Efficient Implementations of Heuristics for Routing and Wavelength Assignment

In this paper a novel approach for modelling Routing and Wavelength Assignment (RWA) problem in wavelength-routed Dense Wavelength Division Multiplexing (DWDM) optical networks is proposed. A new idea based on Artificial Bee Colony (ABC) algorithm is introduced for solving RWA problem which is known to be an NP-hard problem. In the proposed ABC-RWA approach every food source represents a possible and feasible lightpath between each original and destination node pair in demand matrix. The positions of food sources are modified by some artificial bees in the population where the aim is to discover the places of food sources. The food source with the highest nectar value seems to be a solution which is evaluated by the fitness function. The simulation results demonstrate the ability and efficiency of proposed approach for solving RWA in real-world optical networks. The proposed approach could be extended for dynamic RWA schemes in real-time applications and employed by network resilience architectures.

In this paper, we compare performance of fixed-grid Wavelength Division Multiplexing (WDM) and Elastic Optical Networks (EONs) in dynamic provisioning of many-to-many (m2m) flows. Currently, with a growth of services relying on many-to-many communication paradigm such as distributed computing, inter-Data Center communication, content delivery networking or other requiring high-bandwidth in group communication, it is vital to deliver new solutions facilitating these demanding transmissions. Therefore, the authors investigate provisioning of m2m traffic in high-performance optical networks. This work focuses on dynamic Routing and Wavelength Assignment (RWA) problem in WDM networks as well as Routing and Spectrum Allocation (RSA) problem in EONs for m2m flows using replicated communication through auxiliary rendezvous servers.

We address the issue of inapproximability of the wavelength assignment problem in wavelength division multiplexing (WDM) optical networks. We prove that in an n-node WDM optical network with m lightpaths and maximum load L, if NP ≠ ZPP, for any constant δ>0, no polynomial time algorithm can achieve approximation ratio n1/2−δ or m1−δ, where NP is the class of problems which can be solved by nondeterministic polynomial time algorithms, and ZPP is the class of problems that can be solved by polynomial randomized algorithms with zero probability of error. Furthermore, the above result still holds even when L=2. We also prove that no algorithm can guarantee the number of wavelengths to be less than $$(\sqrt{n}/2)L$$ or (m/2)L. This is the first time inapproximability results are established for the wavelength assignment problem in WDM optical networks. We also notice the following fact, namely, there is a polynomial time algorithm for wavelength assignment which achieves approximation ratio of O(m(log log m)2/(log m)3). Therefore, the above lower bound of m1−δ is nearly tight.

The routing and wavelength assignment (RWA) problem is a classic and challenging problem in wavelength-division multiplexing (WDM) optical networks and has shown to be NP-hard. This paper studies the min-RWA problem with the objective of minimizing the number of required wavelengths and presents a new powerful neighborhood called Shift-and-Shaking (SAS). The proposed SAS integrates a high-level shift move to change the wavelength of one lightpath and two low-level ejection chain-based shaking (ECS) procedures to find the best routings for the related lightpaths. This new neighborhood is embedded into a simple iterated local search algorithm, called SAS-ILS, for solving min-RWA. The proposed SAS-ILS is tested on three sets of totally 113 widely studied instances in the literature. Comparison with other state-of-the-art algorithms shows that the SAS-ILS is able to improve 22 previous best known results, while matching the best known results for the remaining ones within short computational time.

This paper proposes the optimal design of lightpath Routing and Wavelength Assignment (RWA) problem in Wavelength Division Multiplexing (WDM) networks without wavelength conversion. We formulate RWA as a mixed Integer Linear Programming (ILP) problem where the objective is to minimize the cost of wavelength assignment to the fiber links in the network. The Lagrangean relaxation technique and the optimization-based heuristics are used to solve this problem. Two sets of computational experiments are performed to test the algorithms for the maximum carried traffic and minimum wavelength requirements in three different network topologies (GTE, ARPA, OCT network). Based on solution quality to the computational experiments, the error gaps between the upper bound and the lower bound are close enough that the near optimal solutions could be obtained. On the other hand, we also show that the solution quality degrade gracefully under more and more heavy traffic network environment. By assessing solution quality and the computational time, we propose the efficient and effective optimization-based algorithms based on the Lagrangean relaxation method for the RWA problem in the WDM networks without wavelength conversion.

