A Tabu search algorithm for static routing and wavelength assignment problem

Static routing and wavelength assignment (RWA) is usually formulated as an optimization problem with the objective of minimizing wavelength usage (MWU). Existing solution methodologies for the MWU problem are usually based on a two-step approach, where routing and wavelength assignment are done independently. Though this approach can reduce computational cost, the optimality of the solution is compromised. We propose a novel tabu search (TS) algorithm, which considers routing and wavelength assignment jointly without increasing the computational complexity. The performance of the proposed TS algorithm is compared with the integer linear programming (ILP) method, which is known to solve the MWU to optimality. The results for both small and large networks show that our proposed TS algorithm works almost as well as the ILP solution and is much more computationally efficient.     

Comparison of ILP formulations for the RWA problem

We present a review of the integer linear programming (ILP) formulations that have been proposed for the routing and wavelength assignment problem in WDM optical networks assuming asymmetrical traffic. We show that all formulations proposed under asymmetrical traffic assumptions, both link and path formulations, are equivalent in terms of the upper bound value provided by the optimal solution of their linear programming relaxation, although their number of variables and constraints widely differ. We propose improvements for some of the formulations that result in further reductions in the number of variables and constraints.Under the objective of minimizing the blocking rate, we propose an experimental comparison of the best lower and upper bounds that are available. We then discuss the easiness of exact ILP solution depending on the formulations. We observe that LP relaxation bounds often provide solutions with a value very close to the optimal ILP one. We solve exactly for the first time several RWA (Routing and Wavelength Assignment) realistic instances, including those proposed by Krishnaswamy and Sivarajan [R. Krishnaswamy, K. Sivarajan, Algorithms for routing and wavelength assignment based on solutions of LP-relaxation, IEEE Communications Letters 5 (10) (2001) 435–437], with a proof of the optimality.     

An algorithm for optimal assignment of a wavelength in a tree topology and its application in WDM networks

In this paper, we present a polynomial time algorithm that gives an optimal solution to the routing and wavelength assignment (RWA) problem in a tree topology. One of the major design issues in wavelength-division multiplexed networks is the assignment of the limited number of wavelengths among network stations so that greater capacity can be achieved. The problem of RWA is known to be NP-hard problem. Many researchers have tackled the problem of RWA with a number of efficient heuristic algorithms. This paper presents an algorithm that optimally assigns a single wavelength to maximize one-hop traffic in a tree topology. The algorithm uses dynamic programming and is shown to be optimal with a time complexity of O(N/sup 4/). We also propose a heuristic scheme to use our optimal algorithm for wavelength assignment in a general graph. The heuristic works on the tree subgraphs of a given graph and the remaining spare wavelengths can be assigned with an existing RWA policy.     

Routing and wavelength assignment in optical networks from edgedisjoint path algorithms

Routing and wavelength assignment (RWA) problems in wavelength-routed optical networks are typically solved using a combination of integer programming and graph coloring. Such techniques are complex and make extensive use of heuristics. We explore an alternative solution technique in the well-known maximum edge disjoint paths (EDP) problem which can be naturally adapted to the RWA problem. Maximum EDP is NP-hard, but now it is known that simple greedy algorithms for it are as good as any of the more complex heuristic solutions. In this paper we investigate the performance of a simple greedy maximum edge disjoint paths algorithm applied to the RWA problem and compare it with a previously known solution method     

Optimal regenerator assignment and resource allocation strategies for translucent optical networks

Physical layer impairments in wavelength-routed networks limit the maximum distance, a signal can travel in the optical domain, without significant distortion. Therefore, signal regeneration is required at some intermediate nodes for long-haul lightpaths. In translucent WDM networks, sparsely located regenerators at certain nodes can be used to offset the impact of physical layer impairments. The routing and wavelength assignment (RWA) techniques in such translucent networks need to take into consideration the availability of regenerators and the maximum optical reach of the transparent lightpaths (without any regeneration). Although there has been significant research interest in RWA algorithms for translucent networks, much of the research has focused on dynamic RWA techniques. Only a handful of recent papers have considered the static (offline) case, and they typically propose heuristic algorithms to solve this complex design problem for practical networks. In this paper, we propose a generalized integer linear program (ILP) based formulation for static regenerator assignment and RWA in translucent WDM optical networks, with sparse regenerator placement. To the best of our knowledge, such a formulation that optimally allocates resources for a set of lightpaths for translucent networks, given the physical network, the locations of the regenerators, and the maximum optical reach has not been considered before. The proposed formulation is important for two reasons. First, it can serve as a benchmark for evaluating different heuristic approaches that may be developedin the future. Second, we show that using a novel node representation technique, it is possible to drastically reduce the number of integer variables. This means that unlike existing ILP formulations, our approach can actually be used to generate optimal solutions for practical networks, with hundreds of lightpath demands.     

Dynamic Routing and Wavelength Assignment in Survivable WDM Networks

Dense wavelength division multiplexing (DWDM) networks are very attractive candidates for next generation optical Internet and intelligent long-haul core networks. In this paper we consider DWDM networks with wavelength routing switches enabling the dynamic establishment of lightpaths between each pair of nodes. The dynamic routing and wavelength assignment (RWA) problem is studied in multifiber networks, assuming both protection strategies: dedicated and shared. We solve the two subproblems of RWA simultaneously, in a combined way using joint methods for the wavelength selection (WS) and wavelength routing (WR) tasks. For the WS problem in contrast to existing strategies we propose a new, network state based selection method, which tries to route the demand on each wavelength, and selects the best one according to different network metrics (such as available channels, wavelengths per fiber and network load). For the WR problem we propose several weight functions for using in routing algorithms (Dijkstra or Suurballe), adapting dynamically to the load of the links and to the length of the path. The combination of different wavelength selection and routing (WS&WR) methods enables wide configuration opportunities of our proposed algorithm allowing good adaptation to any network state. We also propose the extension of the RWA algorithm for dedicated and shared protection and a new method for applying shared protection in dynamic WDM environment. The detailed analysis of the strategies demonstrate that our RWA algorithm provides significantly better performance than previous methods in terms of blocking probability whether with or without protection methods.     

On the routing and wavelength assignment in multifiber WDM networks

This paper addresses the problem of routing and wavelength assignment (RWA) in multifiber WDM networks with limited resources. Given a traffic matrix, the number of fibers per link, and the number of wavelengths a fiber can support, we seek to maximize the carried traffic of connections. We formulate the problem as an integer linear program (ILP), and show that the lightpaths selected by this formulation can indeed be established by properly configuring the optical switches. An upper bound on the carried traffic can be computed by solving the linear programming (LP)-relaxation of the ILP formulation. It is shown that this bound can be also computed exactly, and in polynomial-time, by solving a significantly simplified LP which considers only one wavelength. The bound can, thus, easily scale to an arbitrarily large number of wavelengths. Furthermore, we demonstrate that any instance of the RWA problem is also an instance of the more general maximum coverage problem. This allows us to take a greedy algorithm for maximum coverage and obtain an algorithm which provides solutions for the RWA problem that are guaranteed to be within a factor of (1-(1/e)) of the optimal solution. Each iteration of the greedy algorithm selects a set of lightpaths that realizes, using one wavelength, the maximum number of connection requests not previously realized. Computational results confirm the high efficiency of our proposed algorithm.     

Wavelength converter placement under different RWA algorithms in wavelength-routed all-optical networks

