A Genetic Algorithm for the Set Partitioning Problem

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 ight 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 tness deenition, parent selection and population replacement are modiied. 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 high-quality solutions. In addition a number of the ideas presented (separate tness, unntness scores and subgroup population replacement) are applicable to any genetic algorithm for constrained problems.

[1]  J. P. Arabeyre,et al.  The Airline Crew Scheduling Problem: A Survey , 1969 .

[2]  G. Nemhauser,et al.  Integer Programming , 2020 .

[3]  E. Balas,et al.  Set Partitioning: A survey , 1976 .

[4]  Michael Fisher,et al.  Computational results for very large air crew scheduling problems , 1981 .

[5]  Roy E. Marsten,et al.  Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications , 1981, Networks.

[6]  D. Ryan,et al.  On the integer properties of scheduling set partitioning models , 1988 .

[7]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[8]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[9]  M. Fisher,et al.  Optimal solution of set covering/partitioning problems using dual heuristics , 1990 .

[10]  J F Barutt,et al.  AIRLINE CREW SCHEDULING : SUPERCOMPUTERS AND ALGORITHMS , 1990 .

[11]  Kalyanmoy Deb,et al.  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms , 1990, FOGA.

[12]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[13]  Michael M. Skolnick,et al.  Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints , 1993, ICGA.

[14]  Bull,et al.  An Overview of Genetic Algorithms: Pt 2, Research Topics , 1993 .

[15]  M. Padberg,et al.  Solving airline crew scheduling problems by branch-and-cut , 1993 .

[16]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[17]  David Beasley,et al.  An overview of Genetic Algorithms: Pt1, Fundamentals , 1993 .

[18]  Gerald L. Thompson,et al.  The column subtraction algorithm: An exact method for solving weighted set covering, packing and partitioning problems , 1994, Comput. Oper. Res..

[19]  David Mark Levine,et al.  A parallel genetic algorithm for the set partitioning problem , 1995 .