• Management Science and Financial Engineering
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• v.20 no.1
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• pp.1-9
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• 2014

In multi-objective scheduling problems, the objectives are usually in conflict. To obtain a satisfactory compromise and resolve the issue of NP-hardness, most existing works have suggested employing meta-heuristic methods, such as genetic algorithms. In this research, we propose a novel data-driven approach for generating a single solution that compromises multiple rules pursuing different objectives. The proposed method uses a data mining technique, namely, random forests, in order to extract the logics of several historic schedules and aggregate those. Since it involves learning predictive models, future schedules with the same previous objectives can be easily and quickly obtained by applying new production data into the models. The proposed approach is illustrated with a simulation study, where it appears to successfully produce a new solution showing balanced scheduling performances.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.11a
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• pp.93-96
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• 2003

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We establish some necessary and sufficient conditions for a gknap to admit a fully polynomial approximation scheme, or FPTAS, To do so, we recapture the scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a condition that a gknap does not have an FP-TAS. This condition is more general than the strong NP-hardness.

• Korean Management Science Review
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• v.30 no.3
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• pp.55-70
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• 2013

In this study we suggested two optimization models to determine conversion weight of convertible bonds. The problem of this study is same as that of Park and Shim [1]. But this study used Value-at-Risk (VaR) for risk measurement instead of CVaR, Conditional-Value-at-Risk. In comparison with conventional Markowitz portfolio models, which use the variance of return, our models used VaR. In 1996, Basel Committee on Banking Supervision recommended VaR for portfolio risk measurement. But there are difficulties in solving optimization models including VaR. Benati and Rizzi [5] proved NP-hardness of general portfolio optimization problems including VaR. We adopted their approach. But we developed efficient algorithms with time complexity O(nlogn) or less for our models. We applied examples of our models to the convertible bond issued by a semiconductor company Hynix.

• Journal of Korean Institute of Industrial Engineers
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• v.38 no.1
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• pp.1-6
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• 2012

We consider a two-dimensional vector packing problem in which each item has size in x- and y-coordinates. The purpose of this paper is to provide a ground work on how hard two-dimensional vector packing problems are for large items. We prove that the problem with each item greater than 1/2-${\varepsilon}$ either in x- or y-coordinates for 0 < ${\varepsilon}$ ${\leq}$ 1/6 has no APTAS unless P = NP.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.26 no.2
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• pp.54-60
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• 2018

This paper contains the multi-mission scheduling optimization of UAV within a given operating time. Mission scheduling optimization problem is one of combinatorial optimization, and it has been shown to be NP-hard(non-deterministic polynomial-time hardness). In this problem, as the size of the problem increases, the computation time increases dramatically. So, we applied the genetic algorithm to this problem. For the application, we set the mission scenario, objective function, and constraints, and then, performed simulation with MATLAB. After 1000 case simulation, we evaluate the optimality and computing time in comparison with global optimum from MILP(Mixed Integer Linear Programming).

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.191-198
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• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.

• Journal of the Society of Naval Architects of Korea
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• v.51 no.3
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• pp.239-245
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• 2014

This paper deal with the block storage planning problem of storing and retrieving assembly blocks in a temporary storage yard with limited capacity, which is one of the critical managerial problems in shipbuilding. The block storage planning problem is required to minimize the number of relocations of blocks while the constraints for storage and retrieval time windows are satisfied. We first show NP-hardness of the block storage planning problem. Next we propose a heuristic algorithm to generate good quality solutions for larger instances in very short computational time. The proposed heuristic algorithm was validated by comparing the results with the mathematical model presented in the previous study.

• Management Science and Financial Engineering
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• v.18 no.1
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• pp.13-20
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• 2012

This paper considers a revenue maximization problem on a single processor. Each job is identified as its processing time, initial reward, reward decreasing rate, and preferred start time. If the processor starts a job at time zero, revenue of the job is its initial reward. However, the revenue decreases linearly with the reward decreasing rate according to its processing start time till its preferred start time and finally its revenue is zero if it is started the processing after the preferred time. Our objective is to find the optimal sequence which maximizes the total revenue. For the problem, we characterize the optimal solution properties and prove the NP-hardness. Based upon the characterization, we develop a branch-and-bound algorithm for the optimal sequence and suggest five heuristic algorithms for efficient solutions. The numerical tests show that the characterized properties are useful for effective and efficient algorithms.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.2
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• pp.593-609
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• 2012

We propose a scheme to reduce the overhead associated with channel state information (CSI) feedback required for opportunistic scheduling in wireless access networks. We study the case where CSI is partially overheard by mobiles and thus one can suppress transmitting CSI reports for time varying channels of inferior quality. We model the mechanism of feedback suppression as a Bayesian network, and show that the problem of minimizing the average feedback overhead is NP-hard. To deal with hardness of the problem we identify a class of feedback suppression structures which allow efficient computation of the cost. Leveraging such structures we propose an algorithm which not only captures the essence of seemingly complex overhearing relations among mobiles, but also provides a simple estimate of the cost incurred by a suppression structure. Simulation results are provided to demonstrate the improvements offered by the proposed scheme, e.g., a savings of 63-83% depending on the network size.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.11
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• pp.509-516
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• 2008

The Minimum Letter Flips (MLF) model and the Weighted Minimum Letter Flips (WMLF) model are for solving the haplotype assembly problem. But these two models are effective only when the error rate in SNP fragments is low. In this paper, we first establish a new computational model that employs the related genotype information as an improvement of the WMLF model and show its NP-hardness, and then propose an efficient genetic algorithm to solve the haplotype assembly problem. The results of experiments on random data set and a real data set indicate that the introduction of genotype information to the WMLF model is quite effective in improving the reconstruction rate especially when the error rate in SNP fragments is high. And the results also show that genotype information increases the convergence speed of the genetic algorithm.