A Genetic Programming Hyper-Heuristic Approach for Evolving 2-D Strip Packing Heuristics

We present a genetic programming (GP) system to evolve reusable heuristics for the 2-D strip packing problem. The evolved heuristics are constructive, and decide both which piece to pack next and where to place that piece, given the current partial solution. This paper contributes to a growing research area that represents a paradigm shift in search methodologies. Instead of using evolutionary computation to search a space of solutions, we employ it to search a space of heuristics for the problem. A key motivation is to investigate methods to automate the heuristic design process. It has been stated in the literature that humans are very good at identifying good building blocks for solution methods. However, the task of intelligently searching through all of the potential combinations of these components is better suited to a computer. With such tools at their disposal, heuristic designers are then free to commit more of their time to the creative process of determining good components, while the computer takes on some of the design process by intelligently combining these components. This paper shows that a GP hyper-heuristic can be employed to automatically generate human competitive heuristics in a very-well studied problem domain.

[1]  R. Gomory,et al.  Multistage Cutting Stock Problems of Two and More Dimensions , 1965 .

[2]  Nicos Christofides,et al.  An Algorithm for Two-Dimensional Cutting Problems , 1977, Oper. Res..

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

[4]  Ronald L. Rivest,et al.  Orthogonal Packings in Two Dimensions , 1980, SIAM J. Comput..

[5]  Bernard Chazelle,et al.  The Bottomn-Left Bin-Packing Heuristic: An Efficient Implementation , 1983, IEEE Transactions on Computers.

[6]  John E. Beasley,et al.  An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure , 1985, Oper. Res..

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

[8]  L. Fogel,et al.  European Journal Ofoperational Research on Genetic Algorithms for the Packing of Polygons , 1996 .

[9]  Edmund K. Burke,et al.  Examination Timetabling in British Universities: A Survey , 1995, PATAT.

[10]  M. Hifi,et al.  A recursive exact algorithm for weighted two-dimensional cutting , 1996 .

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

[12]  K. Lai,et al.  Developing a simulated annealing algorithm for the cutting stock problem , 1997 .

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

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

[15]  Hongfei Teng,et al.  An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles , 1999, Eur. J. Oper. Res..

[16]  A. Ramesh Babu,et al.  Effective nesting of rectangular parts in multiple rectangular sheets using genetic and heuristic algorithms , 1999 .

[17]  Loris Faina,et al.  An application of simulated annealing to the cutting stock problem , 1999, Eur. J. Oper. Res..

[18]  Mhand Hifi,et al.  Constrained two‐dimensional cutting stock problems a best‐first branch‐and‐bound algorithm , 2000 .

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

[20]  E. Hopper,et al.  An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem , 2001, Eur. J. Oper. Res..

[21]  Pearl Y. Wang,et al.  VLSI placement and area optimization using a genetic algorithm to breed normalized postfix expressions , 2002, IEEE Trans. Evol. Comput..

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

[23]  Sanja Petrovic,et al.  Recent research directions in automated timetabling , 2002, Eur. J. Oper. Res..

[24]  Alex S. Fukunaga,et al.  Automated discovery of composite SAT variable-selection heuristics , 2002, AAAI/IAAI.

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

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

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

[28]  Graham Kendall,et al.  An investigation of a tabu assisted hyper-heuristic genetic algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[29]  Riccardo Poli,et al.  A Simple but Theoretically-Motivated Method to Control Bloat in Genetic Programming , 2003, EuroGP.

[30]  Brenda S. Baker,et al.  Lower bounds for on-line two-dimensional packing algorithms , 1982, Acta Informatica.

[31]  Raymond S. K. Kwan,et al.  Distributed Choice Function Hyper-heuristics for Timetabling and Scheduling , 2004, PATAT.

[32]  Graham Kendall,et al.  A New Placement Heuristic for the Orthogonal Stock-Cutting Problem , 2004, Oper. Res..

[33]  Alex S. Fukunaga,et al.  Evolving Local Search Heuristics for SAT Using Genetic Programming , 2004, GECCO.

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

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

[36]  Andreas Bortfeldt,et al.  A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces , 2006, Eur. J. Oper. Res..

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

[38]  Ansheng Deng,et al.  A new heuristic recursive algorithm for the strip rectangular packing problem , 2006, Comput. Oper. Res..

[39]  Ender Özcan,et al.  Hill Climbers and Mutational Heuristics in Hyperheuristics , 2006, PPSN.

[40]  Graham Kendall,et al.  Evolving Bin Packing Heuristics with Genetic Programming , 2006, PPSN.

[41]  Graham Kendall,et al.  A New Bottom-Left-Fill Heuristic Algorithm for the Two-Dimensional Irregular Packing Problem , 2006, Oper. Res..

[42]  Reha Uzsoy,et al.  Rapid Modeling and Discovery of Priority Dispatching Rules: An Autonomous Learning Approach , 2006, J. Sched..

[43]  Franca Rinaldi,et al.  A two-dimensional strip cutting problem with sequencing constraint , 2007, Eur. J. Oper. Res..

[44]  Graham Kendall,et al.  Automatic heuristic generation with genetic programming: evolving a jack-of-all-trades or a master of one , 2007, GECCO '07.

[45]  Marko Privosnik The scalability of evolved on line bin packing heuristics , 2007, 2007 IEEE Congress on Evolutionary Computation.

[46]  Stefan Helber,et al.  Application of a real-world university-course timetabling model solved by integer programming , 2007, OR Spectr..

[47]  Riccardo Poli,et al.  Generating SAT Local-Search Heuristics Using a GP Hyper-Heuristic Framework , 2007, Artificial Evolution.

[48]  Edmund K. Burke,et al.  A simulated annealing based hyperheuristic for determining shipper sizes for storage and transportation , 2007, Eur. J. Oper. Res..

[49]  Gerhard Wäscher,et al.  An improved typology of cutting and packing problems , 2007, Eur. J. Oper. Res..

[50]  Riccardo Poli,et al.  Linear genetic programming of parsimonious metaheuristics , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

[52]  Ramón Alvarez-Valdés,et al.  Reactive GRASP for the strip-packing problem , 2008, Comput. Oper. Res..

[53]  Rhyd Lewis,et al.  A survey of metaheuristic-based techniques for University Timetabling problems , 2007, OR Spectr..

[54]  Gleb Belov,et al.  One-dimensional heuristics adapted for two-dimensional rectangular strip packing , 2008, J. Oper. Res. Soc..

[55]  Alex S. Fukunaga,et al.  Automated Discovery of Local Search Heuristics for Satisfiability Testing , 2008, Evolutionary Computation.

[56]  Antoine Jouglet,et al.  A new constraint programming approach for the orthogonal packing problem , 2008, Comput. Oper. Res..

[57]  Hiroshi Nagamochi,et al.  Exact algorithms for the two-dimensional strip packing problem with and without rotations , 2009, Eur. J. Oper. Res..

[58]  Edmund K. Burke,et al.  A survey of search methodologies and automated system development for examination timetabling , 2009, J. Sched..

[59]  Ramón Alvarez-Valdés,et al.  A branch and bound algorithm for the strip packing problem , 2009, OR Spectr..

[60]  Graham Kendall,et al.  A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem , 2009, INFORMS J. Comput..

[61]  Jin-Kao Hao,et al.  Adaptive Tabu Search for course timetabling , 2010, Eur. J. Oper. Res..

[62]  Cláudio Alves,et al.  Arc-flow model for the two-dimensional guillotine cutting stock problem , 2010, Comput. Oper. Res..