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.     

Adaptive wavelength routing in all-optical networks

We consider routing and wavelength assignment in wavelength-routed all-optical networks (WAN) with circuit switching. The conventional approaches to address this issue consider the two aspects of the problem disjointly by first finding a route from a predetermined set of candidate paths and then searching for an appropriate wavelength assignment. We adopt a more general approach in which we consider all paths between a source-destination (s-d) pair and incorporate network state information into the routing decision. This approach performs routing and wavelength assignment jointly and adaptively, and outperforms fixed routing techniques. We present adaptive routing and wavelength assignment algorithms and evaluate their blocking performance. We obtain an analytical technique to compute approximate blocking probabilities for networks employing fixed and alternate routing. The analysis can also accommodate networks with multiple fibers per link. The blocking performance of the proposed adaptive routing algorithms are compared along with their computational complexity     

Dynamic Multicast Session Provisioning in WDM Optical Networks with Sparse Splitting Capability

In this work, we study dynamic provisioning of multicast sessions in a wavelength-routed sparse splitting capable WDM network with an arbitrary mesh topology where the network consists of nodes with full, partial, or no wavelength conversion capabilities and a node can be a tap-and-continue (TaC) node or a splitting and delivery (SaD) node. The objectives are to minimize the network resources in terms of wavelength-links used by each session and to reduce the multicast session blocking probability. The problem is to route the multicast session from each source to the members of every multicast session, and to assign an appropriate wavelength to each link used by the session. We propose an efficient online algorithm for dynamic multicast session provisioning. To evaluate the proposed algorithm, we apply the integer linear programming (ILP) optimization tool on a per multicast session basis to solve off-line the optimal routing and wavelength assignment given a multicast session and the current network topology as well as its residual network resource information. We formulate the per session multicast routing and wavelength assignment problem as an ILP. With this ILP formulation, the multicast session blocking probability or success probability can then be estimated based on solving a series of ILPs off-line. We have evaluated the effectiveness of the proposed online algorithm via simulation in terms of session blocking probability and network resources used by a session. Simulation results indicate that our proposed computationally efficient online algorithm performs well even when a fraction of the nodes are SaD nodes.     

Routing and wavelength assignment of scheduled lightpath demands

We present algorithms that compute the routing and wavelength assignment (RWA) for scheduled lightpath demands in a wavelength-switching mesh network without wavelength conversion functionality. Scheduled lightpath demands are connection demands for which the setup and teardown times are known in advance. We formulate separately the routing problem and the wavelength assignment problem as spatio-temporal combinatorial optimization problems. For the former, we propose a branch and bound algorithm for exact resolution and an alternative tabu search algorithm for approximate resolution. A generalized graph coloring approach is used to solve the wavelength assignment problem. We compared the proposed algorithms to an RWA algorithm that sequentially computes the route and wavelength assignment for the scheduled lightpath demands.     

Routing and wavelength assignment based on genetic algorithm

In this letter, the routing and wavelength assignment problem in all optical networks is considered. We improve the Max-RWA model presented by R. M. Krishnaswamy and K. N. Sivarajan (see ibid., vol.5, p.435-7, Oct. 2001) by introducing limited-range wavelength conversions. Considering transmission performance, we propose a new optimization objective, which is to establish the maximum number of connections with the least number of wavelength converters. The modified Max-RWA problem is formulated as a integer linear programming (ILP) problem, and then solved using a genetic algorithm. The extended layered-graph approach is used to assign routes and wavelengths when necessary, thus reducing the complexity of the genetic algorithm. Numerical results obtained for NSFNET are presented     

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.     

Multicast wavelength assignment with sparse wavelength converters to maximize the network capacity using ILP formulation in WDM mesh networks

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.This research was partially supported by the Grant of National Science Council, R.O.C. (NSC 94-2745-E-155-007-URD).     

