• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.17-28
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• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• International conference on construction engineering and project management
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• 2005.10a
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• pp.881-885
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• 2005

Scheduling repetitive projects under limitations on the amounts of available resources (labor and equipment) has been an active subject because of its practical relevance. Traditionally, the limitation is specified as a deterministic (fixed) number, such as 1000 labor-hours. The limitation, however, is often exposed to uncertainty and variability, especially when the project is lengthy. This paper presents a stochastic optimization model to treat the situations where the limitations of resources are expressed as probability functions in lieu of deterministic numbers. The proposed model transfers each deterministic resource constraint into a corresponding stochastic one and then solves the problem by the use of a chance-constrained programming technique. The solution is validated by comparison with simulation results to show that it can satisfy the resource constraints with a probability beyond the desired confidence level.

• Journal of Electrical Engineering and Technology
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• v.12 no.3
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• pp.1064-1072
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• 2017

The power of controlled generators in microgrids randomly fluctuate because of the stochastic volatility of the outputs of photovoltaic systems and wind turbines as well as the load demands. To address and dispatch these stochastic factors for daily operations, a dynamic economic dispatch model with the goal of minimizing the generation cost is established via chance-constrained programming. A Monte Carlo simulation combined with particle swarm optimization algorithm is employed to optimize the model. The simulation results show that both the objective function and constraint condition have been tightened and that the operation costs have increased. A higher stability of the system corresponds to the higher operation costs of controlled generators. These operation costs also increase along with the confidence levels for the objective function and constraints.

• Journal of Electrical Engineering and Technology
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• v.9 no.1
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• pp.80-89
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• 2014

A stochastic optimal power flow (S-OPF) model considering uncertainties of load and wind power is developed based on chance constrained programming (CCP). The difficulties in solving the model are the nonlinearity and probabilistic constraints. In this paper, a limit relaxation approach and an iterative learning control (ILC) method are implemented to solve the S-OPF model indirectly. The limit relaxation approach narrows the solution space by introducing regulatory factors, according to the relationship between the constraint equations and the optimization variables. The regulatory factors are designed by ILC method to ensure the optimality of final solution under a predefined confidence level. The optimization algorithm for S-OPF is completed based on the combination of limit relaxation and ILC and tested on the IEEE 14-bus system.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.12
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• pp.5191-5211
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• 2016

It is essential to satisfy class-specific QoS constraints to provide broadband services for new generation networks. The present study proposes a QoS-driven multicast scheme for wireless networks in which the transmission rate and end-to-end delay are assumed to be bounded during a multiple multicast session. A distributed algorithm was used to identify a cost-efficient sub-graph between the source and destination which can satisfy QoS constraints of a multicast session. The model was then modified as to be applied for wireless networks in which satisfying interference constraints is the main challenge. A discrete power control scheme was also applied for the QoS-aware multicast model to accommodate the effect of transmission power level based on link capacity requirements. We also proposed random power allocation (RPA) and gradient power allocation (GPA) algorithms to efficient resource distribution each of which has different time complexity and optimality levels. Experimental results confirm that the proposed power allocation techniques decrease the number of unavailable links between intermediate nodes in the sub-graph and considerably increase the chance of finding an optimal solution.

• Journal of the Korean Society for Railway
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• v.10 no.6
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• pp.742-750
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• 2007

This paper presents a mathematical model for a double-fleet operation in Korean high speed rail (HSR). KORAIL has a plan to launch new HSR units in 2010, which are composed of 10 railcars. The double-fleet operation assigns a single-unit or two-unit fleet to a segment, accommodating demand fluctuation. The proposed model assumes stochastic demand and uses chance-constrained constraints to assure a preset service level. It can be used in the tactical planning stage of the rail management as it includes several real-world conditions, such as the capacities of the infra-structures and operational procedures. In the solution approach, the expected revenue in the objective function is linearized by using expected marginal revenue, and the chance-constrained constraints are linearized by assuming that demands are normally distributed. Subsequently, the model can be solved by a mixed-integer linear programming solver fur small size problems. The test results of the model applied to Friday morning train schedules for one month sample data from KTX operation in 2004 shows that the proposed model could be utilized to determine the effectiveness of double-fleet operation, which could significantly increase the expected profit and seat utilization rates when properly maneuvered.

• Journal of Korea Water Resources Association
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• v.42 no.4
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• pp.281-295
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• 2009

This study estimates the value of irrigation water in Korea using an economic programming model that is constructed with all the resource endowment constraints, technology restrictions and policy variables. The variability and uncertainty of water resource endowment are incorporated into the model through the chance-constrained technique. Solving the profit maximization problems with gradually reduced water endowments, we derive a series of shadow values of irrigation water. It has been found that uncertainty in water supply raises the damage from water loss, and the marginal damage increases in water loss.

• IE interfaces
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• v.24 no.4
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• pp.408-419
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• 2011

R&D is a foundation for new business chance and productivity improvement leading to enormous expense and a long-term multi-step process. During the R&D process, decision-makers are confused due to the various future uncertainties that influence economic and technical success of the R&D projects. For these reasons, several decision-making models for R&D project investment have been suggested; they are based on traditional methods such as Discounted Cash Flow (DCF), Decision Tree Analysis (DTA) and Real Option Analysis (ROA) or some fusion forms of the traditional methods. However, almost of the models have constraints in practical use owing to limits on application, procedural complexity and incomplete reflection of the uncertainties. In this study, to make the constraints minimized, we propose a new model named Real Option Decision Tree Model which is a conceptual combination form of ROA and DTA. With this model, it is possible for the decision-makers to simulate the project value applying the uncertainties onto the decision making nodes.

• Structural Engineering and Mechanics
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• v.65 no.6
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• pp.707-719
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• 2018

In this article, a new method is introduced to improve the local search capability of meta-heuristic algorithms using the projection of the path on the border of constraints. In a mathematical point of view, the Gradient Projection Method is applied through a new approach, while the imposed limitations are removed. Accordingly, the gradient vector is replaced with a new meta-heuristic based vector. Besides, the active constraint identification algorithm, and the projection method are changed into less complex approaches. As a result, if a constraint is violated by an agent, a new path will be suggested to correct the direction of the agent's movement. The presented procedure includes three main steps: (1) the identification of the active constraint, (2) the neighboring point determination, and (3) the new direction and step length. Moreover, this method can be applied to some meta-heuristic algorithms. It increases the chance of convergence in the final phase of the search process, especially when the number of the violations of the constraints increases. The method is applied jointly with the authors' newly developed meta-heuristic algorithm, entitled Star Graph. The capability of the resulted hybrid method is examined using the optimal design of truss and frame structures. Eventually, the comparison of the results with other meta-heuristics of the literature shows that the hybrid method is successful in the global as well as local search.

• Journal of Digital Convergence
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• v.16 no.11
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• pp.487-493
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• 2018

In recent years, various virtual reality contents have been explosively developed, and the 'chance operation' in previous studies was mentioned. This study tries to implement the Step Sequencer in the virtual reality. Through the theoretical background analysis and case studies of virtual reality, three major experiential values such as Value of Overcoming Constraints, Value of Strengthening Experience, and Value of Creating New Experience were induced. A convergencestep sequencer with the presence and immersion elements was developed and presented so that the music contents divided into 4 areas can be understood easily controlled more conveniently while keeping the identity of the step sequencer. It is expected that various convergence VR contentscan be developed in the future studies.