• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.5B
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• pp.295-303
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• 2007

An algorithm is proposed to seek a local optimal solution of the network utility maximization problem in a wireless mesh network, where the architecture being considered is an infrastructure/backbone wireless mesh network. The objective is to achieve proportional fairness amongst the end-to-end flows in wireless mesh networks. In order to establish the communication constraints of the flow rates in the network utility maximization problem, we have presented necessary and sufficient conditions for the achievability of the flow rates. Since wireless mesh networks are generally considered as a type of ad hoc networks, similarly as in wireless multi-hop network, the network utility maximization problem in wireless mesh network is a nonlinear nonconvex programming problem. Besides, the gateway/bridge functionalities in mesh routers enable the integration of wireless mesh networks with various existing wireless networks. Thus, the rate optimization problem in wireless mesh networks is more complex than in wireless multi-hop networks.

• Korean Management Science Review
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• v.15 no.1
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• pp.77-85
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• 1998

In this paper a face optimization algorithm is developed for solving the problem (P) of optimizing a linear function over the set of efficient solutions of a multiple objective linear program. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. Perhaps due to its inherent difficulty, relatively few attempts have been made to solve problem (P) in spite of the potential benefits which can be obtained by solving problem (P). The algorithm for solving problem (P) is guaranteed to find an exact optimal or almost exact optimal solution for the problem in a finite number of iterations.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.53-56
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• 2000

The problem ( Ρ ) of optimizing a linear function d$\^$T/x over the set of efficient set for a multiple objective linear program ( Μ ) is difficult because the efficient set is nonconvex. There some interesting properties between the objective linear vector ｄ and the matrix of multiple objectives C and those properties lead us to establish criteria to solve ( Ρ ) with a linear program. In this paper we investigate a system of the linear equations C$\^$T/${\alpha}$=d and construct two linearly independent positive vectors ${\mu}$, ν such that ${\alpha}$=${\mu}$-ν. From those vectors ${\mu}$, ν, solving an weighted sum linear program for finding an efficient extreme point for the ( Μ ) is a way to get an optimal solution ( Ρ ). Therefore our theory gives an easy way of solving nonconvex program ( Ρ ) with a weighted sum linear program.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.6
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• pp.1375-1383
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• 1994

The water distribution system problem consists of finding a minimum cost system design subject to hydraulic and operational constraints. Since the municipal water distribution system problem is nonconvex with multiple local minima, classical optimization methods find a local optimum. An outer flow search - inner optimization procedure is proposed for choosing a better local minimum for the water distribution systems. The pipe network is judiciously subjected to the outer search scheme which chooses alternative flow configurations to find an optimal flow division among pipes. Because the problem is nonconvex, a global search scheme called Stochastic Probing method is employed to permit a local optimum seeking method to migrate among various local minima. A local minimizer is employed for the design of least cost diameters for pipes in the network. The algorithm can also be employed for optimal design of parallel expansion of existing networks. In this paper one municipal water distribution system is considered. The optimal solutions thus found have significantly smaller costs than the ones reported previously by other researchers.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1303-1309
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• 2011

Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.

• Journal of Electrical Engineering and Technology
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• v.9 no.1
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• pp.15-26
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• 2014

This paper proposes a Modified Particle Swarm Optimization with Time Varying Acceleration Coefficients (MPSO-TVAC) for solving economic load dispatch (ELD) problem. Due to prohibited operating zones (POZ) and ramp rate limits of the practical generators, the ELD problems become nonlinear and nonconvex optimization problem. Furthermore, the ELD problem may be more complicated if transmission losses are considered. Particle swarm optimization (PSO) is one of the famous heuristic methods for solving nonconvex problems. However, this method may suffer to trap at local minima especially for multimodal problem. To improve the solution quality and robustness of PSO algorithm, a new best neighbour particle called 'rbest' is proposed. The rbest provides extra information for each particle that is randomly selected from other best particles in order to diversify the movement of particle and avoid premature convergence. The effectiveness of MPSO-TVAC algorithm is tested on different power systems with POZ, ramp-rate limits and transmission loss constraints. To validate the performances of the proposed algorithm, comparative studies have been carried out in terms of convergence characteristic, solution quality, computation time and robustness. Simulation results found that the proposed MPSO-TVAC algorithm has good solution quality and more robust than other methods reported in previous work.

• Proceedings of the Korean Information Science Society Conference
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• 2012.06d
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• pp.219-221
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• 2012

The concave utility in the Network Utility Maximization (NUM) problem is only suitable for elastic flows. In networks with multiclass traffic, the utility can be concave, linear, step or sigmoidal. Hence, the basic NUM becomes a nonconvex optimization problem. The current approach utilizes the standard dual-based decomposition method. It does not converge in case of scarce resource. In this paper, we propose an algorithm that always converges to a local optimal solution to the nonconvex NUM after solving a series of convex approximation problems. Our techniques can be applied to any log-concave utilities.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.73-81
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• 2013

In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method [2] and DY method [5], which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1334-1341
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• 2008

This paper introduces an approach of Hybrid Particle Swarm Optimization(HPSO) for a security-constrained economic dispatch(SCED) with line flow constraints. To reduce a early convergence effect of PSO algorithm, we proposed HPSO algorithm considering a mutation characteristic of Genetic Algorithm(GA). In power system, for considering N-1 line contingency, we have chosen critical line contingency through a process of Screening and Selection based on PI(performance Index). To prove the ability of the proposed HPSO in solving nonlinear optimization problems, SCED problems with nonconvex solution spaces are considered and solved with three different approach(Conventional GA, PSO, HPSO). We have applied to IEEE 118 bus system for verifying a usefulness of the proposed algorithm.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.850-851
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• 2007

This paper presents an efficient approach for solving the economic dispatch (ED) problems with prohibited operating zones using an improved particle swarm optimization (PSO). Although the PSO-based approaches have several advantages suitable to the heavily constrained nonconvex optimization problems, they still have the drawbacks such as local optimal trapping due to the premature convergence (i.e., exploration problem) and insufficient capability to find nearly-by extreme points (i.e., exploitation problem). This paper proposes an improved PSO framework adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. The proposed method is applied to ED problem with prohibited operating zones. Also, the results are compared with those of the state-of-the-art methods.