Random-Key Metaheuristic and Linearization for the Quadratic Multiple Constraints Variable-Sized Bin Packing Problem Article Swipe
This paper addresses the Quadratic Multiple Constraints Variable-Sized Bin Packing Problem (QMC-VSBPP), a challenging combinatorial optimization problem that generalizes the classical bin packing by incorporating multiple capacity dimensions, heterogeneous bin types, and quadratic interaction costs between items. We propose two complementary methods that advance the current state-of-the-art. First, a linearized mathematical formulation is introduced to eliminate quadratic terms, enabling the use of exact solvers such as Gurobi to compute strong lower bounds - reported here for the first time for this problem. Second, we develop RKO-ACO, a continuous-domain Ant Colony Optimization algorithm within the Random-Key Optimization framework, enhanced with adaptive Q-learning parameter control and efficient local search. Extensive computational experiments on benchmark instances show that the proposed linearized model produces significantly tighter lower bounds than the original quadratic formulation, while RKO-ACO consistently matches or improves upon all best-known solutions in the literature, establishing new upper bounds for large-scale instances. These results provide new reference values for future studies and demonstrate the effectiveness of evolutionary and random-key metaheuristic approaches for solving complex quadratic packing problems. Source code and data available at https://github.com/nataliaalves03/RKO-ACO
Related Topics
Concepts
Mathematical optimization
Metaheuristic
Bin packing problem
Linearization
Quadratic equation
Quadratic programming
Benchmark (surveying)
Mathematics
Quadratic assignment problem
Bin
Optimization problem
Sequential quadratic programming
Upper and lower bounds
Combinatorial optimization
Quadratically constrained quadratic program
Parallel metaheuristic
Computer science
Quadratic unconstrained binary optimization
Ant colony optimization algorithms
Algorithm
Extremal optimization
Local search (optimization)
Constraint (computer-aided design)
Ant colony
Quadratic function
Branch and bound
Heuristics
Metadata
- Type
- article
- Landing Page
- http://arxiv.org/abs/2511.12367
- https://arxiv.org/pdf/2511.12367
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7106092845
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W7106092845Canonical identifier for this work in OpenAlex
- Title
-
Random-Key Metaheuristic and Linearization for the Quadratic Multiple Constraints Variable-Sized Bin Packing ProblemWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-15Full publication date if available
- Authors
-
Santos, Natalia A., Jeske, Marlon, Chaves, Antonio A.List of authors in order
- Landing page
-
https://arxiv.org/abs/2511.12367Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2511.12367Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2511.12367Direct OA link when available
- Concepts
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Mathematical optimization, Metaheuristic, Bin packing problem, Linearization, Quadratic equation, Quadratic programming, Benchmark (surveying), Mathematics, Quadratic assignment problem, Bin, Optimization problem, Sequential quadratic programming, Upper and lower bounds, Combinatorial optimization, Quadratically constrained quadratic program, Parallel metaheuristic, Computer science, Quadratic unconstrained binary optimization, Ant colony optimization algorithms, Algorithm, Extremal optimization, Local search (optimization), Constraint (computer-aided design), Ant colony, Quadratic function, Branch and bound, HeuristicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| abstract_inverted_index.benchmark | 111 |
| abstract_inverted_index.classical | 20 |
| abstract_inverted_index.efficient | 104 |
| abstract_inverted_index.eliminate | 55 |
| abstract_inverted_index.instances | 112 |
| abstract_inverted_index.parameter | 101 |
| abstract_inverted_index.problems. | 173 |
| abstract_inverted_index.quadratic | 32, 56, 127, 171 |
| abstract_inverted_index.reference | 153 |
| abstract_inverted_index.solutions | 138 |
| abstract_inverted_index.Q-learning | 100 |
| abstract_inverted_index.Random-Key | 94 |
| abstract_inverted_index.approaches | 167 |
| abstract_inverted_index.best-known | 137 |
| abstract_inverted_index.framework, | 96 |
| abstract_inverted_index.instances. | 148 |
| abstract_inverted_index.introduced | 53 |
| abstract_inverted_index.linearized | 49, 117 |
| abstract_inverted_index.random-key | 165 |
| abstract_inverted_index.Constraints | 6 |
| abstract_inverted_index.challenging | 13 |
| abstract_inverted_index.demonstrate | 159 |
| abstract_inverted_index.dimensions, | 27 |
| abstract_inverted_index.experiments | 109 |
| abstract_inverted_index.formulation | 51 |
| abstract_inverted_index.generalizes | 18 |
| abstract_inverted_index.interaction | 33 |
| abstract_inverted_index.large-scale | 147 |
| abstract_inverted_index.literature, | 141 |
| abstract_inverted_index.(QMC-VSBPP), | 11 |
| abstract_inverted_index.Optimization | 90, 95 |
| abstract_inverted_index.consistently | 131 |
| abstract_inverted_index.establishing | 142 |
| abstract_inverted_index.evolutionary | 163 |
| abstract_inverted_index.formulation, | 128 |
| abstract_inverted_index.mathematical | 50 |
| abstract_inverted_index.optimization | 15 |
| abstract_inverted_index.combinatorial | 14 |
| abstract_inverted_index.complementary | 40 |
| abstract_inverted_index.computational | 108 |
| abstract_inverted_index.effectiveness | 161 |
| abstract_inverted_index.heterogeneous | 28 |
| abstract_inverted_index.incorporating | 24 |
| abstract_inverted_index.metaheuristic | 166 |
| abstract_inverted_index.significantly | 120 |
| abstract_inverted_index.Variable-Sized | 7 |
| abstract_inverted_index.continuous-domain | 87 |
| abstract_inverted_index.state-of-the-art. | 46 |
| abstract_inverted_index.https://github.com/nataliaalves03/RKO-ACO | 180 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.83384224 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |