Algoritmo genético para el problema logístico de asignación de la mochila (Knapsack Problem)

The present work addresses the case study of a national trading company through the Knapsack Problem (KP). This logistic problem consists on determining the products to be stored that have the best cost-benefit ratio for the company without affecting its storage capacity. This is the reason why the KP a binary multi-criterion problem of NP-hard complexity. While there are exact tools that can solve some instances of this problem, in practice these can have a significant cost to the company which may limit their acquisition. Due to this, a free-access proposal which consists of a Genetic Algorithm (GA) was developed to solve the KP in a feasible way for the company. The GA uses random crossing, uniform crossing and mutation operators. The performance of the GA was evaluated with an optimal value, showing a percentage error smaller than 4% when compared to an exact commercial tool.

[1]  Seyda Topaloglu,et al.  A multi-start iterated local search algorithm for the generalized quadratic multiple knapsack problem , 2017, Comput. Oper. Res..

[2]  Kazuo Iwama,et al.  Removable Online Knapsack Problems , 2002, ICALP.

[3]  Hans Kellerer,et al.  Knapsack problems , 2004 .

[4]  Sergio Nesmachnow,et al.  Estudio empírico de operadores de cruzamiento en un algoritmo genético aplicado al problema de steiner generalizado , 2003 .

[5]  José Luis Verdegay Galdeano,et al.  Algoritmos genéticos: fundamentos, extensiones y aplicaciones , 1995 .

[6]  T. Ormerod,et al.  Human performance on the traveling salesman problem , 1996, Perception & psychophysics.

[7]  Alfredo Olivera Heurísticas para problemas de ruteo de vehículos , 2004 .

[8]  Lalit M. Patnaik,et al.  Genetic algorithms: a survey , 1994, Computer.

[9]  R. Carraway,et al.  An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns , 1993 .

[10]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[11]  M. Wiecek,et al.  Dynamic programming approaches to the multiple criteria knapsack problem , 2000 .

[12]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[13]  Daniel Vanderpooten,et al.  The lexicographic α-robust knapsack problem , 2011, Int. Trans. Oper. Res..

[14]  Silvano Martello,et al.  Heuristics for the General Multiple Non-linear Knapsack Problem , 2016, Electron. Notes Discret. Math..

[15]  Xin Yao,et al.  An iterative pseudo-gap enumeration approach for the Multidimensional Multiple-choice Knapsack Problem , 2017, Eur. J. Oper. Res..

[16]  Sebastian Stiller,et al.  Packing a Knapsack of Unknown Capacity , 2014, STACS.

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