Solving binary cutting stock with matheuristics using particle swarm optimization and simulated annealing

In last decade, researchers have focused on improving existing methodologies through hybrid algorithms; these are a combination of algorithms between a metaheuristic with other metaheuristic and an exact method, to solve combinatorial optimization problems in the best possible way. This work presents a benchmark of different methodologies to solve the binary cutting stock problem using a column generation framework, this framework is divided into master and subproblem, master problem is solved using a classical integer linear programming, and the subproblem is solved using metaheuristic algorithms (genetic algorithm, simulated annealing and particle swarm optimization). This benchmark analysis is aimed to compare hybrid metaheuristics results with an exact methodology.

[1]  Manuel Iori,et al.  Bin packing and cutting stock problems: Mathematical models and exact algorithms , 2016, Eur. J. Oper. Res..

[2]  V. Cerný.  Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm , 1985 .

[3]  Nicholas R. Jennings,et al.  A hybrid exact algorithm for complete set partitioning , 2016, Artif. Intell..

[4]  Kusum Deep,et al.  A Modified Binary Particle Swarm Optimization for Knapsack Problems , 2012, Appl. Math. Comput..

[5]  Marcos Nereu Arenales,et al.  The usable leftover one-dimensional cutting stock problem - a priority-in-use heuristic , 2013, Int. Trans. Oper. Res..

[6]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[7]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[8]  R. W. Haessler,et al.  Cutting stock problems and solution procedures , 1991 .

[9]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[10]  Christian S. Perone,et al.  Pyevolve: a Python open-source framework for genetic algorithms , 2009, SEVO.

[11]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[12]  Cipriano A. Santos,et al.  Solving Binary Cutting Stock with Matheuristics , 2014, MICAI.

[13]  Hao-Chun Lu,et al.  An integrated algorithm for cutting stock problems in the thin-film transistor liquid crystal display industry , 2013, Comput. Ind. Eng..

[14]  Marcos Nereu Arenales,et al.  The one-dimensional cutting stock problem with usable leftover - A heuristic approach , 2009, Eur. J. Oper. Res..

[15]  Ali Ekici,et al.  Solution approaches for the cutting stock problem with setup cost , 2013, Comput. Oper. Res..

[16]  Sascha Kurz,et al.  Minimal Proper Non-IRUP Instances of the One-Dimensional Cutting Stock Problem , 2014, Discret. Appl. Math..

[17]  Yaodong Cui,et al.  A heuristic for the one-dimensional cutting stock problem with usable leftover , 2010, Eur. J. Oper. Res..

[18]  Reza Tavakkoli-Moghaddam,et al.  Solving an one-dimensional cutting stock problem by simulated annealing and tabu search , 2012 .

[19]  Marcos Nereu Arenales,et al.  The one-dimensional cutting stock problem with usable leftovers - A survey , 2014, Eur. J. Oper. Res..

[20]  Marc Parizeau,et al.  DEAP: evolutionary algorithms made easy , 2012, J. Mach. Learn. Res..

[21]  Yu-Chien Ko,et al.  A note on “Reducing the number of binary variables in cutting stock problems” , 2014, Optim. Lett..