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Mathematical Problems in Engineering
Volume 2013, Article ID 706350, 8 pages
Research Article

Trim Loss Optimization by an Improved Differential Evolution

1Department of Computer Engineering, Sungkyunkwan University, Suwon 440746, Republic of Korea
2Department of Applied Science and Engineering, IIT Roorkee, Roorkee 247667, India

Received 10 April 2013; Accepted 24 June 2013

Academic Editor: Alexander P. Seyranian

Copyright © 2013 Musrrat Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The “trim loss problem” (TLP) is one of the most challenging problems in context of optimization research. It aims at determining the optimal cutting pattern of a number of items of various lengths from a stock of standard size material to meet the customers’ demands that the wastage due to trim loss is minimized. The resulting mathematical model is highly nonconvex in nature accompanied with several constraints with added restrictions of binary variables. This prevents the application of conventional optimization methods. In this paper we use synergetic differential evolution (SDE) for the solution of this type of problems. Four hypothetical but relevant cases of trim loss problem arising in paper industry are taken for the experiment. The experimental results compared with those of the other techniques show the competence of the SDE to solve the problem.