• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.45
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• pp.291-299
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• 1998

We present a variant for the generalized continuous multiple-choice knapsack problem[1], which additionally has the well-known generalized lower bound constraints. The presented problem is characterized by some variables which only belong to the simple upper bound constraints and the others which are partitioned into both the continuous multiple-choice constraints and the generalized lower bound constraints. By exploiting some extended structural properties, an efficient algorithm of order Ο($n^2$1og n) is developed, where n is the total number of variables. A numerical example is presented.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.661-667
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• 1997

We consider a generalized problem of the continuous multiple choice knapsack problem and study on the LP relaxation of the candidate problems which are generated in the branch and bound algorithm for solving the generalized problem. The LP relaxed candidate problem is called the generalized continuous multiple choice linear knapsack problem and characterized by some variables which are partitioned into continuous multiple choice constraints and the others which only belong to simple upper bound constraints. An efficient algorithm of order O($n^2logn$) is developed by exploiting some structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.

• Journal of Korean Institute of Industrial Engineers
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• v.40 no.4
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• pp.396-403
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• 2014

The multi-divisional knapsack problem is defined as a binary knapsack problem where each mutually exclusive division has its own capacity. In this paper, we present an extension of the multi-divisional knapsack problem that has generalized multiple-choice constraints. We explore the linear programming relaxation (P) of this extended problem and identify some properties of problem (P). Then, we develop a transformation which converts the problem (P) into an LP knapsack problem and derive the optimal solutions of problem (P) from those of the converted LP knapsack problem. The solution procedures have a worst case computational complexity of order $O(n^2{\log}\;n)$, where n is the total number of variables. We illustrate a numerical example and discuss some variations of problem (P).

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.607-613
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• 2011

This paper reviews search methods of multiple reasonable paths to implement multimodal public transportation network of Seoul. Such a large scale multimodal public transportation network as Seoul, the computation time of path finding algorithm is a key and the result of path should reflect route choice behavior of public transportation passengers. Search method of alternative path is divided by removing path method and deviation path method. It analyzes previous researches based on the complexity of algorithm for large-scale network. Applying path finding algorithm in public transportation network, transfer and loop constraints must be included to be able to reflect real behavior. It constructs the generalized cost function based on the smart card data to reflect travel behavior of public transportation. To validate the availability of algorithm, experiments conducted with Seoul metropolitan public multimodal transportation network consisted with 22,109 nodes and 215,859 links by using the deviation path method, suitable for large-scale network.