• 대한수학회지
• /
• 제52권3호
• /
• pp.567-586
• /
• 2015

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control for various observation cases.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
• /
• pp.155-159
• /
• 1993

In this paper, we consider the problem of a stochastic optimal switching control, which can be applied to the control of a system with uncertain demand such as a control problem of a power plant. The dynamic programming method is applied for the formulation of the optimal control problem. We solve the system of Quasi-Variational Inequalities(QVI) using an algoritlim which involves the finite difference approximation and contraction mapping method. A mathematical example of the optimal switching control is constructed. The actual performance of the algorithm is also tested through the solution of the constructed example.

• Korean Journal of Mathematics
• /
• 제23권2호
• /
• pp.283-291
• /
• 2015

In the optimal control problem, at first we search the expected optimal solution by using Pontryagin type's necessary conditions called the maximum principle. Next we use the sufficient conditions to conclude that the searched solution is optimal. In this article the sufficient conditions are studied. The value function is used for sufficient conditions.

• East Asian mathematical journal
• /
• 제31권1호
• /
• pp.91-101
• /
• 2015

An explicit expression of the optimal investment strategy corresponding to the HARA utility function under the constant elasticity of variance (CEV) model has been given by Jung and Kim [6]. In this paper we give an explicit expression of the optimal solution for the extended logarithmic utility function. And we prove an a.s. convergence of the HARA solutions to the extended logarithmic one.

• 한국수자원학회:학술대회논문집
• /
• 한국수자원학회 2009년도 학술발표회 초록집
• /
• pp.905-908
• /
• 2009

In the management of groundwater in coastal areas, saltwater intrusion associated with extensive groundwater pumping, is an important problem. The groundwater optimization model is an advanced method to study the aquifer and decide the optimal pumping rates or optimal well locations. Cheng and Park gave the analytical solutions to the optimization problems basing on Strack's analytical solution. However, the analytical solutions have some limitations of the property of aquifer, boundary conditions, and so on. A simulation-optimization numerical method presented in this study can deal with non-homogenous aquifers and various complex boundary conditions. This simulation-optimization model includes the sharp interface solution which solves the same governing equation with Strack's analytical solution, therefore, the freshwater head and saltwater thickness should be in the same conditions, that can lead to the comparable results in optimal pumping rates and optimal well locations for both of the solutions. It is noticed that the analytical solutions can only be applied on the infinite domain aquifer, while it is impossible to get a numerical model with infinite domain. To compare the numerical model with the analytical solutions, calculation of the equivalent boundary flux was planted into the numerical model so that the numerical model can have the same conditions in steady state with analytical solutions.

• 한국경영과학회:학술대회논문집
• /
• 대한산업공학회/한국경영과학회 1996년도 춘계공동학술대회논문집; 공군사관학교, 청주; 26-27 Apr. 1996
• /
• pp.514-517
• /
• 1996

In solving multi-level knapsack problems, conventional heuristic approaches often assume a short-sighted plan within a static decision enviornment to find a near optimal solution. These conventional approaches are inflexible, and lack the ability to adapt to different problem structures. This research approaches the problem from a totally different viewpoint, and a new method is designed and implemented. This method performs intelligent actions based on memories of historic data and learning. These actions are developed not only by observing the attributes of the optimal solution, the solution space, and its corresponding path to the optimal solution, but also by applying human intelligence, experience, and intuition with respect to the search strategies. The method intensifies, or diversifies the search process appropriately in time and space. In order to create a good neighborhood structure, this method uses two powerful choice rules that emphasize the impact of candidate variables on the current solution with respect to their profit contribution. A side effect of so-called "pseudo moves", similar to "aspirations", supports these choice rules during the evaluation process. For the purpose of visiting as many relevant points as possible, strategic oscillation between feasible and infeasible solutions around the boundary is applied for intensification. To avoid redundant moves, short-term (tabu-lists), intermediate-term (cycle detection), and long-term (recording frequency and significant solutions for diversification) memories are used. Test results show that among the 45 generated problems (these problems pose significant or insurmountable challenges to exact methods) the approach produces the optimal solutions in 39 cases.lutions in 39 cases.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2003년도 ISIS 2003
• /
• pp.380-383
• /
• 2003

