arXiv subjects

Wenqi Huang

Publications and source records attributed to Wenqi Huang.

40 records · Page 3Linked to original sources

arXiv2012

Iterated tabu search for the circular open dimension problem

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 fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. An iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure. After that, if the obtained solution is not feasible, a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution. This process is repeated until a feasible solution has been found or the allowed computation time has been elapsed. Computational experiments based on well-known benchmark instances show that ITS produces quite competitive results with respect to the best known results. For 18 representative CODP instances taken from the literature, ITS succeeds in improving 13 best known results within reasonable time. In addition, for another challenging related variant: the problem of packing arbitrary sized circles into a circular container, ITS also succeeds in improving many best known results. Supplementary experiments are also provided to analyze the influence of the perturbation operator, as well as the acceptance criterion.

cs.OH↗

arXiv2011

Corner Occupying Theorem for the Two-dimensional Integral Rectangle Packing Problem

This paper proves a corner occupying theorem for the two-dimensional integral rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given integral rectangles into an integral rectangular container without overlapping, then we can achieve a feasible packing by successively placing an integral rectangle onto a bottom-left corner in the container. Based on this theorem, we might develop efficient heuristic algorithms for solving the integral rectangle packing problem. In fact, as a vague conjecture, this theorem has been implicitly mentioned with different appearances by many people for a long time.

cs.DM↗

arXiv2011

Bottom-Left Placement Theorem for Rectangle Packing

This paper proves a bottom-left placement theorem for the rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given rectangles into a rectangular container without overlapping, then we can achieve a feasible packing by successively placing a rectangle onto a bottom-left corner in the container. This theorem shows that even for the real-parameter rectangle packing problem, we can solve it after finite times of bottom-left placement actions. Based on this theorem, we might develop efficient heuristic algorithms for solving the rectangle packing problem.

cs.DM↗

arXiv2011

Analysis on the computability over the efficient utilization problem of the four-dimensional space-time

This paper formally proposes a problem about the efficient utilization of the four dimensional space-time. Given a cuboid container, a finite number of rigid cuboid items, and the time length that each item should be continuous baked in the container, the problem asks to arrange the starting time for each item being placed into the container and to arrange the position and orientation for each item at each instant during its continuous baking period such that the total time length the container be utilized is as short as possible. Here all side dimensions of the container and of the items are positive real numbers arbitrarily given. Differs from the classical packing problems, the position and orientation of each item in the container could be changed over time. Therefore, according to above mathematical model, the four-dimensional space-time can be utilized more truly and more fully. This paper then proves that there exists an exact algorithm that could solve the problem by finite operations, so we say this problem is weak computable. Based on the understanding of this computability proof, it is expected to design effective approximate algorithms in the near future. A piggyback work completed is a strict proof on the weak computability over general and natural case of the three-dimensional cuboid packing decision problem that all parameters are positive real numbers.

cs.CC↗