The board packing problem

•The board packing problem (BoPP) is introduced.•BoPP subsumes several natural optimization problems that arise in practice.•We prove that BoPP is NP-hard by reduction from the satisfiability problem.•An evolutionary algorithm is developed that can solve large instances of BoPP.•We introduce benchma...

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Veröffentlicht in:European journal of operational research Jg. 308; H. 3; S. 1056 - 1073
Hauptverfasser: Abraham, Gyula, Dosa, Gyorgy, Hvattum, Lars Magnus, Olaj, Tomas Attila, Tuza, Zsolt
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.08.2023
Schlagworte:
Binary integer programming
Combinatorial optimization
Covering
Genetic algorithm
Location problems
Covering
Location problems
Combinatorial optimization
Genetic algorithm
Binary integer programming
ISSN:0377-2217, 1872-6860
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Zusammenfassung:•The board packing problem (BoPP) is introduced.•BoPP subsumes several natural optimization problems that arise in practice.•We prove that BoPP is NP-hard by reduction from the satisfiability problem.•An evolutionary algorithm is developed that can solve large instances of BoPP.•We introduce benchmark instances and make extensive computer examinations. We introduce the board packing problem (BoPP). In this problem we are given a rectangular board with a given number of rows and columns. Each position of the board has an integer value representing a gain, or revenue, that is obtained if the position is covered. A set of rectangles is also given, each with a given size and cost. The objective is to purchase some rectangles to place on the board so as to maximize the profit, which is the sum of the gain values of the covered cells minus the total cost of purchased rectangles. This problem subsumes several natural optimization problems that arise in practice. A mixed-integer programming model for the BoPP problem is provided, along with a proof that BoPP is NP-hard by reduction from the satisfiability problem. An evolutionary algorithm is also developed that can solve large instances of BoPP. We introduce benchmark instances and make extensive computer examinations.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2023.01.030