-randomized algorithm is essential to model the system and verify with consistency and accuracy the effects of each decision made by the heuristic [31]. In this section, we give an overview of the main optimization problems with synchronization issues, where the implementation of the BR-DEH strategy is suggested as a natural and effective solving procedure. In manufacturing, flow-shop and job-shop optimization problems might require the implementation of a BR-DEH in scenarios characterized by dependencies on machines, resources, and unpredictable inconveniences such as machine failures and down-times. For instance, it is frequent to have a flow shop in which the processing time on a machine depends on the jobs that the machine processed before. This dependency is usually because of tool wear and setup times. In job shops, there are situations in which machines require operators (or resources). A limited number of operators (or resources) are shared between all machines, moving from one machine to another according to their necessity. Both flow shops and job shops can be solved using a BR-DEH when influenced by unpredictable events, such as machine failures or the arrival of unscheduled jobs. An example of a real problem encountered in the literature is processing different jobs by a series of machines modeled as a hybrid flow-shop problem with several additional and realistic constraints [32]. Another example is on-demand production systems when a workflow has parallel processes, specific machine loops or re-entry cycles, in which jobs may re-enter specific processes at some point in the flow-shop chain [33]. Similarly, semiconductor manufacturing can be modeled as a hybrid flow-shop problem with time dependencies and priority constraints [34]. In logistics and transportation, vehicle routing problems with synchronization are addressed and associated with different real-life cases. The adoption of BR-DEH algorithms is suggested when the interference among vehicles is not negligible. This is true for transportation problems related to last-mile delivery networks [35; 36; 37], omnichannel vehicle routing [31], or home healthcare services [38; 39] with traffic and precedence constraints, among others [40]. They are also seen in internal logistics when optimizing paths traveled by AGVs [41]. This involves many well-known operations research problems, such as path finding, minimum spanning tree, traveling salesman problem, and many else. Transportation problems usually face situations characterized by sudden events, such as changes in delivery points or requests and necessities to reorganize the routes. The high dynamism makes them a suitable target for BR-DEH algorithms. A realistic example studied by [PERSON] et al. [42] shows the dynamism of modern transport systems. They present the problem of transporting containers through interconnected networks. Containers are transported from origin to their final destinations on or before a given time frame and may be temporarily stored at network hubs.