The SET COVERing PROBLEM (SCP) is a well-known combinatorial optimization PROBLEM. This paper investigates development of a local branching-based solution approach for the SCP. This solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. The algorithm parameters are tuned by design of experiments approach. The proposed method is tested on the several standard instances. The results show that the algorithm outperforms the best heuristic approaches found in the literature.

An eigen fuzzy SET of a fuzzy relation is often invariant under di, erent computational aspects. The present research introduces a novel concept of eigen spherical fuzzy SET of spherical fuzzy relations along with various composition operators for the , rst time. This study proposed two algorithms to determine the greatest eigen spherical fuzzy SETs and least eigen spherical fuzzy SETs using the max 􀀀,min and min 􀀀,max composition operators, respectively, and illustrated the steps through ow charts. Further, two numerical examples related to di, erent , elds of decision-making PROBLEMs were taken into account for illustrating the proposed methodology. The scope of future work in the , eld of image information retrieval, genetic algorithm for image reconstruction, and notion of eigen spherical fuzzy soft SETs/matrices was duly outlined. The comparative remarks and advantages of the proposed eigen spherical fuzzy SETs were also included for better readability.

Software Defined Network (SDN) is an emerging architecture that can overcome the challenges facing traditional networks. SDN enables administrator/operator to build a simpler and manageable network. New SDN paradigms are encouraged to deploy multiple (rather than centralized) controllers to monitor the entire network. The controller placement PROBLEM is one of the key issues in SDN that affect all its aspects including scalability, convergence time, fault tolerance, and node to controller latency. Many researchers focus on solving this PROBLEM by trying to optimize the location of an arbitrary number of controllers. The related works in this area get less attention to two following important issues: i) Bidirectional end-to-end latency between the switch and its controller instead of propagation latency and ii) finding the minimal number of controllers, which is a prerequisite for locating them. In this paper, we propose a SET COVERing Controller Placement PROBLEM Model (SCCPPM) in order to find the least number of required controllers with respect to carrier-grade latency requirement. The proposed model is carried out on a SET of 124 graphs from the Internet Topology Zoo and solve them with IBM ILOG CPLEX Optimization package. Our results indicate that the number of required controllers for high resilient network is dependent on topology and network size. Moreover, to achieve carrier-grade requirement, 86% of topologies must have more than one controller.

This paper addresses a drayage PROBLEM, which is motivated by the case study of a real carrier. Its trucks carry one or twocontainers from a port to importers and from exporters to the port. Since up to four customers can be served in each route, we propose a SET-COVERing formulation for this PROBLEM where all possible routes are enumerated. This model can beefficiently solved to optimality by a commercial solver, significantly outperforming a previously proposed node-arcformulation. Moreover, the model can be effectively used to evaluate a new distribution policy, which results in anenlarged SET of feasible routes and can increase savings w. r. t. the policy currently employed by the carrier.

In hierarchical service networks, facilities at different levels provide different types of service. For example, in health care systems, general centers provide low-level services, such as primary health care, while specialized hospitals provide high-level services. Because of the demand congestion at service networks, the location of servers and their allocation of demand nodes can have a strong impact on the length of the queue at each server, as well as on the response time to service calls. This study attempts to develop hierarchical location-allocation models for congested systems by employing a queuing theory in a fuzzy framework. The parameters of each model are approximately evaluated and stated as fuzzy-numbers. The COVERage of demand nodes is also considered in an approximate manner and is stated by the degree of membership. Using queuing theory and fuzzy conditions, both referral and nested hierarchical models are developed for the Location SET COVERing PROBLEM (LSCP). To demonstrate the performance of the proposed models, a numerical example is solved in order to compare the results obtained from the existing probabilistic models and the new fuzzy models developed in this paper.