• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.611-628
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• 2021

In this paper, we propose a new branch-reduction-and-bound algorithm to solve the nonlinear knapsack problems by using general discrete monotonic optimization techniques. The specific properties of the problem are exploited to increase the efficiency of the algorithm. Computational experiments of the algorithm on problems with up to 30 variables and 5 different constraints are reported.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.4
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• pp.159-167
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• 2015

We consider a wafer lot transfer/release planning problem from semiconductor wafer fabrication facilities to probing facilities with the objective of minimizing the deviation of workload and total tardiness of customers' orders. Due to the complexity of the considered problem, we propose a two-level hierarchical production planning method for the lot transfer problem between two parallel facilities to obtain an executable production plan and schedule. In the higher level, the solution for the reduced mathematical model with Lagrangian relaxation method can be regarded as a coarse good lot transfer/release plan with daily time bucket, and discrete-event simulation is performed to obtain detailed lot processing schedules at the machines with a priority-rule-based scheduling method and the lot transfer/release plan is evaluated in the lower level. To evaluate the performance of the suggested planning method, we provide computational tests on the problems obtained from a set of real data and additional test scenarios in which the several levels of variations are added in the customers' demands. Results of computational tests showed that the proposed lot transfer/planning architecture generates executable plans within acceptable computational time in the real factories and the total tardiness of orders can be reduced more effectively by using more sophisticated lot transfer methods, such as considering the due date and ready times of lots associated the same order with the mathematical formulation. The proposed method may be implemented for the problem of job assignment in back-end process such as the assignment of chips to be tested from assembly facilities to final test facilities. Also, the proposed method can be improved by considering the sequence dependent setup in the probing facilities.

• Ocean Systems Engineering
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• v.8 no.4
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• pp.381-407
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• 2018

This paper presents a hybrid numerical approach, which combines a two-phase Navier-Stokes model (NS) and the fully nonlinear potential theory (FNPT), for modelling wave-structure interaction. The former governs the computational domain near the structure, where the viscous and turbulent effects are significant, and is solved by OpenFOAM/InterDyMFoam which utilising the finite volume method (FVM) with a Volume of Fluid (VOF) for the phase identification. The latter covers the rest of the domain, where the fluid may be considered as incompressible, inviscid and irrotational, and solved by using the Quasi Arbitrary Lagrangian-Eulerian finite element method (QALE-FEM). These two models are weakly coupled using a zonal (spatially hierarchical) approach. Considering the inconsistence of the solutions at the boundaries between two different sub-domains governed by two fundamentally different models, a relaxation (transitional) zone is introduced, where the velocity, pressure and surface elevations are taken as the weighted summation of the solutions by two models. In order to tackle the challenges associated and maximise the computational efficiency, further developments of the QALE-FEM have been made. These include the derivation of an arbitrary Lagrangian-Eulerian FNPT and application of a robust gradient calculation scheme for estimating the velocity. The present hybrid model is applied to the numerical simulation of a fixed horizontal cylinder subjected to a unidirectional wave with or without following current. The convergence property, the optimisation of the relaxation zone, the accuracy and the computational efficiency are discussed. Although the idea of the weakly coupling using the zonal approach is not new, the present hybrid model is the first one to couple the QALE-FEM with OpenFOAM solver and/or to be applied to numerical simulate the wave-structure interaction with presence of current.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.187-200
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• 1998

This paper presents an original approach for solving short-term power scheduling in extended power system with two fuels in a unit and a limited fuel using Lagrangian relaxations. The underlying model incorporates the full set of costs and constraints including setup, production, ramping, and operational status, and takes the form of a mixed integer nonlinear control problem. Moreover, the mathematical model developed includes two fuels in a unit and a limited fuel, regulation reserve requirements of prespecified group of units. Lagrangian relaxation is used to disaggregate the model by generator into separate subproblems which are then solved with a nested dynamic program including empirical knowledges. The strength of the methodology lies partially in its ability to construct good feasible solutions from information provided by the dual. Thus, the need for branch-and-bound is eliminated. In addition, the inclusion of two fuels in a unit and a limited fuel provides new insight into the limitations of current techniques. Computational experience with the proposed algorithm indicates that Problems containing up to 23 units including 8 unit used two fuels and 24 time periods can be readily solved in reasonable times. Duality gaps of less than 4％ were achieved.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4
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• pp.33-47
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• 1992

A study for the material and geometric nonlinear analysis of segmentally erected cable-supported prestressed concrete plane frames including the time-dependent effects due to load history, creep, shrinkage, aging of concrete, and relaxation of prestressing steel and cable is presented. Updated Lagrangian formulation is used to account for the nonlinear behavior of the structure. For the time-dependent analysis. the time domain is divided into a discrete number of intervals, and a step-forward integration is performed as the solution progresses in the time domain. At each time step. a nonlinear finite element analysis is performed in the space domain. Segmental erection methods are implemented by providing the capability to change the configuration of the structure at any time step of the solution. The computer program CFRAME is developed and a series of numerical examples are presented to study the validity of the program.

