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A Parallel Genetic Algorithm for the Set Partitioning Problem
, 1994
"... In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed stea ..."
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Cited by 69 (1 self)
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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 problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steadystate 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 steadystate genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty realworld 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, highquality 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: A New Formulation and Decomposition Algorithm
 Operations Research
, 1995
"... 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 ..."
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Cited by 38 (6 self)
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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 under Uncertainty
 Transportation Science
, 2001
"... 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 sch ..."
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Cited by 23 (3 self)
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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 stateoftheart 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$('4 s olutions There is currently a great deal of concern about air tra#c conges ion. In June 2000, flight delays were up over 16% from June 1999Phillips and Irwin, 2000. Moreover, air tra#c in America and Europe is expected to double in the next 1015 year s If airport capacity remains cons$ 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...
Application of a Hybrid Genetic Algorithm to Airline Crew Scheduling
 Computers & Operations Research
, 1996
"... This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steadystate genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty realworld problems. It found the ..."
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Cited by 21 (0 self)
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This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steadystate genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty realworld problems. It found the optimal solution for half the problems, and good solutions for nine others. The results were compared to those obtained with branchandcut and branchand bound algorithms. The branchandcut algorithm was significantly more successful than the hybrid algorithm, and the branchandbound 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...
A Genetic Algorithm for the Set Partitioning Problem
, 1995
"... In this paper we present a genetic algorithmbased 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 steadystate genetic algori ..."
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Cited by 17 (0 self)
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In this paper we present a genetic algorithmbased 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 steadystate 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 realworld set partitioning problems provided by the airline industry. Computational results show that the genetic algorithmbased 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...
Crew Pairing Optimization
 OR IN AIRLINE INDUSTRY, GANG YU (ED.)
"... Next to fuel costs, crew costs are the largest direct operating cost of airlines. Therefore much research has been devoted to the planning and scheduling of crews over the last thirty years. The planning and scheduling of crews is usually considered as two problems: the crew pairing problem and the ..."
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Cited by 15 (1 self)
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Next to fuel costs, crew costs are the largest direct operating cost of airlines. Therefore much research has been devoted to the planning and scheduling of crews over the last thirty years. The planning and scheduling of crews is usually considered as two problems: the crew pairing problem and the crew assignment (rostering) problem. These problems are solved sequentially. In this paper we focus on the pairing problem. The aim of the paper is twofold. First, we give an overview of the crew pairing problem and synthesize the optimization methods that have been published previously. Second, we present the Carmen pairing construction system which is in operation at most major European airlines. Our purpose is to identify the particular properties of the Carmen system that have made this system the preferred decision support system for crew pairing optimization in Europe.
A stochastic programming approach to the airline crew scheduling problem
 Transportation Science
, 2000
"... Traditional methods model the billiondollar 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 me ..."
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Cited by 14 (0 self)
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Traditional methods model the billiondollar 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 methodology 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 problem 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
Recent Advances in Exact Optimization of Airline Scheduling Problems
, 1995
"... 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 fle ..."
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Cited by 6 (0 self)
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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.
Parallel Integer Optimization for Crew Scheduling
 ANNALS OF OPERATIONS RESEARCH
, 2000
"... Performance aspects of a Lagrangian relaxation based heuristic for solving large 01 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at ..."
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Cited by 4 (2 self)
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Performance aspects of a Lagrangian relaxation based heuristic for solving large 01 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, GĂ¶teborg, Sweden, based on distributing the variables. A lazy variant of this approach which decouples communication and computation is even useful on networks of workstations. Furthermore,
Crew Pairing Optimization Based on CLP
, 1996
"... 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 contribu ..."
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Cited by 4 (2 self)
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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 ...