Heuristics for multi-period capacity expansion in local telecommunications networks

In this paper, different heuristics are devised to solve a multi-period capacity expansion problem for a local access telecommunications network with a tree topology. This expansion is done by installing concentrators at the nodes and cables on the links of the network. The goal is to find a least cost capacity expansion strategy over a number of periods to satisfy the demand. A local search heuristic is first proposed to improve previously reported results on problem instances based on different cost and demand structures. This heuristic is then integrated into a genetic algorithm to obtain further improvements.     

Diversification strategies in local search for a nonbifurcated network loading problem

This paper examines a variant of the network loading problem, a network design problem found in the telecommunications industry. In this problem, facilities of fixed capacity must be installed on the edges of an undirected network to carry the flow from a central vertex to a set of demand vertices. The objective is to minimize the total installation costs. In this work, the nonbifurcated version of the problem is considered, where the demand at any given vertex must be satisfied through a single path. The proposed heuristics alternate between a construction phase and a local search phase. Each new construction phase, except the first one, is part of a diversification strategy aimed at providing a new starting point for the following local search phase. Different diversification strategies are tested and compared on large-scale instances with up to 500 vertices.     

A tabu search heuristic using genetic diversification for the clustered traveling salesman problem

The clustered traveling salesman problem is an extension of the classical traveling salesman problem where the set of vertices is partitioned into clusters. The objective is to find a least cost Hamiltonian cycle such that the vertices of each cluster are visited contiguously and the clusters are visited in a prespecified order. A tabu search heuristic is proposed to solve this problem. This algorithm periodically restarts its search by merging two elite solutions to form a new starting solution (in a manner reminiscent of genetic algorithms). Computational results are reported on sets of Euclidean problems with different characteristics.     

Multi-period capacity expansion for a local access telecommunications network

In this paper, we examine a multi-period capacity expansion problem for a local access telecommunications network with a tree topology. Capacity expansion is realized through the installation of concentrators at the nodes and cables on the links of the network. Clearly, the installation of concentrators reduces the need for additional cables, and conversely. The goal is to find the least cost alternative to satisfy the demand. A heuristic approach is proposed to solve this problem, where local installation decisions at each node are propagated in the network. This information is then used to adjust prices that guide the decision process from one iteration to the next, until a fixed point is reached. Numerical results are reported on problem instances based on different cost and demand structures.     

Heuristics for Distribution Network Design in Telecommunication

A distribution network problem arises in a lower level of an hierarchical modeling approach for telecommunication network planning. This paper describes a model and proposes a lagrangian heuristic for designing a distribution network. Our model is a complex extension of a capacitated single commodity network design problem. We are given a network containing a set of sources with maximum available supply, a set of sinks with required demands, and a set of transshipment points. We need to install adequate capacities on the arcs to route the required flow to each sink, that may be an intermediate or a terminal node of an arborescence. Capacity can only be installed in discrete levels, i.e., cables are available only in certain standard capacities. Economies of scale induce the use of a unique higher capacity cable instead of an equivalent set of lower capacity cables to cover the flow requirements of any link. A path from a source to a terminal node requires a lower flow in the measure that we are closer to the terminal node, since many nodes in the path may be intermediate sinks. On the other hand, the reduction of cable capacity levels across any path is inhibited by splicing costs. The objective is to minimize the total cost of the network, given by the sum of the arc capacity (cables) costs plus the splicing costs along the nodes. In addition to the limited supply and the node demand requirements, the model incorporates constraints on the number of cables installed on each edge and the maximum number of splices at each node. The model is a NP-hard combinatorial optimization problem because it is an extension of the Steiner problem in graphs. Moreover, the discrete levels of cable capacity and the need to consider splicing costs increase the complexity of the problem. We include some computational results of the lagrangian heuristics that works well in the practice of computer aided distribution network design.     

