scholarly journals A hybrid VNS matheuristic for a bin packing problem with a color constraint

2021 ◽  
pp. 9-9
Author(s):  
Yury Kochetov ◽  
Arteam Kondakov
Keyword(s):  
Column Generation ◽  
Bin Packing ◽  
Packing Problem ◽  
Upper Bounds ◽  
Hard Problem ◽  
Generation Technique ◽  
Bin Packing Problem ◽  
New Variant ◽  
Finite Set ◽  
Np Hard Problem

We study a new variant of the bin packing problem with a color constraint. Given a finite set of items, each item has a set of colors. Each bin has a color capacity, the total number of colors for a bin is the unification of colors for its items and cannot exceed the bin capacity. We need to pack all items into the minimal number of bins. For this NP-hard problem we present approximability results and design a hybrid matheuristic based on the column generation technique. A hybrid VNS heuristic is applied to the pricing problem. The column generation method provides a lower bound and a core subset of the most promising bin patterns. Fast heuristics and exact solution for this core produce upper bounds. Computational experiments for test instances with number of items up to 500 illustrate the efficiency of the approach.

scholarly journals Lower and upper bounds for the Bin Packing Problem with Fragile Objects

2014 ◽  
Vol 163 ◽  
pp. 73-86 ◽  
Author(s):  
François Clautiaux ◽  
Mauro Dell’Amico ◽  
Manuel Iori ◽  
Ali Khanafer
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Bin Packing Problem

scholarly journals Laboratory Samples Allocation Problem

Proceedings ◽  
2018 ◽  
Vol 2 (18) ◽  
pp. 1189
Author(s):  
Diego Noceda Davila ◽  
Luisa Carpente Rodríguez ◽  
Silvia Lorenzo Freire
Keyword(s):  
Linear Programming ◽  
Heuristic Algorithm ◽  
Optimization Problem ◽  
Bin Packing ◽  
Computational Cost ◽  
Packing Problem ◽  
Hard Problem ◽  
Reasonable Cost ◽  
Np Hard Problem ◽  
Low Computational Cost

This work aims to solve the optimization problem associated with the allocation of laboratory samples in plates. The processing of each of these plates is costly both in time and money, therefore the main objective is to minimize the number of plates used. The characteristics of the problem are reminiscent of the well-known bin packing problem, an NP-Hard problem that, although it is feasible to model as a linear programming problem, it cannot be solved at a reasonable cost. This work, proposes the implementation of a heuristic algorithm that provides good results at a low computational cost.

scholarly journals fuzzy approach for the variable cost and size bin packing problem allowing incomplete packing

2021 ◽  
Vol 24 (67) ◽  
pp. 71-89
Author(s):  
Jorge Herrera-Franklin ◽  
Alejandro Rosete ◽  
Milton García-Borroto
Keyword(s):  
Bin Packing ◽  
Solution Method ◽  
Optimization Problems ◽  
Real Life ◽  
Packing Problem ◽  
Variable Cost ◽  
Bin Packing Problem ◽  
Trade Offs ◽  
Np Hard Problem ◽  
The Cost

The Variable Cost and Size Bin Packing Problem (VCSBPP) is a known NP-Hard problem that consists in minimizing the cost of all bins used to pack a set of items. There are many real-life applications of the VCSBPP where the focus is to improve the efficiency of the solution method. In spite of the existence of fuzzy approaches to adapt other optimization problems to real life conditions, VCSBPP has not been extensively studied in terms of relaxations of the crisp conditions. In this sense, the fuzzy approaches for the VCSBPP varies from relaxing the capacity of the bins to the items weights. In this paper we address a non-explored side consisting in relaxing the set of items to be packed. Therefore, our main contribution is a fuzzy version of VCSBPP that allows incomplete packing. The proposed fuzzy VCSBPP is solved by a parametric approach. Particularly, a fast heuristic algorithm is introduced that allows to obtain a set of solutions with interesting trade-offs between cost and relaxation of the original crisp conditions. An experimental study is presented to explore the proposed fuzzy VCSBPP and its solution.

Upper bounds and algorithms for the maximum cardinality bin packing problem

2003 ◽  
Vol 149 (3) ◽  
pp. 490-498 ◽  
Author(s):  
Martine Labbé ◽  
Gilbert Laporte ◽  
Silvano Martello
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
Upper Bounds ◽  
Maximum Cardinality ◽  
Bin Packing Problem
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