Single PON network design with unconstrained splitting stages

A Passive Optical Network (PON) is a network technology for deploying access networks based on passive optical components. In a single PON access network, the client terminals are connected to a Central Office through optical splitters and interconnecting fibers where each splitter splits in equal parts the input optical signal coming from the Central Office over its different output fibers. In this paper, we consider PON topology solutions where the splitting ratio and the number of splitting stages are not constrained to a given target design but, instead, are decided based on the cost of the solutions. We present different Integer Linear Programming formulations to model this problem and provide computational results showing that the optimal solutions can be computed for realistic problem instances. In addition, we describe how the formulations can be adapted for the traditional PON topology approaches and present computational results showing that significant cost gains are obtained with the unconstrained splitting stage approach.     

Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities

We consider a new combinatorial optimization problem that combines network design and facility location aspects. Given a graph with two types of customers and two technologies that can be installed on the edges, the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree. In addition, besides fixed link installation costs, facility opening costs, associated to each node where primary and secondary subtree connect, have to be paid. The problem is called the Two Level Network Design Problem with Transition Facilities (TLNDF).     

Solving a manpower scheduling problem for airline catering using metaheuristics

We study a manpower scheduling problem with job time windows and job-skills compatibility constraints. This problem is motivated by airline catering operations, whereby airline meals and other supplies are delivered to aircrafts on the tarmac just before the flights take-off. Jobs (flights) must be serviced within a given time-window by a team consisting of a driver and loader. Each driver/loader has the skills to service some, but not all, of the airline/aircraft/configuration of the jobs. Given the jobs to be serviced and the roster of workers for each shift, the problem is to form teams and assign teams and start-times for the jobs, so as to service as many flights as possible. Only teams with the appropriate skills can be assigned to a flight. Workload balance among the teams is also a consideration. We present model formulations and investigate a tabu search heuristic and a simulated annealing heuristic approach to solve the problem. Computational experiments show that the tabu search approach outperforms the simulated annealing approach, and is capable of finding good solutions.     

A solution method for a car fleet management problem with maintenance constraints

The problem retained for the ROADEF’99 international challenge was an inventory management problem for a car rental company. It consists in managing a given fleet of cars in order to satisfy requests from customers asking for some type of cars for a given time period. When requests exceed the stock of available cars, the company can either offer better cars than those requested, subcontract some requests to other providers, or buy new cars to enlarge the available stock. Moreover, the cars have to go through a maintenance process at a regular basis, and there is a limited number of workers that are available to perform these maintenances. The problem of satisfying all customer requests at minimum cost is known to be NP-hard. We propose a solution technique that combines two tabu search procedures with algorithms for the shortest path, the graph coloring and the maximum weighted independent set problems. Tests on benchmark instances used for the ROADEF’99 challenge give evidence that the proposed algorithm outperforms all other existing methods (thirteen competitors took part to this contest).     

Connectivity-and-hop-constrained design of electricity distribution networks

This paper addresses the problem of designing the configuration of an interconnected electricity distribution network, so as to maximize the minimum power margin over the feeders. In addition to the limitation of feeder power capacity, the distance (as hop count) between any customer and its allocated feeder is also limited for preventing power losses and voltage drops. Feasibility conditions are studied and a complexity analysis is performed before introducing a heuristic algorithm and two integer linear programming formulations for addressing the problem. A cutting-plane algorithm relying on the generation of two classes of cuts for enforcing connectivity and distance requirements respectively is proposed for solving the second integer linear programming formulation. All the approaches are then compared on a set of 190 instances before discussing their performances.     

Hop constrained Steiner trees with multiple root nodes

We consider a network design problem that generalizes the hop and diameter constrained Steiner tree problem as follows: Given an edge-weighted undirected graph with two disjoint subsets representing roots and terminals, find a minimum-weight subtree that spans all the roots and terminals so that the number of hops between each relevant node and an arbitrary root does not exceed a given hop limit H. The set of relevant nodes may be equal to the set of terminals, or to the union of terminals and root nodes. This article proposes integer linear programming models utilizing one layered graph for each root node. Different possibilities to relate solutions on each of the layered graphs as well as additional strengthening inequalities are then discussed. Furthermore, theoretical comparisons between these models and to previously proposed flow- and path-based formulations are given. To solve the problem to optimality, we implement branch-and-cut algorithms for the layered graph formulations. Our computational study shows their clear advantages over previously existing approaches.     

