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This paper mainly investigates the circular open dimension problem (CODP),which consists of packing a set of circles of known radii into a strip of fixedwidth and unlimited length without overlapping. The objective is to minimizethe length of the strip. An iterated tabu search approach, named ITS, isproposed. ITS starts from a randomly generated solution and attempts to gainimprovements by a tabu search procedure. After that, if the obtained solutionis not feasible, a perturbation operator is subsequently employed toreconstruct the incumbent solution and an acceptance criterion is implementedto determine whether or not accept the perturbed solution. This process isrepeated until a feasible solution has been found or the allowed computationtime has been elapsed. Computational experiments based on well-known benchmarkinstances show that ITS produces quite competitive results with respect to thebest known results. For 18 representative CODP instances taken from theliterature, ITS succeeds in improving 13 best known results within reasonabletime. In addition, for another challenging related variant: the problem ofpacking arbitrary sized circles into a circular container, ITS also succeeds inimproving many best known results. Supplementary experiments are also providedto analyze the influence of the perturbation operator, as well as theacceptance criterion.

Iterated tabu search for the circular open dimension problem