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In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problem--a difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steady-state genetic algorithm in conjunction with a specialized local search heuristic for solving the set partitioning problem. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steady-state genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty real-world set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, high-quality integer feasible solutions were found for problems with 36,699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints.

Despite more than a decade of experimental work in multi-robot systems, important theoretical aspects of multi-robot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multi-robot task allocation (MRTA). Most work on MRTA has been ad hoc and empirical, with many coordination architectures having been proposed and validated in a proof-of-concept fashion, but infrequently analyzed. With the goal of bringing objective grounding to this important area of research, we present a formal study of MRTA problems. A domain-independent taxonomy of MRTA problems is given, and it is shown how many such problems can be viewed as instances of other, well-studied, optimization problems. We demonstrate how relevant theory from operations research and combinatorial optimization can be used for analysis and greater understanding of existing approaches to task allocation, and show how the same theory can be used in the synthesis of new approaches.

This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steady-state genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty real-world problems. It found the optimal solution for half the problems, and good solutions for nine others. The results were compared to those obtained with branch-and-cut and branchand -bound algorithms. The branch-and-cut algorithm was significantly more successful than the hybrid algorithm, and the branch-and-bound algorithm slightly better. 1 Introduction Genetic algorithms (GAs) are search algorithms that were developed by John Holland [17]. They are based on an analogy with natural selection and population genetics. One common application of GAs is for finding approximate solutions to difficult optimization problems. In this paper we describe the application of a hybrid GA (a genetic algorithm combined with a local s...

In this paper we present a genetic algorithm-based heuristic for solving the set partitioning problem. The set partitioning problem is an important combinatorial optimisation problem used by many airlines as a mathematical model for flight crew scheduling. We develop a steady-state genetic algorithm in conjunction with a specialised heuristic feasibility operator for solving the set partitioning problem. Some basic genetic algorithm components, such as fitness definition, parent selection and population replacement are modified. The performance of our algorithm is evaluated on a large set of real-world set partitioning problems provided by the airline industry. Computational results show that the genetic algorithm-based heuristic is capable of producing highquality solutions. In addition a number of the ideas presented (separate fitness, unfitness scores and subgroup population replacement) are applicable to any genetic algorithm for constrained problems. Keywords: combinator...

This paper outlines an alternative solution method which has been incorporated into a system which originated from IMPACS. Improved results on a selection of real bus driver problems are presented. THE DRIVER SCHEDULING PROBLEM

0-1 problems are often difficult to solve. Although special purpose algorithms (exact as well as heuristic) exist for solving particular problem classes or problem instances, there are few general purpose algorithms for solving practical-sized instances of 0-1 problems. This paper deals with a general purpose heuristic algorithm for 0-1 problems. In this paper we compare two methods based on simulated annealing for solving general 0-1 integer programming problems. The two methods differ in the scheme used for neighbourhood transitions in the simulated annealing framework. We compare the performance of the two methods on the set partitioning problem. 1. Introduction 1.1 General Introduction 0-1 integer programming problems are a very important class of integer programming problems. Some of the important problems belonging to this class are knapsack, assignment, matching, covering, packing, partitioning, facility location, travelling salesman, fixed charge network flow, and so on. Many p...

The crew pairing optimization problem is faced by airline companies as an intensive part of the crew scheduling process. Crew scheduling is the assignment of cockpit and cabin crews to the flight legs that a company has to carry out during a predefined period of time. Due to the significant contribution of the crew cost to the overall operating cost of an airline company, the automation of the crew scheduling procedure is highly desirable. However, the crew pairing optimization subproblem of crew scheduling is extremely difficult and combinatorial in nature due to the large number and complexity of the involved constraints. The requirement for optimality makes it even more difficult. Many attempts have been made in the past 40 years to tackle the crew pairing optimization problem using methods from Operations Research. In this paper, an approach based on pure Constraint Logic Programming is presented, which leads to an elegant and flexible modeling of the problem. The whole process is ...

The aircrew-scheduling problem consists of two important subproblems: the tours-of-duty planning problem to generate minimum-cost tours of duty (sequences of duty periods and rest periods) to cover all scheduled flights, and the rostering problem to assign tours of duty to individual crew members. Between 1986 and 1999, Air New Zealand staff and consultants in collaboration with the University of Auckland have developed eight application-specific optimization-based computer systems to solve all aspects of the tours-of-duty planning and rostering processes for Air New Zealand’s national and international operations. These systems have saved NZ$15,655,000 per year while providing crew rosters that better respect crew members’ preferences.

We consider the problem of dynamically routing a driver to cover a sequence of tasks (with no consolidation), using a complex set of driver attributes and operational rules. Our motivating application is dynamic routing and scheduling problems, which require fast response times, the ability to handle a wide range of operational concerns, and the ability to output multiple recommendations for a particular driver. A mathematical formulation is introduced that easily handles real-world operational complexities. Two new optimization-based heuristics are described, one giving faster performance and the second providing somewhat higher solution quality. Comparisons to optimal solutions are provided, which measure the quality of the solutions that our algorithms provide. Experimental tests show that our algorithms provide high quality solutions, and are fast enough to be run in real-time applications. We consider the problem of routing and scheduling a heterogeneous set of drivers to cover a known set of tasks. There is a reward for covering each task, and not all the tasks have to be covered. The reward received can depend on when a task is