Full reference: Sunkanghong Wang, Shaowen Yao, Hao Zhang, Qiang Liu and Lijun Wei. (2023). An arc-flow formulation and a branch-and-price-and-cut algorithm for the bin packing problem with fragile objects. Under revision.
This repository hosts the files backing up the data and experimental results described in our paper A Branch-and-Price-and-Cut Algorithm for the Bin Packing Problem with Fragile Objects referenced above. The paper is now under revision. A link to it will be provided as soon as possible.
If you have any questions, please feel free to reach out to villagerwei@gdut.edu.cn or wskh0929@gmail.com
In the code_BP_2013 folder, you will find the source code of the branch-and-price algorithm we implemented from Martínez et al. (2013).
The BPPFI files that describe the instances are found in the instances/Existing_Instances folder. The instances in this folder are classic benchmark instances created by Clautiaux et al. (2014). This benchmark set consists of 675 instances containing 50, 100 and 200 items, which are classified into 5 classes based on how they are created in terms of weights and fragilities.
The second set of instances is generated randomly using uniform distributions, which can be found in the instances/Random_Instances folder. This group of instances can be represented by a tuple
- The value of
$c$ corresponds to the maximum fragility value among all items, and we consider$c\in {10,50,100}$ . - The value of
$n$ corresponds to the number of items in the instance, and we consider$n\in {200,300,400}$ . - The value of
$R$ corresponds to the range for the fragility of items relative to$c$ , and we consider$R\in {[0.1,1.0],[0.5,1.0]}$ .
We ensure that
- The first
$n-1$ items have fragility$f = \lceil c \times U(R) \rceil$ , where$U(R)$ represents the real number uniformly random in$R$ . The last item has fragility$f=c$ - For each item with known fragility value
$f$ , we uniformly randomize an integer in$[1,f]$ as its weight.
Based on the above rules, we generate
In the results/2013_Results folder, you will find the results of BP(2013):
- The folder named
logcontains the log information output during algorithm operation for all instances. - The folder named
solutionscontains detailed packing patterns for all instances. - The CSV file named
Res-2024-05-07contains calculated statistics for all instances.
The results CSV and OUT files are found inside the results/Our_Results folder. In the folder, you will find the results of our BPC:
- The folder named
outcontains detailed packing patterns for all instances. - The CSV file named
results(19-011)contains calculated statistics for all instances. The meaning of each column is as follows:- Name: the name of the instance,
- Class: the class of the instance,
- |N|: the number of items in the instance,
- #Node: the number of nodes explored in the BPC algorithm,
- #Node-P: the number of nodes explored by the primal heuristic in the BPC algorithm,
- #Col: the number of columns of the root node in the BPC algorithm,
- #PriceCnt: the number of times the pricing subproblem is solved throughout the run of the BPC algorithm,
-
LB0: the initial lower bound
$L_0$ for the BPC algorithm, - LB: the lower bound provided by the column generation procedure in the root node,
- UB0: the initial upper bound computed using the greedy heuristic,
- UB: the best upper bound found by the BPC algorithm,
- Opt: it signifies whether the best upper bound found by the BPC algorithm is the optimal upper bound or not,
- Time: the CPU seconds used to run the BPC algorithm.