A genetic algorithm based exact approach for lifetime maximization of directional sensor networks

This paper addresses the problem of maximizing lifetime of directional wireless sensor networks, i.e., where sensors can monitor targets in an angular sector only and not all the targets around them. These sectors usually do not overlap, and each sensor can monitor at most one sector at a time. An exact method is proposed using a column generation scheme where a two level strategy, consisting of a genetic algorithm and an integer linear programming approach, is used to solve the auxiliary problem. The role of integer linear programming (ILP) approach is limited to either escaping from local optima or proving the optimality of the current solution. Computational results clearly show the advantage of the proposed approach over a column generation approach based on solving the auxiliary problem through ILP approach alone as the proposed approach is several times faster.     

Survivable traffic grooming with path protection at the connection level in WDM mesh networks

Survivable traffic grooming (STG) is a promising approach to provide reliable and resource-efficient multigranularity connection services in wavelength-division-multiplexing (WDM) optical networks. In this paper, we study the STG problem in WDM mesh optical networks employing path protection at the connection level. Both dedicated-protection and shared-protection schemes are considered. Given network resources, the objective of the STG problem is to maximize network throughput. To enable survivability under various kinds of single failures, such as fiber cut and duct cut, we consider the general shared-risk-link-group (SRLG) diverse routing constraints. We first resort to the integer-linear-programming (ILP) approach to obtain optimal solutions. To address its high computational complexity, we then propose three efficient heuristics, namely separated survivable grooming algorithm (SSGA), integrated survivable grooming algorithm (ISGA), and tabu-search survivable grooming algorithm (TSGA). While SSGA and ISGA correspond to an overlay network model and a peer network model, respectively, TSGA further improves the grooming results from SSGA and ISGA by incorporating the effective tabu-search (TS) method. Numerical results show that the heuristics achieve comparable solutions to the ILP approach, which uses significantly longer running times than the heuristics.     

Wavelength assignment for locally twisted cube communication pattern on optical bus network-on-chip

Optical network-on-chip (NoC) is a new designing of Multi-Processor System-on-Chip (MPSoC). Global bus is the simplest logical topology of optical NoC. Static routing and wavelength assignment is one important communication mechanism of optical NoC. This paper addresses the routing and wavelength assignment (RWA) problem for locally twisted cube communication pattern on global bus optical NoC. For that purpose, a routing scheme, that is an embedding scheme, is proposed, and a wavelength assignment scheme under the embedding scheme is designed. The number of required wavelengths is shown to attain the minimum, guaranteeing the optimality of the proposed scheme.     

QoS-driven multicast routing in sparse-splitting optical networks

This paper investigates the quality-of-service (QoS)-driven multicast routing problem in a sparse-splitting optical network. The main objective is to minimize the total cost of wavelength channels utilized by the light-tree while satisfying required QoS parameters. In this paper, both the optical-layer constraints (e.g., optical signal power) and application-layer requirements (e.g., end-to-end delay and inter-destination delay variation) are considered as the QoS parameters. First, integer linear programming (ILP) formulations to solve the optimal multicast routing problem with the given QoS parameters are presented. Solving the ILP formulations for large-scale networks can easily overwhelm the capabilities of state-of-the-art computing facilities, and hence, a heuristic algorithm is proposed to construct a feasible light-tree that satisfies the required QoS parameters in large-scale networks. Simulation results demonstrate the performance of the proposed heuristic algorithm in terms of the cost of utilized wavelength channels.     

Cost Effective Shared Path Protection for WDM Optical Mesh Networks with Partial Wavelength Conversion

