Evolving Bin Packing Heuristics with Genetic Programming

The bin-packing problem is a well known NP-Hard optimisation problem, and, over the years, many heuristics have been developed to generate good quality solutions. This paper outlines a genetic programming system which evolves a heuristic that decides whether to put a piece in a bin when presented with the sum of the pieces already in the bin and the size of the piece that is about to be packed. This heuristic operates in a fixed framework that iterates through the open bins, applying the heuristic to each one, before deciding which bin to use. The best evolved programs emulate the functionality of the human designed ‘first-fit' heuristic. Thus, the contribution of this paper is to demonstrate that genetic programming can be employed to automatically evolve bin packing heuristics which are the same as high quality heuristics which have been designed by humans.

[1]  Jeffrey D. Ullman,et al.  L worst-case performance bounds for rumple one-dimensional packing algorithms siam j , 1974 .

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

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

[4]  Alain Delchambre,et al.  A genetic algorithm for bin packing and line balancing , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

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

[6]  Wansoo T. Rhee,et al.  On Line Bin Packing with Items of Random Size , 1993, Math. Oper. Res..

[7]  Una-May O'Reilly,et al.  Genetic Programming II: Automatic Discovery of Reusable Programs. , 1994, Artificial Life.

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

[9]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

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

[11]  P. Pardalos,et al.  Handbook of Combinatorial Optimization , 1998 .

[12]  E. Coffman,et al.  Bin Packing Approximation Algorithms: Combinatorial Analysis , 1999, Handbook of Combinatorial Optimization.

[13]  P. Nordin.  Genetic Programming III - Darwinian Invention and Problem Solving , 1999 .

[14]  John R. Koza,et al.  Genetic Programming III: Darwinian Invention & Problem Solving , 1999 .

[15]  Graham Kendall,et al.  A Hyperheuristic Approach to Scheduling a Sales Summit , 2000, PATAT.

[16]  Edmund K. Burke,et al.  Practice and Theory of Automated Timetabling III , 2001, Lecture Notes in Computer Science.

[17]  Peter Ross,et al.  Hyper-heuristics: Learning To Combine Simple Heuristics In Bin-packing Problems , 2002, GECCO.

[18]  Graham Kendall,et al.  A Tabu-Search Hyperheuristic for Timetabling and Rostering , 2003, J. Heuristics.

[19]  Graham Kendall,et al.  Hyper-Heuristics: An Emerging Direction in Modern Search Technology , 2003, Handbook of Metaheuristics.

[20]  Peter Ross,et al.  Learning a Procedure That Can Solve Hard Bin-Packing Problems: A New GA-Based Approach to Hyper-heuristics , 2003, GECCO.

[21]  Eric Soubeiga,et al.  Development and application of hyperheuristics to personnel scheduling , 2003 .

[22]  Xiaodong Li,et al.  Multiobjective parsimony enforcement for superior generalisation performance , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[23]  E. Soubeiga,et al.  Multi-Objective Hyper-Heuristic Approaches for Space Allocation and Timetabling , 2005 .

[24]  Edmund K. Burke,et al.  An ant algorithm hyperheuristic for the project presentation scheduling problem , 2005, 2005 IEEE Congress on Evolutionary Computation.

[25]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[26]  L. D. Whitley,et al.  Complexity Theory and the No Free Lunch Theorem , 2005 .

[27]  Sanja Petrovic,et al.  Case-based heuristic selection for timetabling problems , 2006, J. Sched..

[28]  Sanja Petrovic,et al.  A graph-based hyper-heuristic for educational timetabling problems , 2007, Eur. J. Oper. Res..