Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Offline and online power aware resource allocation algorithms with migration and delay constraints

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In order to handle advanced mobile broadband services and Internet of Things (IoT), future Internet and 5G networks are expected to leverage the use of network virtualization, be much faster, have greater capacities, provide lower latencies, and significantly be power efficient than current mobile technologies. Therefore, this paper proposes three power aware algorithms for offline, online, and migration applications, solving the resource allocation problem within the frameworks of network function virtualization (NFV) environments in fractions of a second. The proposed algorithms target minimizing the total costs and power consumptions in the physical network through sufficiently allocating the least physical resources to host the demands of the virtual network services, and put into saving mode all other not utilized physical components. Simulations and evaluations of the offline algorithm compared to the state-of-art resulted on lower total costs by 32%. In addition to that, the online algorithm was tested through four different experiments, and the results argued that the overall power consumption of the physical network was highly dependent on the demands’ lifetimes, and the strictness of the required end-to-end delay. Regarding migrations during online, the results concluded that the proposed algorithms would be most effective when applied for maintenance and emergency conditions.Peer ReviewedPreprin

Improving distributed virtual network embedding with offline optimization

To cope with the complexity of the ever changing internet architecture, network virtualization services are vowed to play an important role in the future. To provide such solutions effectively, internet providers face the problem of optimizing the allocation of virtual networks on their physical resources. Since this problem is known to be NP-hard, heuristic based online solutions tend to provide better response time, however they lead to non-optimal solutions. This paper shows how a periodic live migration of virtual networks, using a state provided by offline optimization, can help an internet provider increase its virtual network load by up to 20%. Due to better packing of virtual load, some physical resources can also be shut down to save energy

Network recovery after massive failures

This paper addresses the problem of efficiently restoring sufficient resources in a communications network to support the demand of mission critical services after a large scale disruption. We give a formulation of the problem as an MILP and show that it is NP-hard. We propose a polynomial time heuristic, called Iterative Split and Prune (ISP) that decomposes the original problem recursively into smaller problems, until it determines the set of network components to be restored. We performed extensive simulations by varying the topologies, the demand intensity, the number of critical services, and the disruption model. Compared to several greedy approaches ISP performs better in terms of number of repaired components, and does not result in any demand loss. It performs very close to the optimal when the demand is low with respect to the supply network capacities, thanks to the ability of the algorithm to maximize sharing of repaired resources