Rerouting tunnels for MPLS network resource optimization

In Multi-Protocol Label Switching (MPLS) networks, traffic demands can be routed along tunnels called Label Switched Paths (LSPs). A tunnel is characterized by a path in the network and a reserved bandwidth. These tunnels can be created and deleted dynamically, depending on traffic demand arrivals or departures. After several operations of this type, the network resource utilization can be unsatisfactory, with congestion or too long routing paths for instance. One way to improve it is to reroute tunnels; the rerouting process depends on the LSP Quality of Service (QoS) requirements.     

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.     

Bounds for short covering codes and reactive tabu search

Given a prime power q, c_q(n,R) denotes the minimum cardinality of a subset H in such that every word in this space differs in at most R coordinates from a multiple of a vector in H. In this work, two new classes of short coverings are established. As an application, a new optimal record-breaking result on the classical covering code is obtained by using short covering. We also reformulate the numbers c_q(n,R) in terms of dominating set on graphs. Departing from this reformulation, the reactive tabu search (a variation of tabu search heuristics) is developed to obtain new upper bounds on c_q(n,R). The algorithm is described and conclusions on the results are drawn; they identify the advantages of using the reactive mechanism for this problem. Tables of lower and upper bounds on c_q(n,R), q=3,4, n≤7, and R≤3, are also presented.     

A linear programming approach to highly precise clock synchronization over a packet network

In this paper, we propose a linear programming-based method suitable for precise and reliable estimation of the skew of a slave clock respective to a master clock using timing information carried over an asynchronous packet network. Solving this problem is key to the viability of deploying low-cost IP-based transport technology in existing GSM networks. The paper is concluded by empirical evidence suggesting that the proposed method indeed has the potential to meet the stringent GSM precision requirements.      

The multi-depot vehicle routing problem with inter-depot routes

This article addresses an extension of the multi-depot vehicle routing problem in which vehicles may be replenished at intermediate depots along their route. It proposes a heuristic combining the adaptative memory principle, a tabu search method for the solution of subproblems, and integer programming. Tests are conducted on randomly generated instances.     

Operational aircraft maintenance routing problem with remaining time consideration

The aircraft maintenance routing problem is one of the most studied problems in the airline industry. Most of the studies focus on finding a unique rotation that will be repeated by each aircraft in the fleet with a certain lag. In practice, using a single rotation for the entire fleet is not applicable due to stochasticity and operational considerations in the airline industry. In this study, our aim is to develop a fast responsive methodology which provides maintenance feasible routes for each aircraft in the fleet over a weekly planning horizon with the objective of maximizing utilization of the total remaining flying time of fleet. For this purpose, we formulate an integer linear programming (ILP) model by modifying the connection network representation. The proposed model is solved by using branch-and-bound under different priority settings for variables to branch on. A heuristic method based on compressed annealing is applied to the same problem and a comparison of exact and heuristic methods are provided. The model and the heuristic method are extended to incorporate maintenance capacity constraints. Additionally, a rolling horizon based procedure is proposed to update the existing routes when some of the maintenance decisions are already fixed.     

Algorithms for the non-bifurcated network design problem

In this paper we consider the non-bifurcated network design problem where a given set of cities must be connected by installing on a given set of links integer multiples of some base capacity so that a set of commodity demands can be routed. Each commodity flow is constrained to run through a single path along the network. The objective is to minimize the sum of capacity installation and routing costs. We present an exact algorithm and four new heuristics. The first heuristic generates an initial feasible solution, then it improves it until a necessary condition for optimality is satisfied. Two heuristics are partial enumeration methods and the last one iteratively applies a tabu search method to different initial feasible solutions. Computational results over a set of test problems from the literature show the effectiveness of the proposed algorithms.     

