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Features for the 0-1 knapsack problem based on inclusionwise maximal solutions
[article]
2022
arXiv
pre-print
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Previously the authors proposed a new class of hard 0-1 knapsack problem instances and demonstrated that the properties of so-called inclusionwise maximal solutions (IMSs) can be important hardness indicators ...
Decades of research on the 0-1 knapsack problem led to very efficient algorithms that are able to quickly solve large problem instances to optimality. ...
We gratefully acknowledge the support provided by the ORDinL project (FWO-SBO S007318N, Data Driven Logistics, 1/1/2018 -31/12/2021). ...
arXiv:2211.09665v1
fatcat:qibpen4u3ranrpd6qqh7uagh3m
Incremental Packing Problems: Algorithms and Polyhedra
2022
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The fully rigid algorithm may output a solution with an arbitrarily bad approximation ratio . ...
This set will be denoted by 𝑆 0 for a chain S = (𝑆 1 , . . . , 𝑆 𝑇 ), by ALG (𝑡) 0 for ALG (𝑡) , by OPT 0 for OPT, etc. We assume that the chain OPT is inclusionwise maximal. ...
Taking 𝜖 sufficiently small, this gives an 𝑂 ( 1 𝑇 )-approximated solution. For the base case 𝑡 = 1, notice that only items 1 and 𝑇 + 1 are (individually) feasible in the knapsack problem. ...
doi:10.7916/52qd-2y13
fatcat:krec66h2czbondvouulutsnimy
Network flows and network design in theory and practice
[article]
2014
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We evaluate the model and our algorithms on a broad set of instances based on real-world logistics networks from ongoing and recent customer projects of 4flow AG. ...
We complement our model by providing various heuristic approaches and mixed integer programming formulations for solving the resulting optimization problem. ...
, 21
weighted abstract flow problem, 21
ZTIME, 4
.1 Preliminaries
.1 Preliminaries
The definition for maximization problems is analogous. ...
doi:10.14279/depositonce-3968
fatcat:y5jued6ernc4hmh2ftc2acec4a
Polyhedral analysis and branch and cut algorithms for some NP-hard spanning subgraph problems
[article]
2023
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A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2024; you can also visit the original URL.
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There is a widespread need to use a quantitative approach for the solution of decision problems that arise in many different areas of real life. ...
The analysis of a real problem occurs in two phases: the representation of the problem through a mathematical model and the development of efficient mathematical methods to determine an optimal solution ...
[48] designed a solution procedure, based on a new formulation for the problem. ...
doi:10.14273/unisa-4538
fatcat:vdh5exm2obd2zgicancvv5gjpi