• Journal of Electrical Engineering and Technology
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• 제3권4호
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• pp.514-519
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• 2008

The non-separable quadratic penalty terms create an inherent difficulty when applying the standard augmented Lagrangian relaxation(ALR) method for decomposing the unit commitment problem into independent subproblems. This paper presents a separable augmented Lagrangian relaxation method for solving the unit commitment problem. The proposed method is designed to have a separable structure by introducing the quadratic terms with additional auxiliary terms in the augmented Lagrangian function. Numerical results are presented to validate the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.89-92
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• 1992

This paper presents an approach for thermal Unit Commitment by Lagrangian Relaxation with fuzzy technique. A proposed algorithm makes it possible to execute optimal decision making between Generation Cost and Load Demand with membership function. In order to test the validity of the proposed method, we applied to Mid-westerm utility system which has 20 thermal units. So, the usefulness of this method is verified.

• Proceedings of the KSME Conference
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• 대한기계학회 2003년도 춘계학술대회
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• pp.1851-1856
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• 2003

A new Lagrangian stochastic dispersion model is developed by combining the GLM(generalized Langevin model) and the elliptic relaxation method. Under the physically plausible assumptions a simple analytical solution of elliptic relaxation is obtained. To compare the performance of our model with other model, the statistics of particle velocity as well as concentration are investigated. Numerical simulation results show good agreement with available experimental data.

• Journal of Korean Society of Industrial and Systems Engineering
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• 제9권13호
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• pp.45-50
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• 1986

본 연구에서 고찰한 surrogate relaxation은 Lagrangian relaxation 방법과는 달리 제약식들을 선형조합으로 묶어 문제를 푼다. 수리계획 분계가 convexity를 만족하지 못하는 경우에는 Lagrangian의 경우와 마찬가지로 surrogate gap이 발생한다. Lagrangian 쌍대이론을 토대로 surrogate optimality condition을 알아보고 수리계획법의 특별 형태인 정수선형계획법에 적용해 보았다. 일반적으로 surrogate gap은 Lagrangian gap 보다 작기 때문에 좀더 근사하게 원 문제의 최적 목적 함수값에 접근할 수 있다. 따라서 branch and bound 알고리즘을 개발할 때 중요한 정보를 제공하는 것이다.

• Proceedings of the KIEE Conference
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• 대한전기학회 2000년도 하계학술대회 논문집 A
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• pp.334-336
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• 2000

In Korea, the CCGTs have been installed to about 25% of the total generating capacity. Generally CCGTs determine the System Marginal Prices(SMP) in Cost Based Generation Pool. So the scheduling of CCGTs is very important in daily generation scheduling. This paper describes the scheduling of CCGTs which considers the operating characteristics of them. We use lagrangian relaxation method which decomposes the unit committment problem into the subproblems of the individual unit. In the CCGT subproblem, we define the cost function of CCGT in two way. In Case study, the daily generation scheduling is performed using the data of Korean thermal system.

• Proceedings of the KIEE Conference
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• 대한전기학회 1998년도 하계학술대회 논문집 C
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• pp.1003-1005
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• 1998

We present the implementation of a Lagrangian Relaxation based large scale thermal Unit Commitment problem. The problem is decomposed into thermal subproblem by using Lagrangian multipliers. The thermal subproblem is solved by using dynamic programmmg. we perform a numerical test using the thermal system of KEPCO over a week (168 hours) period. The programming language used for the test program is C. The result is compared with the priority list method.

• The Transactions of The Korean Institute of Electrical Engineers
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• 제58권1호
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• pp.23-27
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• 2009

The joint dispatch of regional electricity markets can improve the overall economic efficiency of interconnected markets by increasing the combined social welfare of the interconnected markets. This paper presents a new decentralized optimization technique based on Augmented Lagrangian Relaxation (ALR) to perform the joint dispatch of interconnected electricity markets. The Block Coordinate Descent (BCD) technique is applied to decompose the inseparable quadratic term of the augmented Lagrangian equation into individual market optimization problems. The Interior Point/Cutting Plane (IP/CP) method is used to update the Lagrangian multiplier in the decomposed market optimization problem. The numerical example is presented to validate the effectiveness of the proposed decentralized method.

• Journal of Korean Society of Industrial and Systems Engineering
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• 제38권4호
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• pp.109-116
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• 2015

This paper is concerned with the single vendor single buyer integrated production inventory problem. To make this problem more practical, space restriction and lead time proportional to lot size are considered. Since the space for the inventory is limited in most practical inventory system, the space restriction for the inventory of a vendor and a buyer is considered. As product's quantity to be manufactured by the vendor is increased, the lead time for the order is usually increased. Therefore, lead time for the product is proportional to the order quantity by the buyer. Demand is assumed to be stochastic and the continuous review inventory policy is used by the buyer. If the buyer places an order, then the vendor will start to manufacture products and the products will be transferred to the buyer with equal shipments many times. The mathematical formulation with space restriction for the inventory of a vendor and a buyer is suggested in this paper. This problem is constrained nonlinear integer programming problem. Order quantity, reorder points for the buyer, and the number of shipments are required to be determined. A Lagrangian relaxation approach, a popular solution method for constrained problem, is developed to find lower bound of this problem. Since a Lagrangian relaxation approach cannot guarantee the feasible solution, the solution method based on the Lagrangian relaxation approach is proposed to provide with a good feasible solution. Total costs by the proposed method are pretty close to those by the Lagrangian relaxation approach. Sensitivity analysis for space restriction for the vendor and the buyer is done to figure out the relationships between parameters.

• Journal of the Korean Operations Research and Management Science Society
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• 제23권2호
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• pp.47-65
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• 1998

We consider a multiperiod capacity planning problem for determining a mix of flexible and dedicated capacities under budget restriction. These capacities are controlled by purchasing flexible machines and/or new dedicated machines and disposing old dedicated machines. Acquisition and replacement schedules are determined and operations are assigned to the flexible or dedicated machines for the objective of minimizing the sum of discounted costs of acquisition and operation of flexible machines, new dedicated machines, and old dedicated machines. In this research, the Problem is formulated as a mixed integer linear Program and solved by a Lagrangian relaxation approach. A subgradient optimization method is employed to obtain lower bounds and a multiplier adjustment method is devised to improve the bounds. We develop a linear programming based Lagrangian heuristic algorithm to find a good feasible solution of the original problem. Results of tests on randomly generated test problems show that the algorithm gives relatively good solutions in a reasonable amount of computation time.

• Journal of Electrical Engineering and Technology
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• 제7권1호
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• pp.17-22
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• 2012

Lagrangian relaxation is the most widely adopted method for solving unit commitment (UC) problems. It consists of two steps: dual optimization and primal feasible solution construction. The dual optimization step is crucial in determining the overall performance of the solution. This paper intends to evaluate two dual optimization methods - one based on subgradient (SG) and the other based on the cutting plane. Large-scale UC problems with hundreds of thousands of variables and constraints have been generated for evaluation purposes. It is found that the evaluated SG method yields very promising results.