Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Algorithmic Graph Theory

The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions

Coloration de graphes et attribution d'activités dans des quarts de travail

Revue de littérature -- Organisation de la thèse -- Lower bounds and a tabu search algorithm for the minimum deficiency problem -- On a reduction of the interval coloring problem to a series of bandwidth coloring problems -- About equivalent interval colorings of weighted graphs -- Une approche de programmation en nombres entiers pour la résolution d'un problème d'horaire -- Discussion générale et conclusion

Reducing the number of membership functions in linguistic variables

Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations ResearchThe purpose of this thesis was to develop algorithms to reduce the number of membership functions in a fuzzy linguistic variable. Groups of similar membership functions to be merged were found using clustering algorithms. By “summarizing” the information given by a similar group of membership functions into a new membership function we obtain a smaller set of membership functions representing the same concept as the initial linguistic variable. The complexity of clustering problems makes it difficult for exact methods to solve them in practical time. Heuristic methods were therefore used to find good quality solutions. A Scatter Search clustering algorithm was implemented in Matlab and compared to a variation of the K-Means algorithm. Computational results on two data sets are discussed. A case study with linguistic variables belonging to a fuzzy inference system automatically constructed from data collected by sensors while drilling in different scenarios is also studied. With these systems already constructed, the task was to reduce the number of membership functions in its linguistic variables without losing performance. A hierarchical clustering algorithm relying on performance measures for the inference system was implemented in Matlab. It was possible not only to simplify the inference system by reducing the number of membership functions in each linguistic variable but also to improve its performance

The use of relaxation to solve harvest scheduling problems with flow, wildlife habitat, and adjacency constraints

Lagrangean relaxation is presented as a solution technique to solve flow constrained area-based harvest scheduling problems. The best set of multipliers in the Lagrangean approach is obtained through the subgradient method. Guidelines to set some parameters to compute the step size in the subgradient algorithm are provided. An additional procedure to improve the multipliers obtained through the subgradient algorithm is provided. The area-based harvest scheduling problem with adjacency constraints is approached by reducing the number of these constraints required to specify the adjacency relations among harvest units. A heuristic procedure is proposed to to perform this reduction. Such a procedure is based on computing one adjacency constraint per harvest unit. Additional reductions are possible by eliminating the harvest units whose adjacency relations are described by surrounding areas. By using surrogate relaxation the set of adjacency constraints is reduced to one constraint, Combining Lagrangean and surrogate relaxation the area-based harvest scheduling problem with adjacency constraints can be further reduced, so the relaxed problem becomes easier to solve than the original problem. The relaxation approach is used to solve the habitat dispersion problem. Simulated examples show that simultaneously optimizing flow, wildlife and adjacency constraints within an area-based approach will be costlier than previous continuous models have led us to believe

Simulation-Optimization, Markov Chain and Graph Coloring Approaches to Military Manpower Modeling and Deployment Sourcing

The Army manpower system is a integration of numerous elements that can be independently modeled. Identifying and closing gaps in modeling research can reduce workforce inefficiencies and costs. Military manpower models are predominantly focused on forecasting behavior and inventory within given demand requirements. Moreover, research directed towards predicting behavior is almost entirely disaggregated by pecuniary and non-pecuniary goals with disproportionate effort devoted to modeling the external factors that effect such behavior. This thesis proposes modeling approaches to improve the management capabilities of the Army\u27s manpower system. First, we consider a simulation-optimization approach to estimating workforce requirements examines the capabilities and limitations of Monte Carlo simulation and optimization methods within the context of workforce demand forecasting, modeling and planning. Specifically, we focus on these methods as a viable improvement for aligning strategic goals with workforce requirements. A general model is presented for estimating workforce requirements given uncertain demand. Using a real-world data example, we assess the benefits of this methodology to determine an optimal mix of workforce skills while providing the flexibility and robustness to incorporate uncertainty, assess risk and improve effectiveness of the workforce planning process. Second, we address the critical stay-or-leave decision associated with military retention. Personnel retention is one of the most significant challenges faced by the U.S. Army. Central to the problem is understanding the incentives of the stay-or-leave decision for military personnel. Using three years of data from the U.S. Department of Defense, we construct and estimate a Markov chain model of military personnel. Unlike traditional classification approaches, such as logistical regression models, the Markov chain model allows us to describe military personnel dynamics over time and answer a number of managerially relevant questions. Building on the Markov chain model, we construct a finite horizon stochastic dynamic programming model to study the monetary incentives of stay-or-leave decisions. The dynamic programming model computes the expected payoff of staying versus leaving at different stages of the career of military personnel, depending on employment opportunities in the civilian sector. We show that the stay-or-leave decisions from the dynamic programming model possess surprisingly strong predictive power, without requiring personal characteristics that are typically employed in classification approaches. Furthermore, the results of the dynamic programming model can be used as input in classification methods and lead to more accurate predictions. Overall, our work presents an interesting alternative to classification methods and paves the way for further investigations on personnel retention incentives. Finally, a graph coloring approach to deployment sourcing addresses one of the external factors of personnel inventory behavior, deployments. The configuration of persistent unit deployments has the ability to affect everything from individual perceptions of service palatability to operational effectiveness. There is little evidence to suggest any analytical underpinnings to U.S. Army deployment scheduling and unit assignment patterns. This paper shows that the deployment scheduling and unit assignment (DSUA) problem can be formulated as an interval graph such that modifications to traditional graph coloring algorithms provide an efficient mechanism for dealing with multiple objectives

