• Journal of the Korea Convergence Society
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• v.7 no.5
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• pp.213-219
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• 2016

This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.8
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• pp.2722-2742
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• 2014

We propose methods of linear transceiver design for two different power constraints, sum relay power constraint and per relay power constraint, which determine signal processing matrices such as base station (BS) transmitter, relay precoders and user receivers to minimize sum mean square error (SMSE) for multi-relay multi-user (MRMU) networks. However, since the formulated problem is non-convex one which is hard to be solved, we suboptimally solve the problems by defining convex subproblems with some fixed variables. We adopt iterative sequential designs of which each iteration stage corresponds to each subproblem. Karush-Kuhn-Tucker (KKT) theorem and SMSE duality are employed as specific methods to solve subproblems. The numerical results verify that the proposed methods provide comparable performance to that of a full relay cooperation bound (FRCB) method while outperforming the simple amplify-and-forward (SAF) and minimum mean square error (MMSE) relaying in terms of not only SMSE, but also the sum rate.

• Structural Engineering and Mechanics
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• v.65 no.6
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• pp.731-739
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• 2018

This paper presents an optimal pattern for distributing stiffness along a framed tube structure through an analytic equation, which may be used during the preliminary design stage. Most studies in this field are computationally intensive and time consuming, while a hand-calculation method, as presented here, is a more suitable tool for sensitivity analyses and parametric studies. Approach in development of the analytic model is to minimize the mean compliance (external work) for a given volume of material. A variational statement of the problem is made, and a specified deformation-profile is obtained as the necessary condition for a minimum; enforcing this condition, stiffness is then computed. Due to some near-zero values for stiffness, the problem is modified by considering a lower bound constraint. To deal with this constraint, the design domain is assumed to be divided into two zones of constant stiffness and constant curvature; and the problem is restated in terms of these concepts. It will be shown that this methodology allows for easy computation of stiffness through an analytic and dimensionless equation, valid in any system of units. To show practicality of the proposed method, a tubed-system structure with uniform stiffness distribution is redesigned using the proposed model. Comparative analyses of the results reveal that in addition to simplicity of the proposed method, it provides a rather high degree of accuracy for real-world problems.

• Management Science and Financial Engineering
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• v.19 no.2
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• pp.19-29
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• 2013

Refuse collection network design, one of major decision problems in reverse logistics, is the problem of locating collection points and allocating refuses at demand points to the opened collection points. As an extension of the previous models, we consider capacity and maximum allowable distance constraints at each collection point. In particular, the maximum allowable distance constraint is additionally considered to avoid the impractical solutions in which collection points are located too closely. Also, the additional distance constraint represents the physical distance limit between collection and demand points. The objective is to minimize the sum of fixed costs to open collection points and variable costs to transport refuses from demand to collection points. After formulating the problem as an integer programming model, we suggest an optimal branch and bound algorithm that generates all feasible solutions by a simultaneous location and allocation method and curtails the dominated ones using the lower bounds developed using the relaxation technique. Also, due to the limited applications of the optimal algorithm, we suggest two heuristics. To test the performances of the algorithms, computational experiments were done on a number of test instances, and the results are reported.

• Journal of the Korean Institute of Navigation
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• v.20 no.4
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• pp.59-70
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• 1996

A berth assignment problem has a direct impact on assessment of charges made to ships and goods. In this paper, we concerned with of fuzzy mathematical programming models for a berth assignment problem to achieved an efficient berth operation in a fuzzy environment. In this paper, we focus on the berth assignment programming with fuzzy parameters which are based on personal opinions or subjective judgement. From the above point of view, assume that a goal and a constraint are given by fuzzy sets, respectively, which are characterized by membership functions. Let a fuzzy decision be defined as the fuzzy set resulting from the intersection of a goal and constraint. This paper deals with fuzziness in all parameters which are expressed by fuzzy numbers. A fuzzy parameter defined by a fuzzy number means a possibility distribution of the parameters. These fuzzy 0-1 integer programming problems are formulated by fuzzy functions whose concept is also called the extension principle. We deal with a berth assignment problem with triangular fuzzy coefficients and propose a branch and bound algorithm for solving the problem. We suggest three models of berth assignment to minimizing the objective functions such as total port time, total berthing time and maximum berthing time by using a revised Maximum Position Shift(MPS) concept. The berth assignment problem is formulated by min-max and fuzzy 0-1 integer programming. Finally, we gave the numerical solutions of the illustrative examples.

