Adaptive and restarting techniques-based algorithms for circular packing problems

Abstract

International audienceIn this paper, we study the circular packing problem (CPP) which consists of packing a set of non-identical circles of known radii into the smallest circle with no overlap of any pair of circles. To solve CPP, we propose a three-phase approximate algorithm. During its first phase, the algorithm successively packs the ordered set of circles. It searches for each circle's "best" position given the positions of the already packed circles where the best position minimizes the radius of the current containing circle. During its second phase, the algorithm tries to reduce the radius of the containing circle by applying (i) an intensified search, based on a reduction search interval, and (ii) a diversified search, based on the application of a number of layout techniques. Finally, during its third phase, the algorithm introduces a restarting procedure that explores the neighborhood of the current solution in search for a better ordering of the circles. The performance of the proposed algorithm is evaluated on several problem instances taken from the literature

A beam search algorithm for the circular packing problem

“…At each iteration, the heuristic identifies the set of potential best positions of a circle C i , i ∈ N , given the positions of the previously packed circles, and determines for each of these positions the coordinates and radius of the smallest containing circle. Hifi and M'Hallah [1] propose a three-phase approximate heuristic. During its first phase, it successively packs the ordered set of circles.…”

“…These 12 instances, used as benchmark problems in [1,21], are interesting as they have not been specifically constructed for packing non-identical circles into a circle but for packing circles into a rectangle. Moreover, these problems include relatively large problems; thus, reflect the behavior of the proposed heuristics when the problem size increases (the instances can be downloaded from the following web page: http://www.laria.u-picardie.fr/hifi/OR-Benchmark/Circular).…”

“…This paper addresses the circular packing problem (CPP) where the items and objects are circles. This problem is of particular interest in bundling wires that connect a car's sensors to the display board [1,2]. The wires have to pass through a hole that will be drilled on the body of the car.…”

Adaptive beam search lookahead algorithms for the circular packing problem

“…The objective is to determine the radius r of C as well as the coordinates ( x i , y i ) of the center of C i , i ∈ N . This problem, which is a variant of the two‐dimensional open‐dimension problem (Wäscher et al, 2007), has many industrial applications such as bundling wires that connect a car's sensors to the display board (Hifi and M'Hallah, 2008; Sugihara et al, 2004), and grouping cables into pipes for telecommunication and oil‐related companies.…”

An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle

“…Zhang and Deng (2005) combined Huang et al's approach with simulated annealing to explore the neighborhood of the current solution, and tabu search to be used jump out of local minima. Hifi and M'Hallah (2008) proposed a three-phase approximate heuristic. Huang, Li, Li, and Xu (2006) presented two greedy algorithms which used a maximum hole degree rule and a self look-ahead search strategy.…”