TY - JOUR

T1 - A Knapsack Problem for Rectangles under Center-of-Gravity Constraints

AU - Shperling, S. M.

AU - Kochetov, Yu A.

N1 - Funding Information: The work was carried out within the framework of the state assignment for Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF–2022–0019. Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/5

Y1 - 2022/5

N2 - We have a set of rectangles with predefined widths, lengths, and masses and a knapsack ofknown width and length. Our goal is to select a subset of items and find their packing into theknapsack without overlapping so as to minimize the total empty space in the knapsack. Thedeviation of the center of gravity of the items from the knapsack geometric center must not exceedsome threshold along both axes. We use item permutations to represent solutions and the skylineheuristic as a decoding procedure. The center-of-gravity constraint is relaxed and included intothe objective function with penalty. To find the best permutation, we apply the simulatedannealing algorithm with swap neighborhood and a special rule for returning into the feasibledomain. Computational results for test instances with known optimal solutions are discussed.

AB - We have a set of rectangles with predefined widths, lengths, and masses and a knapsack ofknown width and length. Our goal is to select a subset of items and find their packing into theknapsack without overlapping so as to minimize the total empty space in the knapsack. Thedeviation of the center of gravity of the items from the knapsack geometric center must not exceedsome threshold along both axes. We use item permutations to represent solutions and the skylineheuristic as a decoding procedure. The center-of-gravity constraint is relaxed and included intothe objective function with penalty. To find the best permutation, we apply the simulatedannealing algorithm with swap neighborhood and a special rule for returning into the feasibledomain. Computational results for test instances with known optimal solutions are discussed.

KW - 2D packing

KW - center-of-gravity constraint

KW - local search

KW - skyline heuristic

UR - http://www.scopus.com/inward/record.url?scp=85144227929&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/616d0a4c-743f-31c8-9167-b937c4f06ab5/

U2 - 10.1134/S199047892203019X

DO - 10.1134/S199047892203019X

M3 - Article

AN - SCOPUS:85144227929

VL - 16

SP - 563

EP - 571

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -