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.

Airline crew scheduling is concerned with finding a minimum cost assignment of flight crews to a given flight schedule while satisfying restrictions dictated by collective bargaining agreements and the Federal Aviation Administration. Traditionally, the problem has been modeled as a set partitioning problem. In this paper, we present a new model based on breaking the decision process into two stages. In the first stage we select a set of duty periods that cover the flights in the schedule. Then, in the second stage, we attempt to build pairings using those duty periods. We suggest a decomposition approach for solving the model and present computational results for test problems provided by a major carrier. Our formulation provides a tighter linear programming bound than that of the conventional set partitioning formulation but is more difficult to solve. 1 Introduction In this paper we present a new formulation and decomposition approach for the airline crew scheduling problem. The ...

Airline crew scheduling algorithms widely used in practice assume no disruptions. Since disruptions often occur, the actual cost of the resulting crew schedules is often significantly greater. We consider algorithms for finding crew schedules that perform well in practice. The deterministic crew scheduling model is an approximation of crew scheduling under uncertainty under the assumption that all pairings will operate as planned. We seek better approximate solution methods for crew scheduling under un- # Corresponding author. schaefer@engrng.pitt.edu 1 certainty that still remain tractable. We give computational results from three fleets that indicate that the crew schedules obtained from our methodology perform better in operations than the crew schedules found via state-of-the-art methods. We provide a lower bound on the cost of an optimal crew schedule in operations, and demonstrate that some of the crew schedules found using our methodology perform very well relative to this lower bound. For major domes(' carriers crew cos ts ares econd only to fuel cosI$ and can exceed a billion dollars annually. Therefore, airlines devote great e#ort to planning good crew shedules But the planning problem can be very di#cult tosI8 e becaus there are many governmental and contractual regulations concerning pilots and problems found in practice often have billions of pos$('4 s olutions There is currently a great deal of concern about air tra#c conges ion. In June 2000, flight delays were up over 16% from June 1999Phillips and Irwin, 2000. Moreover, air tra#c in America and Europe is expected to double in the next 10-15 year s If airport capacity remains cons$ nt, itis es$fifi ted that each 1% increas e in airport tra#c will bring about a 5% increas in delays Anonymous , 2000. Di...

Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modelling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution method-ology for integrating disruptions in the evaluation of crew schedules. The goal is to use that information to find robust solutions that better withstand disruptions. Such an approach is important because we can proactively consider the effects of certain scheduling decisions. By identifying more robust schedules, cascading delay effects will be minimized. In this paper we describe our stochastic integer programming model for the airline crew scheduling problem and develop a branching algorithm to identify expensive flight connections and find alternative solutions. The branching algorithm uses the structure of the prob-lem to branch simultaneously on multiple variables without invalidating the optimality of the algorithm. We present computational results demonstrating the effectiveness of our branching algorithm. 1

Our ability to solve large, important combinatorial optimization problems has improved dramatically in the decade. The availability of reliable software, extremely fast and inexpensive hardware and high-level languages that make the modeling of complex problems much faster have led to a much greater demand for optimization tools. This paper highlights the major breakthroughs and then describes some very exciting future oppommities. Previously, large research projects required major data collection efforts, expensive mainframes and substantial analyst manpower. Now, we can solve much larger problems on personal computers, much of the necessary data is routinely collected and tools exist to speed up both the modeling and the post-optimality analysis. With the information-technology revolution taking place currently, we now have the oppommity to have our tools embedded into supply-chain systems that determine production and distribution schedules, process-design and location-allocation decisions. These tools can be used industry-wide with only minor modifications being done by each user.

This paper presents the design and implementation of an air-crew assignment system for producing and refining a solution to this problem based on the Artificial Intelligence principles and techniques of abductive reasoning as captured by the framework of Abductive Logic Programming (ALP). The system offers a high-level of flexibility in addressing both the tasks of crew scheduling and rescheduling. It can be used to generate a valid and good quality initial solution and then to help the human operators adjust and refine further this solution in order to meet extra requirements of the problem. These additional needs can arise either due to new foreseen requirements that the company wants to have or experiment with for a particular period in time or due to unexpected events that have occurred while the solution (crew-roster) is in operation. Our work shows the ability and flexibility of abduction, and more specifically of ALP, in tackling problems of this type with complex and changing r...

In this paper we investigate how partial evaluation and program transformations can be used on a real problem, namely that of speeding up airline crew scheduling. Scheduling of crew is subject to many rules and restrictions. These restrictions are expressed in a rule language. However, in a given planning situation much is known to be fixed, so the rule set can be partially evaluated wit respect to this known input. The approach is somewhat novel in that it uses truly static input data as well as static input data where the values are known only to belong to a set of values. The results of the partial evaluation is quite satisfactory: both compilation and running times have decreased by using it. The partial evaluator is now part of the crew scheduling system that Carmen Systems AB markets and which is in use at most of the major European airlines and in daily production. Keywords: Partial evaluation, program transformation, generalized constant propagation, airline crew scheduling. ...

We discuss the formulation and solution of large scale integer optimization problems that arise in the scheduling of transport related services. We first set the context for these problems within the airline industry by discussing the scheduling process. We then discuss the two key activities of fleet assignment and crew scheduling that turn a schedule into an operational plan. We provide current formulations in terms of key objectives and constraints for both the fleet and the crew assignment problems. This is followed by a discussion of the state of the art in solution methodology for each problem. We conclude with ideas about promising areas for further work in the application of combinatorial optimization to airline scheduling.

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 ...

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