In a many-to-many session, a participant distributes and receives traffic flows to/from all others in the same session. It is desirable to achieve both high resource utilization and low power consumption when such sessions are provisioned. In wavelength division multiplexing (WDM) optical networks, traffic grooming has been widely applied as the key technology for aggregating sessions to improve resource utilization. However, the current many-to-many grooming approaches, the lightpath circle and hubbed light-tree, do not make an effort to reduce the power consumption of many-to-many sessions. In this paper, we formulate the green routing and aggregation of many-to-many sessions problem and prove its NP-completeness. For problem solving in WDM optical networks, we apply a rational combined method of lightpaths. Both an integer linear programming-based approach and a novel graph-based heuristic are devised. We further provide an illustrative comparison between our heuristic and the existing benchmarks in terms of power consumption. Extensive simulation results demonstrate that, compared with the benchmarks, our heuristic improves the average power efficiency in the range of 13-19%.

In the past few decades, the architecture of optical networks has undergone significant evolution, from the earliest wavelength-division multiplexing (WDM) optical networks to elastic optical networks (EONs) and later to space-division multiplexing (SDM) EONs, to address the continuous growth of Internet traffic. By 2024, Pbps-level optical networks are expected, far exceeding the capacity limit of single-mode fibers. The massive SDM era is on the horizon. In this context, a newly designed architecture for optical networks called the spatial channel network (SCN) architecture, which achieves high cost efficiency by means of practical hierarchical optical cross-connects, has recently been proposed. However, the evolution of optical network architectures will simultaneously present challenges related to network optimization. For instance, with the evolution from WDM optical networks to EONs, the kernel network optimization problem was transformed from the routing and wavelength assignment (RWA) problem into the routing and spectrum assignment (RSA) problem due to the additionally introduced constraint of spectrum contiguity. Similarly, specially designed algorithms are also expected to be essential for addressing the network optimization problem in SCNs. In this paper, we define this new problem as the routing, spatial channel, and spectrum assignment (RSCSA) problem. We propose an integer linear programming (ILP) model and a heuristic algorithm to solve the RSCSA problem. We examine the performance of the proposed approaches via simulation experiments. The results show that both proposed approaches are effective in finding the optimal solutions or solutions close to the lower bounds. To the best of our knowledge, this is the first work to focus on the network optimization problem in SCNs.

We study the problem of providing real-time service to hard and soft real-time messages in wavelength division multiplexing (WDM) optical networks. We propose and evaluate a set of scheduling algorithms which schedule message transmissions in single-hop WDM passive star networks based on specific time constraints. We compare the performances of our algorithms with that of the typical WDM scheduling algorithm which does not consider the time constraint of the transmitted messages by discrete-event simulations and an analytical model. We find that the improvement on real-time performance can be attributed to our scheduling algorithms where the time constraint of messages has been taken into consideration. This study suggests that when scheduling real-time messages in WDM networks, one has to consider not only the problem of resources allocation in the network but also the problem of sequencing messages based on their time constraints.

Multicast routing for wavelength division multiplexing optical network is a challenging problem in optical networks. The Multicast Routing and Wavelength Assignment (MRWA) problem has been proved to be a NP complete problem. In this paper, the MRWA problem in Wavelength Division Multiplexing (WDM) has been modeled as a Multi-Objective Multicast Routing and Wavelength Assignment (MOMRWA) optimization problem with three optimization objectives, including minimizing the resource cost, minimizing the end-to-end delay and minimizing the used channels. Some Quality of Service metrics have also been considered in MOMRWA. To tackle the MOMRWA problem, a multi-objective genetic algorithm, namely MRWA_SSNSGA-II, has been proposed, which is based on the Steady-State Non-Dominated Sorting Genetic Algorithm II combined with the Efficient Non-Domination Level Update (ENLU) strategy. The purpose of the ENLU strategy is to reduce the computing time of maintaining the Non-Domination Level structure. In order to avoid the loop generated by the gene recombination, a light tree recovery mechanism based on the Minimum Path Cost Heuristic has been proposed. We evaluate our proposed MRWA_SSNSGA-II on a large number of test instances with different sizes. Experimental results demonstrate that MRWA_SSNSGA-II outperformed some recent GA based multi-objective optimization algorithms for MOMRWA problem in terms of the solution quality.

