Natashia Boland

Bio: Natashia Boland is an academic researcher from Georgia Institute of Technology. The author has contributed to research in topics: Integer programming & Shortest path problem. The author has an hindex of 31, co-authored 119 publications receiving 3526 citations. Previous affiliations of Natashia Boland include University of Melbourne & University of Newcastle.

Flight String Models for Aircraft Fleeting and Routing

Abstract: Given a schedule of flight legs to be flown by an airline, the fleet assignment problem is to determine the minimum cost assignment of flights to aircraft types, called fleets, such that each scheduled flight is assigned to exactly one fleet, and the resulting assignment is feasible to fly given a limited number of aircraft in each fleet. Then the airline must determine a sequence of flights, or routes, to be flown by individual aircraft such that assigned flights are included in exactly one route, and all aircraft can be maintained as necessary. This is referred to as the aircraft routing problem. In this paper, we present a single model and solution approach to solve simultaneously the fleet assignment and aircraft routing problems. Our approach is robust in that it can capture costs associated with aircraft connections and complicating constraints such as maintenance requirements. By setting the number of fleets to one, our approach can be used to solve the aircraft routing problem alone. We show how to extend our model and solution approach to solve aircraft routing problems with additional constraints requiring equal aircraft utilization. With data provided by airlines, we provide computational results for the combined fleet assignment and aircraft routing problems without equal utilization requirements and for aircraft routing problems requiring equal aircraft utilization.

Improved preprocessing, labeling and scaling algorithms for the Weight-Constrained Shortest Path Problem

Abstract: Much has been written on shortest path problems with weight, or resource, constraints. However, relatively little of it has provided systematic computational comparisons for a representative selection of algorithms. Furthermore, there has been almost no work showing numerical performance of scaling algorithms, although worst-case complexity guarantees for these are well known, nor has the effectiveness of simple preprocessing techniques been fully demonstrated. Here, we provide a computational comparison of three scaling techniques and a standard label-setting method. We also describe preprocessing techniques which take full advantage of cost and upper-bound information that can be obtained from simple shortest path information. We show that integrating information obtained in preprocessing within the label-setting method can lead to very substantial improvements in both memory required and run time, in some cases, by orders of magnitude. Finally, we show how the performance of the label-setting method can be further improved by making use of all Lagrange multiplier information collected in a Lagrangean relaxation first step. © 2003 Wiley Periodicals, Inc.

A Hybrid Algorithm for the Examination Timetabling Problem

Abstract: Examination timetabling is a well-studied combinatorial optimization problem. We present a new hybrid algorithm for examination timetabling, consisting of three phases: a constraint programming phase to develop an initial solution, a simulated annealing phase to improve the quality of solution, and a hill climbing phase for further improvement. The examination timetabling problem at the University of Melbourne is introduced, and the hybrid method is proved to be superior to the current method employed by the University. Finally, the hybrid method is compared to established methods on the publicly available data sets, and found to perform well in comparison.

Selected Topics in Column Generation

Abstract: Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large-scale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not yet found in textbooks. We emphasize the growing understanding of the dual point of view, which has brought considerable progress to the column generation theory and practice. It stimulated careful initializations, sophisticated solution techniques for the restricted master problem and subproblem, as well as better overall performance. Thus, the dual perspective is an ever recurring concept in our "selected topics."

Flows in Networks

Abstract: In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.