• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.491-502
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• 2014

In this paper, by using the notion of ${\rho}$-(p,r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. Counterexample is constructed to justify that our investigations are more general than the existing work available in the literature.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 제38회 하계학술대회
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• pp.848-849
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• 2007

This paper presents an efficient approach for solving the economic dispatch (ED) problems with valve-point effects using differential evolution (DE). A DE, one of the evolutionary algorithms (EAs), is a novel optimization method capable of handling nonlinear, non-differentiable, and nonconvex functions. And an efficient constraints treatment method (CTM) is applied to handle the equality and inequality constraints. The resultant DE-CTM algorithm is very effective in solving the ED problems with nonconvex cost functions. To verify the superiority of the proposed method, a sample ED problem with valve-point effects is tested and its results are compared with those of previous works. The simulation results clearly show that the proposed DE-CTM algorithm outperforms other state-of-the-art algorithms in solving ED problems with valve-point effects

• Industrial Engineering and Management Systems
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• 제9권1호
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• pp.10-19
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• 2010

This paper presents an extended computing procedure for the global optimization of the triple response system (TRS) where the response functions are nonconvex (nonconcave) quadratics and the input factors satisfy a radial region of interest. The TRS arising from response surface modeling can be approximated using a nonlinear mathematical program involving one primary (objective) function and two secondary (constraints) functions. An optimization algorithm named triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the nondegenerate TRS. In TRSALG, the Lagrange multipliers of target (secondary) functions are computed by using the Hooke-Jeeves search method, and the Lagrange multiplier of the radial constraint is located by using the trust region (TR) method at the same time. To ensure global optimality that can be attained by TRSALG, included is the means for detecting the degenerate case. In the field of numerical optimization, as the family of TR approach always exhibits excellent mathematical properties during optimization steps, thus the proposed algorithm can guarantee the global optimal solution where the optimality conditions are satisfied for the nondegenerate TRS. The computing procedure is illustrated in terms of examples found in the quality literature where the comparison results with a gradient-based method are used to calibrate TRSALG.

• 물과 미래
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• 제28권2호
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• pp.169-180
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• 1995

관망상배관(Looped networks)시스템에서 관수로시스템의 전체비용은 폐회로유량(Loop flows)에 따라 영향을 받는다. 따라서 관망상배관의 최적설계를 위한 수학적모형을 추계학적 최적화방법에 적용하기 위하여 폐회로유량의 섭동(Perturbations)으로 전체비용이 변하게 하였다. 관망상 배관문제의 분석가능영역은 수많은 국지해(Local optimum)를 갖는 비볼록(Nonconvex)이므로 분석가능영역의 효율적인 심사를 위하여 수정추계학적 심사방법을 제안하였으며 이 방법은 국부심사단계(Global search phase)와 국지심사단계(Local search phase)로 구성되어 있다. 국부탐사에서는 점차적으로 국지해를 증진시키며 국지탐사에서는 국부탐사단계에서 교착상태에 있는 국지해로 부터 벗어나게 하거나 최종국지해를 증진시킨다. 제안한 방법의 효율성을 검정하기 위하여 참고문헌에 있는 기존관수로시스템의 병열관로(Parallel pipe line) 확장문제를 표본으로 채택하여 제안한 방법을 적용한 결과 먼저 발표된 연구자들의 비용보다 적은 비용으로 설계할 수 있었다.

• 제어로봇시스템학회논문지
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• 제13권11호
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• pp.1048-1052
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• 2007

This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.

• 제어로봇시스템학회논문지
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• 제15권1호
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• pp.67-71
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• 2009

This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as $H_2/H_{\infty}$ control. Multi-objective control is formulated as an LMI optimization problem with a nonconvex rank condition, which is imposed on the controller gain matirx not Lyapunov matrices. With this rank-constrained formulation, we can expect to reduce conservatism because we can use separate Lyapunov matrices for different control objectives. An iterative penalty method is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method.