Optimization of Spectrum Allocation in Cognitive Radio and Dynamic Spectrum Access Networks

Spectrum has become a treasured commodity. However, many licensed frequency bands exclusively assigned to the primary license holders (also called primary users) remain relatively unused or under-utilized for most of the time. Allowing other users (also called secondary users) without a license to operate in these bands with no interference becomes a promising way to satisfy the fast growing needs for frequency spectrum resources. A cognitive radio adapts to the environment it operates in by sensing the spectrum and quickly decides on appropriate frequency bands and transmission parameters to use in order to achieve certain performance goals. One of the most important issues in cognitive radio networks (CRNs) is intelligent channel allocation which will improve the performance of the network and spectrum utilization. The objective of this dissertation is to address the channel allocation optimization problem in cognitive radio and DSA networks under both centralized architecture and distributed architecture. By centralized architecture we mean the cognitive radio and DSA networks are infrastructure based. That is, there is a centralized device which collects all information from other cognitive radios and produces a channel allocation scheme. Then each secondary user follows the spectrum allocation and accesses the corresponding piece of spectrum. By distributed architecture we mean that each secondary user inside the cognitive radio and DSA networks makes its own decision based on local information on the spectrum usage. Each secondary user only considers the spectrum usage around itself. We studied three common objectives of the channel allocation optimization problem, including maximum network throughput (MNT), max-min fairness (MMF), and proportional fairness (PF). Given different optimization objectives, we developed mathematical models in terms of linear programing and non-linear programing formulations, under the centralized architecture. We also designed a unified framework with different heuristic algorithms for different optimization objectives and the best results from different algorithms can be automatically chosen without manual intervention. We also conducted additional work on spectrum allocation under distributed architecture. First, we studied the channel availability prediction problem. Since there is a lot of usable statistic information on spectrum usage from national and regional agencies, we presented a Bayesian inference based prediction method, which utilizes prior information to make better prediction on channel availability. Finally a distributed channel allocation algorithm is designed based on the channel prediction results. We illustrated that the interaction behavior between different secondary users can be modeled as a game, in which the secondary users are denoted as players and the channels are denoted as resources. We proved that our distributed spectrum allocation algorithm can achieve to Nash Equilibrium, and is Pareto optimal

Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time

Design and provisioning of WDM networks for traffic grooming

Wavelength Division Multiplexing (WDM) is the most viable technique for utilizing the enormous amounts of bandwidth inherently available in optical fibers. However, the bandwidth offered by a single wavelength in WDM networks is on the order of tens of Gigabits per second, while most of the applications\u27 bandwidth requirements are still subwavelength. Therefore, cost-effective design and provisioning of WDM networks require that traffic from different sessions share bandwidth of a single wavelength by employing electronic multiplexing at higher layers. This is known as traffic grooming. Optical networks supporting traffic grooming are usually designed in a way such that the cost of the higher layer equipment used to support a given traffic matrix is reduced. In this thesis, we propose a number of optimal and heuristic solutions for the design and provisioning of optical networks for traffic grooming with an objective of network cost reduction. In doing so, we address several practical issues. Specifically, we address the design and provisioning of WDM networks on unidirectional and bidirectional rings for arbitrary unicast traffic grooming, and on mesh topologies for arbitrary multipoint traffic grooming. In multipoint traffic grooming, we address both multicast and many-to-one traffic grooming problems. We provide a unified frame work for optimal and approximate network dimensioning and channel provisioning for the generic multicast traffic grooming problem, as well as some variants of the problem. For many-to-one traffic grooming we propose optimal as well as heuristic solutions. Optimal formulations which are inherently non-linear are mapped to an optimal linear formulation. In the heuristic solutions, we employ different problem specific search strategies to explore the solution space. We provide a number of experimental results to show the efficacy of our proposed techniques for the traffic grooming problem in WDM networks

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum