A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems

This paper presents a hybrid multi-objective model that combines integer programming (IP) and variable neighbourhood search (VNS) to deal with highly-constrained nurse rostering problems in modern hospital environments. An IP is first used to solve the subproblem which includes the full set of hard constraints and a subset of soft constrains. A basic VNS then follows as a postprocessing procedure to further improve the IP’s resulting solutions. The satisfaction of the excluded constraints from the preceding IP model is the major focus of the VNS. Very promising results are reported compared with a commercial genetic algorithm and a hybrid VNS approach on real instances arising in a Dutch hospital. The comparison results demonstrate that our hybrid approach combines the advantages of both the IP and the VNS to beat other approaches in solving this type of problems. We also believe that the proposed methodology can be applied to other resource allocation problems with a large number of constraints.     

Wavelength assignment for reducing in-band crosstalk attack propagation in optical networks: ILP formulations and heuristic algorithms

Today’s Transparent Optical Networks (TONs) are highly vulnerable to various physical-layer attacks, such as high-power jamming, which can cause severe service disruption or even service denial. The transparency of TONs enables certain attacks to propagate through the network, not only increasing their damage proportions, but also making source identification and attack localization more difficult. High-power jamming attacks causing in-band crosstalk in switches are amongst the most malicious of such attacks. In this paper, we propose a wavelength assignment scheme to reduce their damage assuming limited attack propagation capabilities. This complements our previous work in Furdek et al. (M. Furdek, N. Skorin-Kapov, M. Grbac, Attack-aware wavelength assignment for localization of in-band crosstalk attack propagation, IEEE/OSA Journal of Optical Communications and Networking 2 (11) (2010) 1000–1009) where we investigated infinite jamming attack propagation to find an upper bound on the network vulnerability to such attacks. Here, we consider a more realistic scenario where crosstalk attacks can spread only via primary and/or secondary attackers and define new objective criteria for wavelength assignment, called the PAR (Primary Attack Radius) and SAR (Secondary Attack Radius), accordingly. We formulate the problem variants as integer linear programs (ILPs) with the objectives of minimizing the PAR and SAR values. Due to the intractability of the ILP formulations, for larger instances we propose GRASP (Greedy Randomized Adaptive Search Procedure) heuristic algorithms to find suboptimal solutions in reasonable time. Results show that these approaches can obtain solutions using the same number of wavelengths as classical wavelength assignment, while significantly reducing jamming attack damage proportions in optical networks.     

A survey of vector optimization in infinite-dimensional spaces,part 2

The present survey deals with the state of vector optimization as a mathematical discipline. In this context, the optima are generally defined as maximal pointsy ₀ with respect to a partial order on the criteria space. The survey is restricted to a discussion of that literature which deals with pointsy ₀ which satisfy a maximality condition with respect toy ₀-comparable criteria values; papers which are based on a maximality condition satisfied for all admissible criteria values are included only in a supplementary bibliography. For the former, all aspects of the optimization process are surveyed, ranging from questions of existence to the treatment of duality. Particular attention is paid to questions of proper maximality. The discussion is based on a broad range of definitions and selected theorems from the literature.The authors wish to express their appreciation to O. Saleh and Y. H. Liu for their thoughtful ear, their cogent suggestions, and their untiring legwork in procuring and discussing many of the papers cited in this review. Above all, however, their thanks go to Professors L. Hurwicz and J. M. Borwein for the excellent papers they produced in this area. Their work was a pleasure to read, and it provided the supporting framework without which our task would have been a considerably more difficult one.     

Book review of spectral theory of linear operators and spectral systems in banach algebras,operator theory: advances and applications,Vladimir Müller,Birkhäuser Verlag,Basel-Boston-Berlin, 2003, Volume 139, 381 pages. ISBN 3-7643-6912-4

We explore how randomization can help asymptotic convergence properties of simple directional search-based optimization methods. Specifically, we develop a cheap, iterative randomized Hessian estimation scheme. We then apply this technique and analyse how it enhances a random directional search method. Then, we proceed to develop a conjugate-directional search method that incorporates estimated Hessian information without requiring the direct use of gradients.     

A survey of multicriteria optimization or the vector maximum problem,part I: 1776–1960

In this survey, the history of the subject from 1776 until 1960 is presented. A brief biographical sketch of Vilfredo Pareto is given first. Then, the more or less simultaneous development of the concepts of utility, preference, and welfare theory follows, with results which go back to Hausdorff and Cantor. A brief discussion of the work of Borel and von Neumann as initiators of game theory is included. Each of these areas has developed enough to warrant its own survey; hence, they are reviewed here only insofar as they provide necessary foundations. Thereafter, the concepts of efficiency, vector maximum problem, and Pareto optimality are reviewed in connection with production theory, programming, and economics. The survey is presented within a unified mathematical framework, and the emphasis is on mathematical results, rather than psychological or socio-economic discussion. To enable the reader to draw conclusions without having to obtain each article himself, the results have been presented in somewhat more detail than usual.     

Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory,algorithms and applications

Over the past decade, the field of finite-dimensional variational inequality and complementarity problems has seen a rapid development in its theory of existence, uniqueness and sensitivity of solution(s), in the theory of algorithms, and in the application of these techniques to transportation planning, regional science, socio-economic analysis, energy modeling, and game theory. This paper provides a state-of-the-art review of these developments as well as a summary of some open research topics in this growing field.The research of this author was supported by the National Science Foundation Presidential Young Investigator Award ECE-8552773 and by the AT&T Program in Telecommunications Technology at the University of Pennsylvania.The research of this author was supported by the National Science Foundation under grant ECS-8644098.     

Exploiting special structure in semidefinite programming: A survey of theory and applications

Semidefinite programming (SDP) may be seen as a generalization of linear programming (LP). In particular, one may extend interior point algorithms for LP to SDP, but it has proven much more difficult to exploit structure in the SDP data during computation.     

Strategies of node selection in search procedures for solving combinatorial optimization problems: A survey and a general formalization

Currently, most combinatorial optimization problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. The objective of this work is to propose a survey and a general formalization of the selection strategy of the next node to explore, a feature that is common to all these optimization procedures. This research has been partially supported by TAP98-0494 project     

Dickson’s Lemma,Higman’s Theorem and Beyond: A survey of some basic results in order theory

We provide proofs for the fact that certain orders have no infinite descending chains and no infinite antichains.     

A recursive linear programming analysis of the future of the pulp and paper industry in the United States: Changes in supplies and demands,and the effects of recycling

The impacts of increased paper recycling on the U.S. pulp and paper sector are investigated, using the North American Pulp And Paper (NAPAP) model. This dynamic spatial equilibrium model forecasts the amount of pulp, paper and paperboard exchanged in a multi-region market, and the corresponding prices. The core of the model is a recursive price-endogenous linear programming system that simulates the behavior of a competitive industry. The model has been used to make forecasts of key variables describing the sector from 1986 to 2012, demand for paper would have the greatest impact on the amount of wood used. But the minimum recycled content policies envisaged currently would have no more effect than what will come about due to unregulated market forces.