In this paper, we propose a fuzzy group decision making method for multiple decision maker-multiple objective programming problems to obtain the agreeable solution. In the proposed method, considering the vague nature of human subjective judgement it is assumed that each of multiple decision makers has a fuzzy goal for each of his/her own objective functions. After eliciting the membership functions from the decision makers for their fuzzy goals, total M-Pareto optimal solution concept is defined in membership spaces in order to deal with multiple decision maker-multiple objective programming problems. For generating a candidate of the agreeable solution which is total M-Pareto optimal, the extended weighted minimax problem is formulated and solved for some weighting vector which is specified by the decision makers in their subjective manner, Given the total M-Pareto optimal solution, each of the derision makers must either be satisfied with the current values of the membership functions, or update his/her weighting vector, However, in general, it seems to be very difficult to find the agreeable solution with which all of the decision makers are satisfied perfectly because of the conflicts between their membership functions. In the proposed method, each of the decision makers is requested to estimate the degree of satisfaction for the candidate of the agreeable solution. Using the estimated values or satisfaction of each of the decision makers, the core concept is desnfied, which is a set of undominated candidates. The interactive algorithm is developed to obtain the agreeable solution which satisfies core conditions.

• Corrosion Science and Technology
• /
• 제20권2호
• /
• pp.77-84
• /
• 2021

This study aims to optimize the DL-EPR test solution for duplex stainless steel S31083 using the Taguchi design. The test solution parameters applied to the Taguchi design are H₂SO₄, NaCl, KSCN concentration, and temperature. In the experimental design, an orthogonal array of 4 levels 4 factor L₁₆(4⁴) was used. Output values for the orthogonal array were used for resolution (degree of sensitization) and selective etch (I_a) values. The optimal test solution conditions were selected by comparing the normalized S/N ratio for the two reaction properties. As a result, the H₂SO₄ and NaCl were identified as the main factors influencing the sensitivity measurement, but the delta statistics showed that the KSCN concentration and temperature had relatively low influence. The optimal condition was identified as 1.5 M H₂SO₄+0.03 M KSCN+1.5M NaCl at 30 ℃. The degree of sensitization presented a tendency to depend on the heat treatment temperature and time in the optimal test solution. This investigation confirmed the possibility of optimizing the experiment solution for the DL-EPR test of stainless steel using the Taguchi technique.

• Journal of applied mathematics & informatics
• /
• 제42권5호
• /
• pp.1195-1210
• /
• 2024

This research aims to determine an optimal (best) solution for transporting the logistics at a minimum cost from various sources to various destinations. We proposed a new algorithm for the initial basic feasible solution (IBFS). Developing a new IBFS is the first step towards finding the optimal solution. A new approach for the initial basic feasible solution that reduces iterations and produces the best answer in the initial process of the transportation issue. Different IBFS approaches have been generated in the literature review. Some statistical fundamentals, such as normal distribution and the root mean square technique, are employed to find new IBFS. A TP is transformed into a normal distribution, and penalties are determined using the root mean square method. Excel Solver is used to calculate normal distribution values. The second step involves using a stepping-stone approach to compute the optimum solution. The results of our study were calculated using numerical examples and contrasted with a few other methodologies, such as Vogel's approximation, the Continuous Allocation Method (CAM), the Supply Demand Repair Method (SDRM), and the Karagul-Sahin Approximation Method (KSAM). The conclusion of our proposed method gives more accurate results than the existing approach.

• 대한기계학회논문집A
• /
• 제34권12호
• /
• pp.1793-1803
• /
• 2010

가중치법이나 목표계획법을 이용하여 다목적함수 최적화를 수행할 때 설계자는 각 함수에 적절한 가중치나 목표값을 설정해 주어야 한다. 하지만 파라미터를 잘못 설정하게 되면 파레토 최적해를 얻지못하기 때문에 이는 설계자에게 큰 부담이 된다. 최근에 데이터의 분포특성만을 이용하여 데이터의 평균과 함수 사이의 거리를 표현하는 마하라노비스 거리(MD)를 최소화하는 MTS기법이 개발되었다. 이 방법은 파라미터를 설정하지 않아도 되는 장점이 있지만 최적해가 참고데이터의 평균으로 수렴하는 단점이 있다. 따라서 본 연구에서는 방향성이 없는 기존의 MD에 방향성을 부여한 새로운 거리 척도인 SMD를 제안하였다. 그리고 SMD법이 계산과정에서 각 함수의 가중치를 자동으로 반영하고 평균에서 가장 멀리 위치한 한 점을 항상 파레토 최적해로 제공한다는 것을 2개의 단순예제를 통해 검증하였다.