Fast Fourier Transform(FFT) represents a common communication pattern shared by a large class of scientific and engineering problems and wavelength assignment is a key issue to increase efficiency and reduce cost in Wavelength Division Multiplexing (WDM) optical networks. In this paper, we propose a new scheme for the wavelength assignment of parallel FFT communication pattern on WDM linear arrays. By lattice embedding, the number of wavelengths required to realize parallel FFT communication pattern on WDM linear arrays significantly improves the known result. Our proposed embedding method also provides a new approach to the hypercube layout problem considering connections dimension by dimension rather than all connections as in the traditional approach.

In WDM networks, static Routing Wavelength Assignment (RWA) problem is NP-complete. The Integer Linear Programming (ILP) is too complicated to implement. In most existing algorithms, it is usually split into routing and wavelength assignment, which is not completely precise. Mainly motivated by that imprecision, the Layered-Graph model was introduced into static RWA problem, which can consider the routing and wavelength assignment jointly. Three proposed algorithms using this model are described in this paper. Their performances are also evaluated by series of exhaustive simulations.

The widespread deployment of wireless telecommunication networks and growing Internet traffic globally leads to a substantial increase in signal traffic demands in fiber optic networks. This demand surge places significant pressure on the survivability of optical networks, specifically when faced with fiber cable failures that prevent failed optical fibers from satisfying connection requests. To address this challenge, in this paper, we consider integrated planning of regenerator installation, optical connection routing, and wavelength assignment (RWA) for wavelength division multiplexing (WDM) optical networks under link failures. To the best of our knowledge, we are the first to consider such an integrated problem. We minimize the number of backup regenerators required to fulfill all connection requests under all potential link failures while accounting for the wavelength and routing constraints. We formulate the problem as an integer program, while its size exponentially increases with the network size by nature. To solve large-scale instances for practical uses in the industry, we propose efficient algorithms to generate near-optimal solutions that are practically implementable. We perform extensive numerical experiments to demonstrate the effectiveness of our approach in solving real-world instances provided by our industry partners. The results show that our approach can efficiently obtain high-quality solutions while ensuring a minimal increase in backup regenerators as the network grows. Our solutions also offer valuable insights into planning a cost-effective and reliable fiber optic network for network operators.

To utilize the wavelength resources of Internet protocol (IP) over wavelength division multiplexing (WDM) optical networks, a multi-constrained multicast traffic grooming algorithm is proposed in this paper. This algorithm can achieve multicast traffic grooming in IP over WDM optical networks under multi-constraints, including the number of optical transceivers, wavelength conversion capability and wavelength splitting capability. We simulated the traffic grooming algorithm using the topology of GEANT. Emulation results show that our algorithm has a lower blocking proportion compared with the multi-hop traffic grooming algorithm, which can achieve multicast traffic grooming more effectively.

In general, multicast routing and wavelength assignment (MC-RWA) can be subdivided in routing and wavelength assignment issues in wavelength-division multiplexing (WDM) mesh networks. Previous studies on WDM multicast have mainly focused on WDM multicast routing. The multicast wavelength assignment problem is studied in this paper. A unicast routing path can be established by a lightpath in an all-optical network. However, in the multicasting case, a multicast routing tree can be established by a single light-tree or several lightpaths, or a combination of several light-trees and lightpaths. We propose a wavelength assignment algorithm for finding an optimal combination of lightpaths and light-trees to construct a newly required multicast session. First of all, two cost functions are given to evaluate the establishing cost for each feasible wavelength, and then find a set of wavelengths that covers all destinations with the minimal cost using Integer Linear Programming (ILP) formulation. We focus on maximizing the total number of users served in a multicast session and the network capacity. The simulation results show that the proposed algorithm can improve system resource utilization and reduce the blocking probability compared with the First-Fit algorithm.

A fundamental problem in computer and communication networks is the wavelength assignment (WA) problem: given a set of routing paths on a network, assign wavelengths (channels) to the paths such that the paths with the same wavelength are edge-disjoint. The optimization problem here is to minimize the number of wavelengths. A popular network topology is a tree of rings. It is known NP-hard to find the minimum number of wavelengths for the WA problem on a tree of rings. Let L be the maximum number of paths on any edge in the network. Then L is a lower bound on the number of wavelengths for the WA problem. We give a polynomial time algorithm which uses at most 3L wavelengths for the WA problem on a tree of rings with node degree at most eight. This improves the previous result of 4L. We also show that some instances of the WA problem require at least 3L wavelengths on a tree of rings, implying that the 3L upper bound is optimal for the worst case instances. In addition, we prove that our algorithm has approximation ratios 2 and 2.5 for a tree of rings with node degrees at most four and six, respectively.