Genetic Algorithms for the Multiple Container Packing Problem

This paper presents two variants of Genetic Algorithms (GAs) for solving the Multiple Container Packing Problem (MCPP), which is a combinatorial optimization problem comprising similarities to the Knapsack Problem and the Bin Packing Problem. Two different representation schemes are suggested, namely direct encoding and order based encoding. While order based encoded solutions are always feasible, a repair algorithm is used in case of direct encoding to ensure feasibility. Additionally, local improvement operators have been applied to both GA variants. The proposed algorithms were empirically compared by using various sets of differently sized test data. Order based encoding performed better for problems with fewer items, whereas direct encoding exhibited advantages when dealing with larger problems. The local improvement operators lead in many cases not only to better final results but also to shorter running times because of higher convergence rates.

[1]  Yanfeng Sun,et al.  The genetic algorithm for 0-1 programming with linear constraints , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[2]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[3]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[4]  John E. Beasley,et al.  A genetic algorithm for the generalised assignment problem , 1997, Comput. Oper. Res..

[5]  Robert Hinterding,et al.  Mapping, order-independent genes and the knapsack problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  G. Raidl,et al.  An improved genetic algorithm for the multiconstrained 0-1 knapsack problem , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[8]  Anne L. Olsen.  Penalty functions and the knapsack problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[9]  D. Fogel.  Evolutionary algorithms in theory and practice , 1997, Complex..

[10]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[11]  Thomas Bäck,et al.  The zero/one multiple knapsack problem and genetic algorithms , 1994, SAC '94.

[12]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[13]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[14]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[15]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[16]  Emanuel Falkenauer,et al.  A hybrid grouping genetic algorithm for bin packing , 1996, J. Heuristics.

[17]  Hasan Pirkul,et al.  Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality , 1985, Math. Program..

[18]  Günter Rudolph,et al.  Significance of Locality and Selection Pressure in the Grand Deluge Evolutionary Algorithm , 1996, PPSN.

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

[20]  Thomas Bäck,et al.  Evolutionary computation: Toward a new philosophy of machine intelligence , 1997, Complex..