Minimizing the sum of makespan on multi-agent single-machine scheduling with release dates

Competitive scheduling problems occur in integrated-services packet-switched networks, in which different applications compete for the same resource. Requests of each application arrive over time and contain multiple packets. This process can be described as a multi-agent single-machine scheduling (MSS) problem with release dates, where several packets (jobs) share a common network (processor) but are maintained by several competitive applications (agents) that optimize their criteria. The objective is to minimize the sum of makespans belonging to several agents individually. The NP-hardness of the model indicates that it cannot be optimally solved in polynomial time. For small-scale instances, an effective branch and bound (B&B) algorithm integrated with an elaborately designed pruning rule and a lower bound is developed to achieve exact solutions. Given the quality of service requirements and the periodical maintenance of networks, this problem is generalized to the weighted and periodic maintenance versions, respectively. For the weighted version, a hybrid discrete artificial bee colony (HDABC) algorithm integrated with effective improvement strategies is developed to achieve satisfactory solutions for medium-scale instances. For the periodic maintenance version, a deep reinforcement learning (DRL) method is introduced to obtain high-quality solutions in dynamic situation. Results of computational evaluation demonstrate the effectiveness of the proposed methods