Packing unequal circles using formulation space search

López, Claudia O.; Beasley, John E.

doi:10.1016/j.cor.2012.11.022

Cited by 37 publications

(12 citation statements)

References 36 publications

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“…For some of the containers considered they improve on the best result previously known. López and Beasley [36] use FSS to solve the packing problem with non-identical circles in different shaped containers. They present computational results which were compared with benchmark problems and also proposed some new instances.…”

Section: Formulation Space Searchmentioning

confidence: 99%

Packing unequal rectangles and squares in a fixed size circular container using formulation space search

López

Beasley

2018

Computers & Operations Research

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In this paper we formulate the problem of packing unequal rectangles/squares into a fixed size circular container as a mixed-integer nonlinear program. Here we pack rectangles so as to maximise some objective (e.g. maximise the number of rectangles packed or maximise the total area of the rectangles packed). We show how we can eliminate a nonlinear maximisation term that arises in one of the constraints in our formulation. We indicate the amendments that can be made to the formulation for the special case where we are maximising the number of squares packed. A formulation space search heuristic is presented and computational results given for publicly available test problems involving up to 30 rectangles/squares. Our heuristic deals with the case where the rectangles are of fixed orientation (so cannot be rotated) and with the case where the rectangles can be rotated through ninety degrees.

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Section: Formulation Space Searchmentioning

confidence: 99%

Packing unequal rectangles and squares in a fixed size circular container using formulation space search

López

Beasley

2018

Computers & Operations Research

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“…Setting a value for R to ensure that these three conditions are met is easily done and so, for space reasons, we omit details here. Examples of correction procedures can be found in our earlier work [19][20][21].…”

Section: Correction Proceduresmentioning

confidence: 99%

Packing a fixed number of identical circles in a circular container with circular prohibited areas

López

Beasley

2018

Optim Lett

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In this paper we consider the problem of packing a fixed number of identical circles inside the unit circle container, where the packing is complicated by the presence of fixed size circular prohibited areas. Here the objective is to maximise the radius of the identical circles. We present a heuristic for the problem based upon formulation space search. Computational results are given for six test problems involving the packing of up to 100 circles. One test problem has a single prohibited area made up from the union of circles of different sizes. Four test problems are annular containers, which have a single inner circular prohibited area. One test problem has circular prohibited areas that are disconnected.

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“…Fu et al [16] proposed an iterated tabu search procedure to improve the randomly generated solution, then a perturbation operator was subsequently employed to reconstruct the current solution and an acceptance criterion was implemented to determine whether to accept the perturbed solution or not. Lopez and Beasley [17] viewed the problem as being one of scaling the radii of the unequal circles so that they could be packed into the container, and their algorithm was also composed of an optimization phase which was based on the formulation space search method, while the improvement phase created a perturbation of the current solution by swapping two circles.…”

Section: Introductionmentioning

confidence: 99%

An action-space-based global optimization algorithm for packing circles into a square container

Huang

Chenkai

2015

Computers & Operations Research

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Packing unequal circles using formulation space search

Cited by 37 publications

References 36 publications

Packing unequal rectangles and squares in a fixed size circular container using formulation space search

Packing unequal rectangles and squares in a fixed size circular container using formulation space search

Packing a fixed number of identical circles in a circular container with circular prohibited areas

An action-space-based global optimization algorithm for packing circles into a square container

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