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On three soft rectangle packing problems with guillotine constraints

Bui, Quoc Trung and Vidal, Thibaut and Ha, Minh Hoang (2019) On three soft rectangle packing problems with guillotine constraints. Journal of global optimization, 74 (1). pp. 45-62. ISSN 0925-5001

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We investigate how to partition a rectangular region of length L1 and height L2 into n rectangles of given areas (a1,…,an) using two-stage guillotine cuts, so as to minimize either (i) the sum of the perimeters, (ii) the largest perimeter, or (iii) the maximum aspect ratio of the rectangles. These problems play an important role in the ongoing Vietnamese land-allocation reform, as well as in the optimization of matrix multiplication algorithms. We show that the first problem can be solved to optimality in O(nlogn) , while the two others are NP-hard. We propose mixed integer linear programming formulations and a binary search-based approach for solving the NP-hard problems. Experimental analyses are conducted to compare the solution approaches in terms of computational efficiency and solution quality, for different objectives.

Item Type: Article
Subjects: Information Technology (IT)
ISI-indexed journals
Divisions: Faculty of Information Technology (FIT)
Depositing User: Hà Minh Hoàng
Date Deposited: 25 Jun 2019 15:42
Last Modified: 25 Jun 2019 15:42

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