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Title: Formulation space search for two-dimensional packing problems
Author: Lopez Soto, Claudia Orquidea
Awarding Body: Brunel University
Current Institution: Brunel University
Date of Award: 2013
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The two-dimension packing problem is concerned with the arrangement of items without overlaps inside a container. In particular we have considered the case when the items are circular objects, some of the general examples that can be found in the industry are related with packing, storing and transportation of circular objects. Although there are several approaches we want to investigate the use of formulation space search. Formulation space search is a fairly recent method that provides an easy way to escape from local optima for non-linear problems allowing to achieve better results. Despite the fact that it has been implemented to solve the packing problem with identical circles, we present an improved implementation of the formulation space search that gives better results for the case of identical and non-identical circles, also considering that they are packed inside different shaped containers, for which we provide the needed modifications for an appropriate implementation. The containers considered are: the unit circle, the unit square, two rectangles with different dimension (length 5, width 1 and length 10 width 1), a right-isosceles triangle, a semicircle and a right-circular quadrant. Results from the tests conducted shown several improvements over the best previously known for the case of identical circles inside three different containers: a right-isosceles triangle, a semicircle and a circular quadrant. In order to extend the scope of the formulation space search approach we used it to solve mixed-integer non-linear problems, in particular those with zero-one variables. Our findings suggest that our implementation provides a competitive way to solve these kind of problems.
Supervisor: Beasley, J. E. Sponsor: Mexican National Council for Science and Technology (CONACyT)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Metaheuristic ; Circle packing ; Mixed integer non linear programming ; Identical and non identical circles ; Different containers