In this paper, we study routing and wavelength assignment of connection requests in survivable WDM optical mesh networks employing shared path protection with partial wavelength conversion while 100% restorability is guaranteed against any single failures. We formulate the problem as a linear integer program under a static traffic model. The objective is to minimize the total cost of wavelength-links and wavelength converters used by working paths and protection paths of all connections. A weight factor is used which is defined as the cost ratio of a wavelength converter and a wavelength-link. Depending on the relative cost of bandwidth and wavelength conversion, the optimization objective allows a proper tradeoff between the two. The proposed algorithm, the shortest-widest-path-first (SWPF) algorithm, uses a modified Dijkstra's algorithm to find a working path and a protection path for each connection request in the wavelength graph transformed from the original network topology. When there are multiple candidate paths that have the same minimum total cost, the path along which the maximum number of converters used at each node is minimized is chosen by the SWPF algorithm. We have evaluated the effectiveness of the proposed algorithm via extensive simulation. The results indicate that the performance of the proposed algorithm is very close to that of the optimal solutions obtained by solving the ILP formulation and outperforms existing heuristic algorithms in terms of total number of converters used and the maximum number of converters required at each node in the network. The proposed algorithm also achieves slightly better performance in terms of total cost of wavelength-links and converters used by all connections. We also investigated shared path protection employing converter sharing. The results show that the technique can reduce not only the total number of converters used in the network but also the maximum number of converters required at each node, especially when a large number of converters are needed in the network. In this study, although the ILP formulation is based on static traffic, the proposed algorithm is also applicable to routing dynamic connection requests.     

Logically rearrangeable multihop lightwave networks

The optimization problem of rearrangeable multihop lightwave networks is considered. The authors formulate the flow and wavelength assignment problem, when minimizing the maximum flow in the network, as a mixed integer optimization problem subject to linear constraints. The problem is decomposed into two independent subproblems, the wavelength assignment (or connectivity problem) and the flow assignment (or routing problem). A simple heuristic provides a meaningful formulation to the connectivity problem, in a form similar to a transportation problem. An algorithm is then proposed which finds a heuristic initial logical connectivity diagram and the corresponding routing, and then iterates from that solution by applying branch-exchange operations to the connectivity diagram. The algorithm was tested on illustrative traffic matrices for an 8 node network with two transmitters and two receivers per node, and an improvement in achievable throughput over the Perfect Shuffle interconnection pattern was shown in all cases     

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.     

A Lagrangian-Relaxation Based Network Profit Optimization For Mesh SONET-Over-WDM Networks

In Wavelength Division Multiplexing (WDM) networks, the huge capacity of wavelength channels is generally much larger than the bandwidth requirement of individual traffic streams from network users. Traffic grooming techniques aggregate low-bandwidth traffic streams onto high-bandwidth wavelength channels. In this paper, we study the optimization problem of grooming the static traffic in mesh Synchronous Optical Network (SONET) over WDM networks. The problem is formulated as a constrained integer linear programming problem and an innovative optimization objective is developed as network profit optimization. The routing cost in the SONET and WDM layers as well as the revenue generated by accepting SONET traffic demands are modelled. Through the optimization process, SONET traffic demands will be selectively accepted based on the profit (i.e., the excess of revenue over network cost) they generate. Consiering the complexity of the network optimization problem, a decomposition approach using Lagrangian relaxation is proposed. The overall relaxed dual problem is decomposed into routing and wavelength assignment and SONET traffic routing sub-problems. The subgradient approach is used to optimize the derived dual function by updating the Lagrange multipliers. To generate a feasible network routing scheme, a heuristic algorithm is proposed based on the dual solution. A systematic approach to obtain theoretical performance bounds is presented for an arbitrary topology mesh network. This is the first time that such theoretical performance bounds are obtained for SONET traffic grooming in mesh topology networks. The optimization results of sample networks indicate that the roposed algorithm achieves good sub-optimal solutions. Finally, the influence of various network parameters is studied.     

基于改进蚁群算法的卫星光网络波长分配方法

路由与波长分配是下一代光网络的需要解决的核心问题之一。本文采用智能蚁群算法,研究了卫星光网络的路由与波长分配问题,为通信请求寻找最优的数据传输光路径。基于请求区域受限策略(Restricted Request Area,RRA)和链路波长负载平衡策略,建立了考虑传输延迟和波长连续性约束的双主星分布式星群节点结构光网络系统模型。利用智能蚁群路由和波长分配(Smart Ant Colony Routing AndWavelength Assignment,SAC-RWA)算法求解系统模型,以找到具有稀疏波长转换的卫星光网络中最小成本波长路径。所提出的算法允许单个蚂蚁同时完成路由和波长分配,仿真结果表明,RRA能够明显改进卫星光网络的性能,以略微增加拥塞率的代价显著降低了计算复杂度。     

