An Attribute Grammar Decoder for the 01 MultiConstrained Knapsack Problem

We describe how the standard genotype-phenotype mapping process of Grammatical Evolution (GE) can be enhanced with an attribute grammar to allow GE to operate as a decoder-based Evolutionary Algorithm (EA). Use of an attribute grammar allows GE to maintain context-sensitive and semantic information pertinent to the capacity constraints of the 01 Multiconstrained Knapsack Problem (MKP). An attribute grammar specification is used to perform decoding similar to a first-fit heuristic. The results presented are encouraging, demonstrating that GE in conjunction with attribute grammars can provide an improvement over the standard context-free mapping process for problems in this domain.

[1]  Jens Gottlieb,et al.  Permutation-based evolutionary algorithms for multidimensional knapsack problems , 2000, SAC '00.

[2]  G. Raidl Weight-codings in a genetic algorithm for the multi-constraint knapsack problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[4]  Donald E. Knuth,et al.  Semantics of context-free languages , 1968, Mathematical systems theory.

[5]  John R. Koza,et al.  Genetic programming (videotape): the movie , 1992 .

[6]  Carlos Cotta,et al.  A Hybrid Genetic Algorithm for the 0-1 Multiple Knapsack Problem , 1997, ICANNGA.

[7]  Günther R. Raidl,et al.  The Effects of Locality on the Dynamics of Decoder-Based Evolutionary Search , 2000, GECCO.

[8]  R. Hinterding Representation, constraint satisfaction and the knapsack problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[9]  Peter Nordin,et al.  Genetic programming - An Introduction: On the Automatic Evolution of Computer Programs and Its Applications , 1998 .

[10]  Conor Ryan,et al.  Grammatical evolution , 2007, GECCO '07.

[11]  Günther R. Raidl,et al.  Characterizing Locality in Decoder-Based EAs for the Multidimensional Knapsack Problem , 1999, Artificial Evolution.

[12]  Jens Gottlieb,et al.  On the Effectivity of Evolutionary Algorithms for the Multidimensional Knapsack Problem , 1999, Artificial Evolution.

[13]  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.

[14]  Michael O’Neill,et al.  Solving Knapsack Problems with Attribute Grammars , 2004 .

[15]  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.

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

[17]  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).

[18]  Jens Gottlieb Evolutionary Algorithms for Multidimensional Knapsack Problems: the Relevance of the Boundary f the Feasible Region , 1999, GECCO.

[19]  Günther R. Raidl,et al.  On the Importance of Phenotypic Duplicate Elimination in Decoder-Based Evolutionary Algorithms , 2002 .

[20]  Michael O'Neill,et al.  Grammatical evolution - evolutionary automatic programming in an arbitrary language , 2003, Genetic programming.

[21]  Vidroha Debroy,et al.  Genetic Programming , 1998, Lecture Notes in Computer Science.

[22]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[23]  Michael O'Neill,et al.  Grammatical Evolution: Evolving Programs for an Arbitrary Language , 1998, EuroGP.

[24]  Conor Ryan,et al.  Grammatical Evolution , 2001, Genetic Programming Series.

[25]  Rudolf F. Albrecht,et al.  Artificial Neural Nets and Genetic Algorithms , 1995, Springer Vienna.