An efficient tabu algorithm for the single row facility layout problem

The general goal of the facility layout problem is to arrange a given number of facilities to minimize the total cost associated with the known or projected interactions between them. One of the special classes of the facility layout problem is the Single Row Facility Layout Problem (SRFLP), which consists of finding an optimal linear placement of rectangular facilities with varying dimensions on a straight line. This paper first presents and proves a theorem to find the optimal solution of a special case of SRFLP. The results obtained by this theorem prove to be very useful in reducing the computational efforts when a new algorithm based on tabu search for the SRFLP is proposed in this paper. Computational results of the proposed algorithm on benchmark problems show the greater efficiency of the algorithm compared to the other heuristics for solving the SRFLP.     

Solving a multicoloring problem with overlaps using integer programming

This paper presents a new generalization of the graph multicoloring problem. We propose a Branch-and-Cut algorithm based on a new integer programming formulation. The cuts used are valid inequalities that we could identify to the polytope associated with the model. The Branch-and-Cut system includes separation heuristics for the valid inequalities, specific initial and primal heuristics, branching and pruning rules. We report on computational experience with random instances.     

Bandwidth packing with priority classes

The bandwidth packing problem is defined as the selection and routing of messages from a given list of messages with prespecified requirements on demand for bandwidth. The messages have to be routed over a network with given topology so that the generated revenue is maximized. Messages to be routed are classified into two priority classes. An integer programming based formulation of this problem is proposed and a Lagrangean relaxation based methodology is described for solving this problem. A general purpose heuristic is then developed for generating feasible solutions of good quality. Several numerical experiments are conducted using a number of problem parameters such as number of messages, ratio of messages for lower and higher priority classes, capacity of links, and demand distribution of messages belonging to different classes and high quality solutions to the priority bandwidth packing problem are generated under the different situations.     

The maximum covering/shortest path problem: A multiobjective network design and routing formulation

In this paper the authors introduce the maximum covering/shortest path problem and the maximum population/shortest path problem, a special case of the former model. Both models are formulated as two objective integer programs. A summary of the results of a sample problem for the latter formulation is given. Possible modifications to, and extensions and applications of both models are also presented. With these formulations the authors extend the concept of ‘coverage’ from facility location analysis to network design and routing analysis.     

Partial integration of frequency allocation within antenna positioning in GSM mobile networks

In this article we propose to partially integrate the antenna positioning (APP) and frequency allocation problems (FAP). The traditional wireless network design process examines these two major issues sequentially in order to avoid the very high complexity associated with the simultaneous resolution of the two problems. The proposed integration involves the introduction of interference protection guarantees within the APP. It is customary to define such guarantees in an intermediate step and to use them as input to FAP, in order to protect against interference in critical areas. The proposed approach consists of selecting these protections while solving the APP, allowing the optimization procedure to exploit the degrees of freedom that this would offer. Results on two real-life problem instances indicate a significant improvement in interference levels and resource utilization.     

Time-indexed formulations for scheduling chains on a single machine: An application to airborne radars

Airborne radars are widely used to perform a large variety of tasks in an aircraft (searching, tracking, identifying targets, etc.) Such tasks play a crucial role for the aircraft and they are repeated in a “more or less” cyclic fashion. This defines a scheduling problem that impacts a lot on the quality of the radar output and on the overall safety of the aircraft.     

A hybrid tabu search/branch & bound approach to solving the generalized assignment problem

A new approach for solving the generalized assignment problem (GAP) is proposed that combines the exact branch & bound approach with the heuristic strategy of tabu search (TS) to produce a hybrid algorithm for solving GAP. The algorithm described uses commercial software to solve sub-problems generated by the TS guiding strategy. The TS approach makes use of the concept of referent domain optimisation and introduces novel add/drop strategies. In addition, the linear programming relaxation of GAP that forms part of the branch & bound approach is itself helpful in suggesting which variables might take binary values. Computational results on benchmark test instances are presented and compared with results obtained by the standard branch & bound approach and also several other heuristic approaches from the literature. The results show the new algorithm performs competitively against the alternatives and is able to find some new best solutions for several benchmark instances.