Maing-Kyu Kang

A fast algorithm for two-dimensional pallet loading problems of large size

Abstract This paper concerns the two-dimensional pallet loading problem (PLP), which requires the determination of the orthogonal layout that loads the maximum number of identical small rectangles (i.e., boxes or products) onto a large rectangle (i.e., pallet or container) without overlapping. Although many algorithms have been developed for this problem, the large amount of time required to find efficient layouts for a large PLP presents great practical difficulties. In this paper, we develop a heuristic that finds efficient layouts with low complexity. We also propose a new algorithm, using the heuristic as a sub-algorithm, which rapidly finds complicated solutions having a 5-block structure. Finally, computational results show that the new algorithm can be successfully applied to large PLPs with sizes exceeding 6800 boxes.

A best-first branch and bound algorithm for unconstrained two-dimensional cutting problems

This paper is concerned with the problem of unconstrained two-dimensional cutting of small rectangular pieces, each of which has its own profit and size, from a large rectangular plate so as to maximize the profit-sum of the pieces produced. Hifi and Zissimopouloss recursive algorithm using G and Kangs upper bound is presently the most efficient exact algorithm for the problem. We propose a best-first branch and bound algorithm based upon the bottom-up approach that is more efficient than their recursive algorithm. The proposed algorithm uses efficient upper bound and branching strategies that can reduce the number of nodes that must be searched significantly. We demonstrate the efficiency of the proposed algorithm through computational experiments.

Determination of the candidate arc set for the asymmetric traveling salesman problem

As size of the traveling salesman problem (TSP) increases, it is unreasonable to find efficiently an optimum or near-optimum. Instead of considering all arcs, if we select and consider only some arcs more likely to be included in an optimal solution, we can find efficiently an optimum or near-optimum. A candidate arc set is a group of some good arcs. For the lack of study in the asymmetric TSP, it needs to research systematically for the candidate arc set of the asymmetric TSP. In this paper, we suggest a regression function determining a candidate arc set for the asymmetric TSP. We established the regression function based on 2100 experiments, and we proved the goodness of fit for it through various 787 problems. Also, we applied it to the Out-of-Kilter heuristic. We tested it on 220 random instances and 23 real-world instances. Because the complexity of the heuristic depends on the number of arcs and we considered only the candidate arc set, we found good solutions about 2-5 fold faster than considering all arcs.

A clustering algorithm using the ordered weight sum of self-organizing feature maps

Clustering is to group similar objects into clusters. Until now there are a lot of approaches using Self-Organizing Feature Maps(SOFMs). But theyhave problems with a small output-layer nodes and initial weight. This paper suggests one-dimensional output-layer nodes in SOFMs. The number of output-layer nodes is more than those of clusters intended to find and the order of output-layer nodes is ascending in the sum of the output-layer nodes weight. We can find input data in SOFMs output node and classify input data in output nodes using the Euclidean Distance. The suggested algorithm was tested on well-known IRIS data and machine-part incidence matrix. The results of this computational study demonstrate the superiority of the suggested algorithm.