• Journal of Advanced Navigation Technology
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• v.25 no.6
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• pp.543-549
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• 2021

In this paper, a robust transfer alignment method is proposed for a strapdown inertial navigation system(SDINS) with norm-bounded parametric uncertainties. The uncertainties are described by the energy bound constraint, i.e., sum quadratic constraint(SQC). It is shown that the SQC can be coverted into an indefinite quadratic cost function in the Krein space. Krein space Kalman filter is designed by modifying the measurement matrix and the variance of measurement noises in the conventional Kalman filter. Since the proposed Krein space Kalman filter has the same recursive structure as a conventional Kalman filter, the proposed filter can easily be designed. The simulation results show that the proposed filter achieves robustness against measurement time delay and high dynamic environment of the vehicle.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.181-197
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• 2001

A heuristic method TABU-CSP using Tabu Search (TS) is described for solving Constraint Satisfaction Problems (CSPs). The method is started with a complete but inconsistent solution of a binary CSP and obtained in prespecified number of iterations either a consistent solution or a near optimal solution with an acceptable number of conflicts. The repair in the solution at each iterative step is done by using two heuristics alternatively. The first heuristic is a min-conflicts heuristic that chooses a variable with the maximum number of conflicts and reassigns it the value which leads to the minimum number of conflicts. If the acceptable solution is not reached after the search continued for a certain number of iterations, the min-conflict heuristic is changed and the variable selected least number of times is chosen for repair. If an acceptable solution is not reached, the method switches back to the min-conflict heuristic and proceeds further. This allowed the method to explore a different region of search space space for the solution as well as to prevent cycling. The demonstration of the method is shown on a toy problem [9]which has no solution. The method is then tested on various randomly generated CSPs with different starting solutions. The performance of the proposed method in terms of the average number of consistency is checked and the average number of conflicts is conflicts is compared with that of the Branch and Bound(BB) method used to obtain the same solution. In almost all cases, the proposed method moves faster to the acceptable solution than BB.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.3
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• pp.101-109
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• 2008

This paper considers an integrated decision for scheduling and outsourcing(or, subcontracting) of a finite number of jobs(or, orders) in a time-sensitive make-to-order manufacturing environment. The jobs can be either processed in a parallel in-house facilities or outsourced to subcontractors. We should determine which jobs should be processed in-house and which jobs should be outsourced. And, we should determine the schedule for the jobs to be processed in-house. If a job is determined to be processed in-house, then the scheduling cost(the completion time of the Job) is imposed. Otherwise(if the job should be outsourced), then an additional outsourcing cost is imposed. The objective is to minimize the linear combination of scheduling and outsourcing costs under a budget constraint for the total available outsourcing cost. In the problem analysis, we first characterize some solution properties and then derive dynamic programming and branch-and- bound algorithms. An efficient heuristic is also developed. The performances of the proposed algorithms are evaluated through various numerical experiments.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.1
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• pp.16-22
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• 2016

This paper addresses the load usage scheduling in the HEMS for residential power consumers. The HEMS would lead the residential users to change their power usage, so as to minimize the cost in response to external information such as a time-varying electricity price, the outside temperature. However, there may be a consumer's inconvenience in the change of the power usage. In order to improve this, it is required to understand the pattern of load usage according to the external information. Therefore, this paper suggests a methodology to model the load usage pattern, which classifies home appliances according to external information affecting the load usage and models the usage pattern for each appliance based on a copula function representing the correlation between variables. The modeled pattern would be reflected as a constraint condition for an optimal load usage scheduling problem in HEMS. To explain an application of the methodology, a case study is performed on an electrical water heater (EWH) and an optimal load usage scheduling for EHW is performed based on the branch-and-bound method. From the case study, it is shown that the load usage pattern can contribute to an efficient power consumption.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.369-380
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• 2001

Although extensive efforts have been devoted to the optimal design of composite laminated plates in recent years, some practical issues still need further research. Two of them are: the handling of the ply angle as either continuous or discrete; and that of the uncertainties in material properties, which were treated as continuous and ignored respectively in most researches in the past. In this paper, an algorithm for stacking sequence optimization which deals with discrete ply angles and that for thickness optimization which considers uncertainties in material properties are used for a two step optimization of composite laminated plates. In the stacking sequence optimization, the branch and bound method is modified to handle discrete variables; and in the thickness optimization, the convex modeling is used in calculating the failure criterion, given as constraint, to consider the uncertain material properties. Numerical results show that the optimal stacking sequence is found with fewer evaluations of objective function than expected with the size of feasible region taken into consideration; and the optimal thickness increases when the uncertainties of elastic moduli considered, which shows such uncertainties should not be ignored for safe and reliable designs.