• Journal of Theoretical and Applied Mechanics
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• v.1 no.1
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• pp.97-109
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• 1995

In this paper, a finite viscoelastic continuum model for rubber and its finite element analysis are presented. This finite viscoelatic model based on continuum mechanics is an extended model of Johnson and Wuigley's 1-D model. In this extended model, continuum based kinematic measures are rigorously defied and by using this kinematic measures, elastic stage law and flow rule are introduced. In kinematics, three configuration are introduced. In kinematics, three configuration are introduced. They are reference, current and virtual visco configurations. In elastic state law, it is assumed that at a certain time, there exists an elastic potential which describes the recoverable elastic energy. From this elastic potential, elastic state law is derived. The proposed flow rule is based on phenomenological observation. The flow rule gives precise relaxation response. In finite element approximation, mixed Lagrangian description is used, where total and similar method of updated Lagrangian descriptions are used together. This approach reduces the numerical job and gives simple nonlinear syatem of equations. To satisfy the incompressible condition, penalty-type modified Mooney-Rivlin energy function is adopted. By this method nearly incompressible condition is obtain the virtual visco configuration. For verification, uniaxial stretch tests are simulated for various stretch rates. The simulated results show good agreement with experiments. As a practical experiments. As a preactical example, pressurized rubber plate is simulated. The result shows finite viscoelastic effects clearly.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2595-2618
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• 2018

In this paper, we investigate secure communication with the presence of multiple eavesdroppers (Eves) in a two-tier downlink dense heterogeneous network, wherein there is a macrocell base station (MBS) and multiple femtocell base stations (FBSs). Each base station (BS) has multiple users. And Eves attempt to wiretap a macrocell user (MU). To keep Eves ignorant of the confidential message, we propose a physical-layer security scheme based on cross-layer cooperation to exploit interference in the considered network. Under the constraints on the quality of service (QoS) of other legitimate users and transmit power, the secrecy rate of system can be maximized through jointly optimizing the beamforming vectors of MBS and cooperative FBSs. We explore the problem of maximizing secrecy rate in both non-colluding and colluding Eves scenarios, respectively. Firstly, in non-colluding Eves scenario, we approximate the original non-convex problem into a few semi-definite programs (SDPs) by employing the semi-definite relaxation (SDR) technique and conservative convex approximation under perfect channel state information (CSI) case. Furthermore, we extend the frame to imperfect CSI case and use the Lagrangian dual theory to cope with uncertain constraints on CSI. Secondly, in colluding Eves scenario, we transform the original problem into a two-tier optimization problem equivalently. Among them, the outer layer problem is a single variable optimization problem and can be solved by one-dimensional linear search. While the inner-layer optimization problem is transformed into a convex SDP problem with SDR technique and Charnes-Cooper transformation. In the perfect CSI case of both non-colluding and colluding Eves scenarios, we prove that the relaxation of SDR is tight and analyze the complexity of proposed algorithms. Finally, simulation results validate the effectiveness and robustness of proposed scheme.

• Journal of the military operations research society of Korea
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• v.11 no.2
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• pp.15-22
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• 1985

Planning for the expansion of production capacity is of vital importance in many applications within the private and public sectors. This paper considers a sequencing expansion problem in which capacity can be added only at discrete points in time. Given the demand forecast of each period, capacity and cost of each expansion project, we are to determine the sequence of expansion necessary to provide sufficient capacity to meet the demand in all periods at minimum cost. This problem is formulated as a pure integer programming and solved by branch and bound method using Lagrangian relaxation. At first, simple sequencing expansion problem is presented, and in the latter part, extension to include precedence between projects is suggested.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.191-194
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• 2003

Location-allocation problem is known as one of the important problem faced in Industrial Engineering and Operations Research fielde. There are many variations on this problem for different applications, however, most of them consider no obstacle existing. Since the location-allocation problem with obstacles is very complex and with many infeasible solutions, no direct method is effective to solve it. In this paper we propose a hybrid Genetic Algorithm (hGA) method for solving this problem. The proposed hGA is based on Lagrangian relaxation method and Dijkstra's shortest path algorithm. To enhance the proposed hGA, a Fuzzy Logic Controller (FLC) approach is also adopted to auto-tune the GA parameters.