An Ant-Based Approach for Dynamic RWA in Optical WDM Networks

In this paper, we propose a new ant-based algorithm for the dynamic routing and wavelength assignment (RWA) problem in optical WDM networks under the wavelength continuity constraint. Unlike conventional approaches, which usually require centralized global network information, our new RWA algorithm constructs the routing solution in a distributed manner by means of cooperative ants. To facilitate the ants’ foraging task, we adopt in our algorithm a probabilistic routing table structure for route selection. The new algorithm is highly adaptive in that it always keeps a suitable number of ants in the network to cooperatively explore the network states and continuously update the routing tables, so that the route for a connection request can be determined promptly by the current states of routing tables with only a small setup delay. Some new schemes for path scoring and path searching are also proposed to enhance the performance of our ant-based algorithm. Extensive simulation results upon three typical network topologies indicate that the proposed algorithm has a very good adaptability to traffic variations and it outperforms both the fixed routing algorithm and the promising fixed–alternate routing algorithm in terms of blocking probability. The ability to guarantee both a low blocking probability and a small setup delay makes the new ant-based routing algorithm very attractive for both the optical circuit switching networks and future optical burst switching networks     

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.     

Survivability Approaches Using p-Cycles in WDM Mesh Networks Under Static Traffic

The major challenge in survivable mesh networks is the design of resource allocation algorithms that allocate network resources efficiently while at the same time are able to recover from a failure quickly. This issue is particularly more challenging in optical networks operating under wavelength continuity constraint, where the same wavelength must be assigned on all links in the selected path. This paper proposes two approaches to solve the survivable routing and wavelength assignment RWA problem under static traffic using p-cycles techniques. The first is a non-jointly approach, where the minimum backup capacity against any single span failure is set up first. Then the working lightpaths problem is solved by first generating the most likely candidate routes for each source and destination s-d pair. These candidate routes are then used to formulate the overall problem as an ILP problem. Alternatively, for a more optimum solution, the problem can be solved jointly, where the working routes and the backup p-cycles are jointly formulated as an ILP problem to minimize the total capacity required. Furthermore, only a subset of high merit cycles that are most likely able to protect the proposed working paths is used in the formulation. Reducing the number of candidate cycles in the final formulation plays a significant role in reducing the number of variables required to solve the problem. To reduce the number of candidate cycles in the formulation, a new metric called Route Sensitive Efficiency (RSE) - has been introduced to pre-select a reduced number of high merit cycle candidates. The RSE ranks each cycle based on the number of links of the primary candidate routes that it can protect. The two approaches were tested and their performances were compared.     

基于强化学习的光传送网路由波长优化

针对光传送网中动态业务的路由和波长问题,提出一种基于强化学习的深度路由波长分配算法DeepRWA。算法基于软件定义网络架构,通过强化学习灵活地调整控制光传送网,实现光网络路由波长分配策略优化。针对路由选择问题,结合链路上的波长使用情况,使用A3C算法选择合适的路由,使得阻塞率最小;针对波长分配问题,使用首次命中算法选择波长。考虑阻塞率、资源利用率、策略熵、价值损失、运行时间及收敛速度等多个指标,利用14节点NSFNET网络拓扑仿真实验。结果表明:当信道中包含18个波长时,与传统KSP-FF算法相比,所提出的路由波长分配算法的阻塞率降低了0.06,资源利用率提高了0.02,但运行时间有增加;在波长数超过45以后,与传统KSP-FF算法相比,所提算法保持阻塞率和资源利用率的同时,运行时间开始降低;当信道中包含波长数为58时,与传统KSP-FF算法相比,所提算法运行时间减少了0.07 ms。由此可见,提出的算法使路由选择和波长分配得到了优化。