Sparse wavelength conversion and appropriate routing and wavelength assignment (RWA) algorithms are the two key factors in improving the blocking performance in wavelength-routed all-optical networks. It has been shown that the optimal placement of a limited number of wavelength converters in an arbitrary mesh network is an NP-complete problem. There have been various heuristic algorithms proposed in the literature, in which most of them assume that a static routing and random-wavelength assignment RWA algorithm is employed. However, the existing work shows that fixed-alternate routing and dynamic routing RWA algorithms can achieve much better blocking performance. Our study further demonstrates that the wavelength converter placement and RWA algorithms are closely related in the sense that a well-designed wavelength converter placement mechanism for a particular RWA algorithm might not work well with a different RWA algorithm. Therefore, the wavelength converter placement and the RWA have to be considered jointly. The objective of this paper is to investigate the wavelength converter placement problem under the fixed-alternate routing (FAR) algorithm and least-loaded routing (LLR) algorithm. Under the FAR algorithm, we propose a heuristic algorithm called minimum blocking probability first for wavelength converter placement. Under the LLR algorithm, we propose another heuristic algorithm called weighted maximum segment length. The objective of the converter placement algorithms is to minimize the overall blocking probability. Extensive simulation studies have been carried out over three typical mesh networks, including the 14-node NSFNET, 19-node EON, and 38-node CTNET. We observe that the proposed algorithms not only outperform existing wavelength converter placement algorithms by a large margin, but they also can achieve almost the same performance compared with full wavelength conversion under the same RWA algorithm.     

An Optimization Approach to Routing and Wavelength Assignment in WDM All‐Optical Mesh Networks without Wavelength Conversion

This paper considers a routing and wavelength assignment problem (RWAP) for the implementation of efficient Wavelength Division Multiplexing all‐optical mesh networks without wavelength conversion. For a given physical network and required connections, the solution to the RWAP consists in how to select a suitable path and wavelength among the many possible choices for each connection so that no two paths using the same wavelength pass through the same link, while minimizing the number of required wavelengths. We introduce an integer programming formulation of the RWAP, which has an exponential number of variables, and propose an algorithm to solve it based on the column generation technique. The proposed algorithm can yield high quality solutions and tight lower bounds at the same time. Though the proposed algorithm cannot guarantee optimal solutions, computational results show that the algorithm yields provably good solutions within a reasonable time.     

Routing and wavelength assignment strategies in optical networks

We consider the routing and wavelength assignment (RWA) problem on wavelength division multiplexing (WDM) networks without wavelength conversion. When the physical network and required connections are given, RWA is the problem to select a suitable path and wavelength among the many possible choices for each connection such that no two paths using the same wavelength pass through the same link. In WDM optical networks, there is need to maximize the number of connections established and to minimize the blocking probability using limited resources. This paper presents efficient RWA strategies, which minimizes the blocking probability. Simulation results show that the performance of the proposed strategies is much better than the existing strategy.     

QoS aware traffic grooming and integrated routing on IP over WDM networks

In this article, we consider traffic grooming and integrated routing in IP over WDM networks. The challenges of this problem come from jointly considering traffic grooming, IP routing, and lightpath routing and wavelength assignment (RWA). Due to the high bandwidth of optical fiber, there exists a mismatch between the capacity needed by an IP flow and that provided by a single lightpath. Traffic grooming is therefore used to increase the network utilization by aggregating multiple IP flows in a single lightpath. However, traffic grooming incurs additional delays that might violate Quality-of-Service (QoS) requirements of IP users. In this work, the tradeoff between traffic grooming and IP QoS routing is well-formulated as a mixed integer and linear optimization problem, in which the revenue from successfully provisioning IP paths is to be maximized. Problem constraints include IP QoS, routing, optical RWA, and the WDM network capacity. We propose a novel Lagrangean relaxation (LGR) algorithm to perform constraint relaxation and derive a set of subproblems. The Lagrangean multipliers are used in the proposed algorithm to obtain a solution in consideration of grooming advantage and resource constraints simultaneously. Through numerical experiments and comparisons between the proposed algorithm and a two-phase approach, LGR outperforms the two-phase approach under all experimental cases. In particular, the improvement ratio becomes even more significant when the ratio of IP flow to the wavelength capacity is smaller.     

Routing framework for all-optical DWDM metro and long-haul transport networks with sparse wavelength conversion capabilities

In this paper, we propose a novel routing framework for all-optical dense wavelength-division-multiplexing transport networks with sparse wavelength conversion capabilities. The routing framework includes an integer linear programming formulation to handle the static lightpath establishment problem and a novel open shortest path first protocol extension that advertises the availability of wavelength usage and wavelength conversion resources. Our routing framework addresses the limitations of the extensions presented in the literature because it also includes: 1) an efficient flooding protocol that is suitable for the dynamic nature of these networks and 2) an efficient route and wavelength computation engine that minimizes connection costs without hindering the blocking probability.     

Modeling the routing and spectrum allocation problem for flexgrid optical networks

Flexgrid optical networks are attracting huge interest due to their higher spectrum efficiency and flexibility in comparison with traditional wavelength switched optical networks based on the wavelength division multiplexing technology. To properly analyze, design, plan, and operate flexible and elastic networks, efficient methods are required for the routing and spectrum allocation (RSA) problem. Specifically, the allocated spectral resources must be, in absence of spectrum converters, the same along the links in the route (the continuity constraint) and contiguous in the spectrum (the contiguity constraint). In light of the fact that the contiguity constraint adds huge complexity to the RSA problem, we introduce the concept of channels for the representation of contiguous spectral resources. In this paper, we show that the use of a pre-computed set of channels allows considerably reducing the problem complexity. In our study, we address an off-line RSA problem in which enough spectrum needs to be allocated for each demand of a given traffic matrix. To this end, we present novel integer lineal programming (ILP) formulations of RSA that are based on the assignment of channels. The evaluation results reveal that the proposed approach allows solving the RSA problem much more efficiently than previously proposed ILP-based methods and it can be applied even for realistic problem instances, contrary to previous ILP formulations.     

The most congested cutset: deriving a tight lower bound for the chromatic number in the RWA problem

Routing and wavelength assignment (RWA) is an important issue in the design of routing protocols in an all-optical network. A solution for the RWA problem should determine the least possible number of wavelengths, also known as the chromatic number. In this letter, we introduce the concept of cutset congestion, and show that the congestion of the most congested cutset of a graph representing the network is a tight lower bound for the chromatic number in the RWA problem. In contrast to other existing techniques, our method can be applied to any network and any traffic pattern.     

Routing and wavelength assignment in optical WDM networks with maximum quantity of edge disjoint paths

In the present paper, routing and wavelength assignment (RWA) in optical WDM networks is discussed. Previous techniques based on the combination of integer linear programming based lpsolver and graph coloring are complex and require extensive use of heuristics such as rounding heuristic which makes them slow and sometimes practically not reasonable. Another method employs the greedy approach in graph theory for obtaining available edge disjoint paths. Even though it is fast, it produces a solution for any connection request which is far from the optimal utilization of wavelengths. We propose a novel algorithm, which is based on the maximum flow to have the maximum quantity of edge disjoint paths. Here, we compare the offered method with previous edge disjoint paths algorithms applied to the RWA. Comprehensive computer simulation shows that the proposed method outperforms previous ones significantly in terms of running time. Furthermore, the new method shows compatible or better performance comparing to others in number of wavelengths used.The earlier version was published in ICCS 2004, Poland (Krakow). This research was supported by the Ministry of Information and Communication, Korea under the Information Technology Research Center support program supervised by the Institute of Information Technology Assessment, IITA-2005-(C1090-0501-0019).     

Survivable lightpath provisioning in WDM mesh networks under shared path protection and signal quality constraints

This paper addresses the problem of survivable lightpath provisioning in wavelength-division-multiplexing (WDM) mesh networks, taking into consideration optical-layer protection and some realistic optical signal quality constraints. The investigated networks use sparsely placed optical-electrical-optical (O/E/O) modules for regeneration and wavelength conversion. Given a fixed network topology with a number of sparsely placed O/E/O modules and a set of connection requests, a pair of link-disjoint lightpaths is established for each connection. Due to physical impairments and wavelength continuity, both the working and protection lightpaths need to be regenerated at some intermediate nodes to overcome signal quality degradation and wavelength contention. In the present paper, resource-efficient provisioning solutions are achieved with the objective of maximizing resource sharing. The authors propose a resource-sharing scheme that supports three kinds of resource-sharing scenarios, including a conventional wavelength-link sharing scenario, which shares wavelength links between protection lightpaths, and two new scenarios, which share O/E/O modules between protection lightpaths and between working and protection lightpaths. An integer linear programming (ILP)-based solution approach is used to find optimal solutions. The authors also propose a local optimization heuristic approach and a tabu search heuristic approach to solve this problem for real-world, large mesh networks. Numerical results show that our solution approaches work well under a variety of network settings and achieves a high level of resource-sharing rates (over 60% for O/E/O modules and over 30% for wavelength links), which translate into great savings in network costs.     

Optimal Scheduling for Minimum Delay in Passive Star Coupled WDM Optical Networks

In this paper, a local optimization framework is proposed, which is able to include system constraints including channel availability, receiver availability and tuning overhead by linear mathematical formulations so that it is sufficient to obtain the optimal performance in terms of message delay. A mixed integer linear programming (MILP) based scheme for passive star coupled WDM optical networks is presented. Based on the new solution, the wavelength assignment and message sequence that guarantee the delivery of the given traffic request, while minimizing the average delay can be achieved. Moreover, the negative effect of the tuning overhead has been incorporated into the new algorithm, which has been ignored in most of the previous work. Numerical results obtained suggest that the proposed scheme is a promising approach for optimizing the network performance in terms of average message delay.     

A New Method for Solving Routing and Wavelength Assignment Problems in Optical Networks

The standard Lagrangian relaxation (SLR) method is an efficient method for solving the routing and wavelength assignment (RWA) problems in optical networks. However, previous work did not deal with multiple connection requests with identical source and destination pairs, which are frequently encountered in practice and can cause serious issues when using SLR. More specifically, in solving the dual subproblems after the wavelength capacity constraints are relaxed, the shortest path algorithms such as Dijkstra's typically assign the same route to such connection requests, which possibly leads to a poor RWA solution. In this paper, we introduce a new method, i.e., the successive subproblem solving (SSS) method and one of its implementations, within the Lagrangian relaxation framework. The essence of SSS is to introduce coupled penalty terms and use the surrogate subgradients for search direction at the high level. The homogenous subproblems at the low level are then solved sequentially to avoid the nondecomposable difficulty. Theoretical analysis is performed to provide convergence proof. Numerical results are presented to show that the new method is effective and efficient.     

Heuristic and Hybrid Methods for Solving Optimal Multiple Multicast Problem on WDM Ring Network

The Optimal Multiple Multicast Problem (OMMP) on wavelength division multiplexing (WDM) ring networks without wavelength conversion is considered in this paper. When the physical network and the set of multicast requests are given, OMMP is the problem that selects a suitable path (or paths) and wavelength (or wavelengths) among the many possible choices for each multicast request such that not any pair of paths using the same wavelength pass through the same link. In this paper, a formulation of OMMP is given; this problem is NP-hard since the famous RWA problem which has been proved NP-hard is a special case of OMMP. In this paper, the OMMP is divided into two subproblems: path routing and wavelength assignment subproblems. For each subproblem, two heuristic algorithms are proposed to solve it. Moreover, a hybrid method which combines heuristic and simulated annealing algorithm is proposed to find the near optimal solution. Experimental results indicate that these algorithms are efficient.     

A New Linear Programming Approach to Decoding Linear Block Codes

In this paper, we propose a new linear programming formulation for the decoding of general linear block codes. Different from the original formulation given by Feldman, the number of total variables to characterize a parity-check constraint in our formulation is less than twice the degree of the corresponding check node. The equivalence between our new formulation and the original formulation is proven. The new formulation facilitates to characterize the structure of linear block codes, and leads to new decoding algorithms. In particular, we show that any fundamental polytope is simply the intersection of a group of the so-called minimum polytopes, and this simplified formulation allows us to formulate the problem of calculating the minimum Hamming distance of any linear block code as a simple linear integer programming problem with much less auxiliary variables. We then propose a branch-and-bound method to compute a lower bound to the minimum distance of any linear code by solving a corresponding linear integer programming problem. In addition, we prove that, for the family of single parity-check (SPC) product codes, the fractional distance and the pseudodistance are both equal to the minimum distance. Finally, we propose an efficient algorithm for decoding SPC product codes with low complexity and maximum-likelihood (ML) decoding performance.