A Two-Dimensional Genetic Algorithm and Its Application to Aircraft Scheduling Problem

Genetic algorithms have become increasingly important for researchers in resolving difficult problems because they can provide feasible solutions in limited time. Using genetic algorithms to solve a problem involves first defining a representation that describes the problem states. Most previous studies have adopted one-dimensional representation. Some real problems are, however, naturally suitable to two-dimensional representation. Therefore, a two-dimensional encoding representation is designed and the traditional genetic algorithm is modified to fit the representation. Particularly, appropriate two-dimensional crossover and mutation operations are proposed to generate candidate chromosomes in the next generations. A two-dimensional repairing mechanism is also developed to adjust infeasible chromosomes to feasible ones. Finally, the proposed approach is used to solve the scheduling problem of assigning aircrafts to a time table in an airline company for demonstrating the effectiveness of the proposed genetic algorithm.

[1]  Jennifer Ryan,et al.  A Two-Dimensional Genetic Algorithm for the Ising Problem , 1991, Complex Syst..

[2]  K. De Jong.  Adaptive System Design: A Genetic Approach , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Luis Gerardo de la Fraga,et al.  Binary Genetic Encoding for the Synthesis of Mixed-Mode Circuit Topologies , 2012, Circuits Syst. Signal Process..

[4]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[5]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Peter M. Todd,et al.  Designing Neural Networks using Genetic Algorithms , 1989, ICGA.

[7]  Byung Ro Moon,et al.  On Multi-Dimensional Encoding/Crossover , 1995, ICGA.

[8]  Hiroshi Katayama,et al.  Uniform workload assignments for assembly line by GA-based amelioration approach , 2010 .

[9]  Dingwei Wang,et al.  Aircraft Ground Service Scheduling Problems and Their Genetic Algorithm With Hybrid Assignment and Sequence Encoding Scheme , 2013, IEEE Systems Journal.

[10]  C. Srinivas,et al.  Sensitivity Analysis to Determine the Parameters of Genetic Algorithm for Machine Layout , 2014 .

[11]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[12]  Edwin R. Hancock,et al.  Genetic algorithm parameter sets for line labelling , 1997, Pattern Recognit. Lett..

[13]  G. Rodriguez,et al.  Applications of evolutionary algorithms in the design automation of analog integrated circuits , 2010 .

[14]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[15]  Peter J. Angeline,et al.  Evolutionary Module Acquisition , 1993 .

[16]  Kuang Tsan Lin,et al.  Information Hiding Based on Binary Encoding Methods and Crossover Mechanism of Genetic Algorithms , 2013, ICGEC.

[17]  C. G. Shaefer,et al.  The ARGOT Strategy: Adaptive Representation Genetic Optimizer Technique , 1987, ICGA.

[18]  Bogdan Filipič,et al.  An Interactive Genetic Algorithm for Controller Parameter Optimization , 1993 .

[19]  Giuseppe Aiello,et al.  A multi objective genetic algorithm for the facility layout problem based upon slicing structure encoding , 2012, Expert Syst. Appl..

[20]  Kenneth A. De Jong,et al.  An Analysis of the Interacting Roles of Population Size and Crossover in Genetic Algorithms , 1990, PPSN.

[21]  Hideyuki Takagi,et al.  Dynamic Control of Genetic Algorithms Using Fuzzy Logic Techniques , 1993, ICGA.

[22]  Nichael Lynn Cramer,et al.  A Representation for the Adaptive Generation of Simple Sequential Programs , 1985, ICGA.

[23]  Felix T. S. Chan,et al.  Optimizing replenishment polices using Genetic Algorithm for single-warehouse multi-retailer system , 2012, Expert Syst. Appl..

[24]  Tung-Kuan Liu,et al.  Method of Inequality-Based Multiobjective Genetic Algorithm for Domestic Daily Aircraft Routing , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[25]  D.E. Goldberg,et al.  Classifier Systems and Genetic Algorithms , 1989, Artif. Intell..

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

[27]  James P. Cohoon,et al.  Genetic Placement , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[28]  Hiroaki Kitano,et al.  Empirical Studies on the Speed of Convergence of Neural Network Training Using Genetic Algorithms , 1990, AAAI.

[29]  José Rui Figueira,et al.  Single row facility layout problem using a permutation-based genetic algorithm , 2011, Eur. J. Oper. Res..

[30]  Amir Sadrzadeh,et al.  A genetic algorithm with the heuristic procedure to solve the multi-line layout problem , 2012, Comput. Ind. Eng..

[31]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[32]  Gaganpreet Kaur,et al.  Neural Networks using Genetic Algorithms , 2013 .

[33]  Rajarshi Das,et al.  A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization , 1989, ICGA.

[34]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[35]  Willard Korfhage,et al.  Process scheduling using genetic algorithms , 1995, Proceedings.Seventh IEEE Symposium on Parallel and Distributed Processing.

[36]  David Levine,et al.  Application of a hybrid genetic algorithm to airline crew scheduling , 1996, Comput. Oper. Res..

[37]  Philip R. Thrift,et al.  Fuzzy Logic Synthesis with Genetic Algorithms , 1991, ICGA.

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