• 한국산학기술학회논문지
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• 제16권1호
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• pp.97-105
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• 2015

다중반응표면 최적화는 다수의 반응변수(품질특성치)를 최적화하는 입력변수의 조건을 찾는 것을 목적으로 한다. 다중반응표면 최적화를 위해 제안된 가중평균제곱오차(Weighted Mean Squared Error, WMSE) 최소화법은 평균제곱오차의 구성요소인 제곱편차와 분산에 서로 다른 가중치를 부여하는 방법이다. 지금까지 WMSE 최소화법과 관련하여, 개별 반응변수의 WMSE를 구성한 후 이들의 가중합을 최소화하는 가중합 기반 WMSE 최소화법이 제안되었다. 그러나 가중합 기반법은 목적함수 공간에서 볼록하지 않은 구간이 있고 이 구간에서 가장 선호되는 해가 존재할 경우 이 해를 찾아내지 못한다는 한계를 지니고 있다. 본 논문에서는 기존의 가중합 기반법의 한계점을 극복하기 위하여 Tchebycheff Metric 기반 WMSE 최소화법을 제안하고자 한다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권7호
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• pp.2650-2667
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• 2021

In this paper, we derive the expression of the cache hitting probability with random caching policy and propose the joint optimization algorithm based on difference of convex algorithm (DCA) in the three-tier caching heterogeneous cellular network assisted by macro base stations, helpers and users. Under the constraint of the caching capacity of caching devices, we establish the optimization problem to maximize the cache hitting probability of the network. In order to solve this problem, a convex function is introduced to convert the nonconvex problem to a difference of convex (DC) problem and then we utilize DCA to obtain the optimal caching probability of macro base stations, helpers and users for each content respectively. Simulation results show that when the density of caching devices is relatively low, popular contents should be cached to achieve a good performance. However, when the density of caching devices is relatively high, each content ought to be cached evenly. The algorithm proposed in this paper can achieve the higher cache hitting probability with the same density.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제17권7호
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• pp.1823-1840
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• 2023

In order to improve spectral efficiency and reduce power consumption for reconfigurable intelligent surface (RIS) assisted wireless communication systems, a joint design considering irregular RIS topology, RIS on-off switch, power allocation and phase adjustment is investigated in this paper. Firstly, a multi-dimensional variable joint optimization problem is established under multiple constraints, such as the minimum data requirement and power constraints, with the goal of maximizing the system energy efficiency. However, the proposed optimization problem is hard to be resolved due to its property of nonlinear nonconvex integer programming. Then, to tackle this issue, the problem is decomposed into four sub-problems: topology design, phase shift adjustment, power allocation and switch selection. In terms of topology design, Tabu search algorithm is introduced to select the components that play the main role. For RIS switch selection, greedy algorithm is used to turn off the RISs that play the secondary role. Finally, an iterative optimization algorithm with high data-rate and low power consumption is proposed. The simulation results show that the performance of the irregular RIS aided system with topology design and RIS selection is better than that of the fixed topology and the fix number of RISs. In addition, the proposed joint optimization algorithm can effectively improve the data rate and energy efficiency by changing the propagation environment.

• Water Engineering Research
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• 제1권1호
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• pp.63-74
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• 2000

This paper presents a two- phase search scheme for optimal pipe expansion of expansion of existing water distribution systems. In pipe network problems, link flows affect the total cost of the system because the link flows are not uniquely determined for various pipe diameters. The two-phase search scheme based on stochastic optimization scheme is suggested to determine the optimal link flows which make the optimal design of existing pipe network. A sample pipe network is employed to test the proposed method. Once the best tree network is obtained, the link flows are perturbed to find a near global optimum over the whole feasible region. It should be noted that in the perturbation stage the loop flows obtained form the sample existing network are employed as the initial loop flows of the proposed method. It has been also found that the relationship of cost-hydraulic gradient for pipe expansion of existing network affects the total cost of the sample network. The results show that the proposed method can yield a lower cost design than the conventional design method and that the proposed method can be efficiently used to design the pipe expansion of existing water distribution systems.