• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.8
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• pp.1485-1495
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• 2009

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the ${\lambda}-P$ function method is used to calculate ED for the fitness function of GA. The ${\lambda}-P$ function method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with two kinds of ED problems, namely ED with multiple fuel units (EDMF) and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all the ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.468-476
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• 2008

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the $\lambda$-P table method is used to calculate ED for the fitness function of GA. The $\lambda$-P table method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with three kinds of ED problems, namely ED considering valve-point effects (EDVP), ED with multiple fuel units (EDMF), and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all three ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.585-604
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• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.5
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• pp.102-109
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• 1985

A new yield maximization procedure by investigating method of the multidimensional Monte Carlo integration is presented. And then maximum yield is obtained by the new modified weight selection algorithm applied to objective function of MOSFET NAND GATE Also this yield maximization procedure can be applied to nonconvex objective function.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.675-685
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• 2010

In this paper, we consider a new class of regularized (nonconvex) generalized mixed variational inequality problems in real Hilbert space. We give the concepts of partially relaxed strongly mixed monotone and partially relaxed strongly $\theta$-pseudomonotone mappings, which are extension of the concepts given by Xia and Ding [19], Noor [13] and Kazmi et al. [9]. Further we use the auxiliary principle technique to suggest a two-step iterative algorithm for solving regularized (nonconvex) generalized mixed variational inequality problem. We prove that the convergence of the iterative algorithm requires only the continuity, partially relaxed strongly mixed monotonicity and partially relaxed strongly $\theta$-pseudomonotonicity. The theorems presented in this paper represent improvement and generalization of the previously known results for solving equilibrium problems and variational inequality problems involving the nonconvex (convex) sets, see for example Noor [13], Pang et al. [14], and Xia and Ding [19].

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.455-464
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• 2014

Unlabeled examples are easier and less expensive to obtain than labeled examples. Semisupervised approaches are used to utilize such examples in an eort to boost the predictive performance. This paper proposes a novel semisupervised classication method named transductive least squares support vector machine (TLS-SVM), which is based on the least squares support vector machine. The proposed method utilizes the dierence convex algorithm to derive nonconvex minimization solutions for the TLS-SVM. A generalized cross validation method is also developed to choose the hyperparameters that aect the performance of the TLS-SVM. The experimental results conrm the successful performance of the proposed TLS-SVM.

• ICROS
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• v.10 no.3
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• pp.27-33
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• 2004

최적화는 시스템공학에서 자주 등장하는 문제이며 흔히 다음과 같은 수학적 계획(mathematical programming) 문제로 표현된다. min f(x) (P) subject to g(x) ≤ 0 h(x) ： 0 여기서 x∈R/sup n/, f：R/sup n/→R, g：R/sup n/→R/sup l/, h：R/sup n/→R/sup m/, 그리고 n m이다. 만약 목적함수(objective function)와 가능 영역(feasible region)이 볼록(convex)하다면, 예를 틀어 f(x)와 g(x)가 아래로 볼록하고 h(x)가 선형이라면. 이는 볼록 문제(convex problem)이며 오직 하나의 지역 최소점(local minimum)을 가진다. 그러나 많은 경우. 예를 들어 h(x)가 비선형이라면, 여러 개의 지역 최소점을 가질 수 있는 비 볼록 문제(nonconvex problem)가 된다. 이때 진정한 최소점을 찾는 것. 즉 전역 최적화 (global optimization)가 요구된다.(중략)

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.7
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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.

• Water Engineering Research
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• v.1 no.1
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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.

• Journal of Korean Society for Geospatial Information Science
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• v.8 no.1 s.15
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• pp.51-63
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• 2000

Dynamic traffic assignment(DTA) has been a topic of substantial research during the past decade. While DTA is gradually maturing, many aspects of DTA still need improvement, especially regarding its formulation and solution algerian Recently, with its promise for In(Intelligent Transportation System) and GIS(Geographic Information System) applications, DTA have received increasing attention. This potential also implies higher requirement for DTA modeling, especially regarding its solution efficiency for real-time implementation. But DTA have many mathematical difficulties in searching process due to the complexity of spatial and temporal variables. Although many solution algorithms have been studied, conventional methods cannot iud the solution in case that objective function or constraints is not convex. In this paper, the genetic algorithm to find the solution of DTA is applied and the Merchant-Nemhauser model is used as DTA model because it has a nonconvex constraint set. To handle the nonconvex constraint set the GENOCOP III system which is a kind of the genetic algorithm is used in this study. Results for the sample network have been compared with the results of conventional method.