Solving nonconvex trim loss problem using an efficient hybrid Particle Swarm Optimization

Trim loss is one of the most common problem arising in process industries. Its mathematical model is a nonconvex mixed integer nonlinear programming problem subject to several constraints. In this paper we consider four hypothetical cases, taken from literature [1] and propose an efficient approach based on Particle Swarm Optimization namely ILXPSO for solving trim loss problem. The numerical results when compared with the results available in literature [1] show the efficiency and robustness of the proposed algorithm.

[1]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[2]  Michael C. Georgiadis,et al.  An algorithm for the determination of optimal cutting patterns , 2002, Comput. Oper. Res..

[3]  Ralf Östermark,et al.  Solving a nonlinear non-convex trim loss problem with a genetic hybrid algorithm , 1999, Comput. Oper. Res..

[4]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[5]  A. I. Hinxman The trim-loss and assortment problems: A survey , 1980 .

[6]  Ramón Alvarez-Valdés,et al.  A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems , 2005, J. Oper. Res. Soc..

[7]  Robert W. Haessler,et al.  Controlling Cutting Pattern Changes in One-Dimensional Trim Problems , 1975, Oper. Res..

[8]  Patrizia Beraldi,et al.  The stochastic trim-loss problem , 2009, Eur. J. Oper. Res..

[9]  Ramón Alvarez-Valdés,et al.  A tabu search algorithm for large-scale guillotine (un)constrained two-dimensional cutting problems , 2002, Comput. Oper. Res..

[10]  Gerhard Wäscher An LP-based approach to cutting stock problems with multiple objectives , 1990 .

[11]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[12]  Iiro Harjunkoski,et al.  Numerical and environmental considerations on a complex industrial mixed integer non-linear programming (MINLP) problem , 1999 .

[13]  C. Adjiman,et al.  Global optimization of mixed‐integer nonlinear problems , 2000 .

[14]  Kusum Deep,et al.  Information sharing strategy among particles in Particle Swarm Optimization using Laplacian operator , 2009, 2009 IEEE Swarm Intelligence Symposium.

[15]  Iiro Harjunkoski,et al.  Different transformations for solving non-convex trim-loss problems by MINLP , 1998, Eur. J. Oper. Res..

[16]  Different formulations for solving trim loss problems in a paper-converting mill with ILP , 1996 .

[17]  Gleb Belov,et al.  A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting , 2006, Eur. J. Oper. Res..

[18]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[19]  Xianjun Shen,et al.  General Particle Swarm Optimization Based on Simulated Annealing for Multi-Specification One-dimensional Cutting Stock Problem , 2006, 2006 International Conference on Computational Intelligence and Security.

[20]  Gleb Belov,et al.  Solving one-dimensional cutting stock problems exactly with a cutting plane algorithm , 2001, J. Oper. Res. Soc..