Assignment of add–drop multiplexer (ADM) rings and digital cross-connect system (DCS) mesh in telecommunication networks

This paper discusses a design of a hybrid ring–mesh network in a survivable communication network. Given a set of traffic demands, the problem is to assign each traffic demand to rings and mesh such that the cost of add–drop multiplexer (ADM) and digital cross-connect system (DCS) equipment required is minimized. This assignment problem can be considered together with the fibre routing of nodes on rings and mesh. As a solution procedure, a tabu search is developed with recency-based short-term and frequency-based long-term memory structures. In computational experiments, the proposed tabu search is compared with the solutions obtained by the branch and bound procedure of CPLEX. We see that the tabu search provides a nearly optimal solution within sufficiently short time periods for all test problems with a gap of approximately 1–4% from the lower bound.     

Heuristics for multiple facility location in a network using the variance criterion

In cyclic networks the p-variance location problem is NP-hard, and therefore it is suitable to use heuristic methods to find approximate solutions to the problem. To this end, two strategies are explored, the first using combinatorial search procedures over the vertex set, whereas the second searches for the solution over the entire network. The initial vertex set solutions are generated by using tabu search, variable neighbourhood search and interchange procedures. The heuristics have been tested on instances of up to 30 vertices and 70 edges, and their performances compared.     

An integrated approach for collection network design,capacity planning and vehicle routing in reverse logistics

This study considers network design, capacity planning and vehicle routing for collection systems in reverse logistics. The network design and capacity planning problems are to determine the static locations and capacities of collection points as well as the dynamic allocations of demand points to the opened collection points over a planning horizon, and the vehicle routing problem is to determine the number and routes of vehicles in such a way that each collection point must be visited exactly once by one vehicle starting and terminating at the depot while satisfying the return demands at collection points and the vehicle capacity. The objective is to minimize the sum of fixed costs to open collection points and to acquire vehicles as well as variable costs to transport returns at demand points to the opened collection points and travel the opened collection points by vehicles. Unlike the location-routing problems, the integrated problem considered in this study has several features: multi-period dynamic model, capacity planning for collection points, maximum allowable collection distances, etc. To solve the integrated problem, two types of tabu search algorithms, hierarchical and integrated ones, are suggested, and their test results are reported. In particular, the efficiency of the integrated approach is shown by comparing the two algorithm types.     

A tabu search approach for solving a difficult forest harvesting machine location problem

This paper deals with two main problems in forest harvesting. The first is that of selecting the locations for the machinery to haul logs from the points where they are felled to the roadside. The second consists in designing the access road network connecting the existing road network with the points where machinery is installed. Their combination induces a very important and difficult problem to solve in forest harvesting. It can be formulated as a combination of two difficult optimization problems: a plant location problem and a fixed charge network flow problem. In this paper, we propose a solution approach based on tabu search. The proposed heuristic includes several enhancements of the basic tabu search framework. The main difficulty lies in evaluating neighboring solutions, which involves decisions related to location of machinery and to road network arcs. Hence, the neighborhood is more complex than in typical applications of metaheuristics. Minimum spanning tree algorithms and Steiner tree heuristics are used to deal with this problem. Numerical results indicate that the heuristic approach is very attractive and leads to better solutions than those provided by state-of-the-art integer programming codes in limited computation times, with solution times significantly smaller. The numerical results do not vary too much when typical parameters such as the tabu tenure are modified, except for the dimension of neighborhood.     

An Application of Tabu Search Heuristic for the Maximum Edge-Weighted Subgraph Problem

The purpose of this article is to describe an efficient search heuristic for the Maximum Edge-weighted Subgraph (MEwS) problem. This problem requires to find a subgraph such that the sum of the weights associated with the edges of the subgraph is maximized subject to a cardinality constraint. In this study a tabu search heuristic for the MEwS problem is proposed. Different algorithms to obtain an initial solution are presented. One neighborhood search strategy is also proposed. Preliminary computational results are reported for randomly generated test problems of MEwS problem with different densities and sizes. For most of test problems, the tabu search heuristic found good solutions. In addition, for large size test problems, the tabu search outperformed the local search heuristic appearing in the literature.     

Optimizing capacity,pricing and location decisions on a congested network with balking

In this paper, we consider the problem of making simultaneous decisions on the location, service rate (capacity) and the price of providing service for facilities on a network. We assume that the demand for service from each node of the network follows a Poisson process. The demand is assumed to depend on both price and distance. All facilities are assumed to charge the same price and customers wishing to obtain service choose a facility according to a Multinomial Logit function. Upon arrival to a facility, customers may join the system after observing the number of people in the queue. Service time at each facility is assumed to be exponentially distributed. We first present several structural results. Then, we propose an algorithm to obtain the optimal service rate and an approximate optimal price at each facility. We also develop a heuristic algorithm to find the locations of the facilities based on the tabu search method. We demonstrate the efficiency of the algorithms numerically.     

A ring-mesh topology design problem for optical transport networks

This paper deals with a ring-mesh network design problem arising from the deployment of an optical transport network. The problem seeks to find an optimal clustering of traffic demands in the network such that the total cost of optical add-drop multiplexer (OADM) and optical cross-connect (OXC) is minimized, while satisfying the OADM ring capacity constraint, the node cardinality constraint, and the OXC capacity constraint. We formulate the problem as an integer programming model and propose several alternative modeling techniques designed to improve the mathematical representation of the problem. We then develop various classes of valid inequalities to tighten the mathematical formulation of the problem and describe an algorithmic approach that coordinates tailored routines with a commercial solver CPLEX. We also propose an effective tabu search procedure for finding a good feasible solution as well as for providing a good incumbent solution for the column generation based heuristic procedure that enhances the solvability of the problem. Computational results exhibit the viability of the proposed method.     

Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem

The vehicle routing problem (VRP) under capacity and distance restrictions involves the design of a set of minimum cost delivery routes, originating and terminating at a central depot, which services a set of customers. Each customer must be supplied exactly once by one vehicle route. The total demand of any vehicle must not exceed the vehicle capacity. The total length of any route must not exceed a pre-specified bound. Approximate methods based on descent, hybrid simulated annealing/tabu search, and tabu search algorithms are developed and different search strategies are investigated. A special data structure for the tabu search algorithm is implemented which has reduced notably the computational time by more than 50%. An estimate for the tabu list size is statistically derived. Computational results are reported on a sample of seventeen bench-mark test problems from the literature and nine randomly generated problems. The new methods improve significantly both the number of vehicles used and the total distances travelled on all results reported in the literature.     

A hybridized tabu search approach for the minimum weight vertex cover problem

The minimum weight vertex cover problem is a basic combinatorial optimization problem defined as follows. Given an undirected graph and positive weights for all vertices the objective is to determine a subset of the vertices which covers all edges such that the sum of the related cost values is minimized. In this paper we apply a modified reactive tabu search approach for solving the problem. While the initial concept of reactive tabu search involves a random walk we propose to replace this random walk by a controlled simulated annealing. Numerical results are presented outperforming previous metaheuristic approaches in most cases.     

Strategic oscillation for the capacitated hub location problem with modular links

The capacitated single assignment hub location problem with modular link capacities is a variant of the classical hub location problem in which the cost of using edges is not linear but stepwise, and the hubs are restricted in terms of transit capacity rather than in the incoming traffic. We propose a metaheuristic algorithm based on strategic oscillation, a methodology originally introduced in the context of tabu search. Our method incorporates several designs for constructive and destructive algorithms, together with associated local search procedures, to balance diversification and intensification for an efficient search. Computational results on a large set of instances show that, in contrast to exact methods that can only solve small instances optimally, our metaheuristic is able to find high-quality solutions on larger instances in short computing times. In addition, the new method, which joins tabu search strategies with strategic oscillation, outperforms the previous tabu search implementation.     

A tabu search algorithm applied to the staffing roster problem of Leicestershire police force

This paper presents an application of the tabu search algorithm to a staff rostering problem relevant to Leicestershire Police. The aim is to address the issue of structuring staff rosters to enable effective use of staff to meet the demand on the Police to reduce and deal with crime-related incidents. This problem is defined through the compilation of a time-varying level of required staff and an associated staff roster. The objective is an optimised work set-up, maximising staff resources and the meeting of demand. Optimisation of staff levels to demand is sought through use of a series of tabu search algorithms, making use of two diversification techniques and an intensification technique individually and in compilation. The tabu search is shown to be a well-suited optimisation approach to the type of problem defined, with individual conclusions drawn for each of the technique combinations used.     

Wide area telecommunication network design: application to the Alberta SuperNet

This article proposes a solution methodology for the design of a wide area telecommunication network. This study is motivated by the Alberta SuperNet project, which provides broadband Internet access to 422 communities across Alberta. There are two components to this problem: the network design itself, consisting of selecting which links will be part of the solution and which nodes should house shelters; and the loading problem which consists of determining which signal transport technology should be installed on the selected edges of the network. Mathematical models are described for these two subproblems. A tabu search algorithm heuristic is developed and tested on randomly generated instances and on Alberta SuperNet data.     

Tabu search for solving the black-and-white travelling salesman problem

The black-and-white travelling salesman problem (BWTSP) is an extension to the well-known TSP by partitioning the set of vertices into black and white vertices, and imposing cardinality and length constraints between two consecutive black vertices in a Hamiltonian tour. BWTSP has various applications in aircraft routing, telecommunication network design and logistics. In this paper, we develop several tabu search (TS) heuristics for solving the BWTSP. Our TS is built upon a new efficient neighbourhood structure, which exploits both the permutation and knapsack features of BWTSP. We also embed our TS as a heuristic procedure to improve the upper bound in a mixed-integer linear programming method. Extensive computational experiment on both benchmark and randomly generated instances shows effectiveness and efficiency of our algorithms. Our algorithms are able to obtain optimal and near optimal solutions to small instances in seconds, and find feasible solutions to large instances that have not been solved by the existing methods in the literature.     

A multi-class multi-level capacitated lot sizing model

When demand loading is higher than available capacity, it takes a great deal of effort for a traditional MRP system to obtain a capacity-feasible production plan. Also, the separation of lot sizing decisions and capacity requirement planning makes the setup decisions more difficult. In a practical application, a production planning system should prioritize demands when allocating manufacturing resources. This study proposes a planning model that integrates all MRP computation modules. The model not only includes multi-level capacitated lot sizing problems but also considers multiple demand classes. Each demand class corresponds to a mixed integer programming (MIP) problem. By sequentially solving the MIP problems according to their demand class priorities, this proposed approach allocates finite manufacturing resources and generates feasible production plans. In this paper we experiment with three heuristic search algorithms: (1) tabu search; (2) simulated annealing, and (3) genetic algorithm, to solve the MIP problems. Experimental designs and statistical methods are used to evaluate and analyse the performance of these three algorithms. The results show that tabu search and simulated annealing perform best in the confirmed order demand class and forecast demand class, respectively.     

Optimization of transit route network,vehicle headways and timetables for large-scale transit networks

This paper presents a metaheuristic method for optimizing transit networks, including route network design, vehicle headway, and timetable assignment. Given information on transit demand, the street network of the transit service area, and total fleet size, the goal is to identify a transit network that minimizes a passenger cost function. Transit network optimization is a complex combinatorial problem due to huge search spaces of route network, vehicle headways, and timetables. The methodology described in this paper includes a representation of transit network variable search spaces (route network, headway, and timetable); a user cost function based on passenger random arrival times, route network, vehicle headways, and timetables; and a metaheuristic search scheme that combines simulated annealing, tabu, and greedy search methods. This methodology has been tested with problems reported in the existing literature, and applied to a large-scale realistic network optimization problem. The results show that the methodology is capable of producing improved solutions to large-scale transit network design problems in reasonable amounts of time and computing resources.