2020
DOI: 10.1371/journal.pone.0229358
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Positions and covering: A two-stage methodology to obtain optimal solutions for the 2d-bin packing problem

Abstract: We present a two-stage methodology called Positions and Covering (P&C) to solve the twodimensional bin packing problem (2D-BPP). The objective of this classical combinatorial NP-hard problem is to pack a set of items (small rectangles) in the minimum number of bins (larger rectangles). The first stage is the key-point of the Positions and Covering, where for each item, it is generated in a pseudo-polynomial way a set of valid positions that indicate the possible ways of packing the item into the bin. In the se… Show more

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Cited by 20 publications
(17 citation statements)
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“…In this section, we present the materials and methods used to solve the 2SP. First, we show the adaptation of the P&C proposed by [ 10 ] to solve the 2d-bin packing problem. Then, we describe each part of the methodology for the 2SP.…”
Section: Methodsmentioning
confidence: 99%
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“…In this section, we present the materials and methods used to solve the 2SP. First, we show the adaptation of the P&C proposed by [ 10 ] to solve the 2d-bin packing problem. Then, we describe each part of the methodology for the 2SP.…”
Section: Methodsmentioning
confidence: 99%
“…Else, the H -value is increased by one or in a dichotomous way, the new set of valid positions for the items is generated, and the covering model is solved again. These last three steps represent the main difference with the P&C for the 2D-BPP (see [ 10 ]). The procedure ends when P&C finds a feasible solution of the D-2SP( H ), and the current height becomes the optimal one.…”
Section: Methodsmentioning
confidence: 99%
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“…Traveling Salesman [92] Traveling Salesman [93] Multiple Traveling Salesman [94] Bottleneck Traveling Salesman [95] Cutting Stock [96] Cutting Stock [97] 2D Cutting [98] Packing [99] Packing [100] 2D Packing [101] Bin Packing [102] Knapsack [103] Knapsack [104] Subset Sum [105] Unbounded Knapsack [105] Bounded Knapsack [106] Multiple Knapsack [107] Quadratic Knapsack [108] Scheduling [109] Scheduling [110] Production Scheduling [111] Workforce Scheduling [112] Job-Shop Scheduling [113] Precedence Constrained Scheduling [114] Educational Timetabling [115] Educational Timetabling [116] Facility Location [117] Assignment [118] Quadratic Assignment [119] Spanning Tree [120] Maximum Leaf Spanning Tree [121] Degree Constrained Spanning Tree [122] Minimum Spanning Tree [123] Boolean Satisfiability [124] Boolean Satisfiability [125] Covering [126] Minimum Vertex Cover [127] Set Cover [128] Exact Cover [129] Minimum Edge Cover [130] Vehicle Routing [131] Vehicle Routing…”
Section: Type Problemmentioning
confidence: 99%