• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.857-871
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• 2022

In this work, we formulated a mathematical model for divorce in marriage and extended in to an optimal control model. Firstly, we qualitatively established the model positivity and boundedness. Also we saw sensitivity analysis of the model and identified the positive and negative indices parameters. An optimal control model were developed by incorporating three time dependent control strategies (couple relationship education, reducing getting married too young & consulting separators to renew their marriage) on the deterministic model. The Pontryagin's maximum principle were used for the derivation of necessary conditions of the optimal control problem. Finally, with Newton's forward and backward sweep method numerical simulation were performed on optimality system by considering four integrated strategies. So that we reached to a result that using all three strategies simultaneously (the strategy D) is an optimal control in order to effectively control marriage divorce over a specified period of time. From this we conclude that, policymakers and stakeholders should use the indicated control strategy at a time in order to fight against Divorce in a population.

• Journal of IKEEE
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• v.11 no.1 s.20
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• pp.1-14
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• 2007

In this paper, a design of an integral augmented nonlinear optimal variable structure system(INOVSS) is presented for the prescribed output control of uncertain MIMO systems under persistent disturbances. This algorithm basically concerns removing the problems of the reaching phase and combining with the nonlinear optimal control theory. By means of an integral nonlinear sliding surface, the reaching phase is completely removed. The ideal sliding dynamics of the integral nonlinear sliding surface is obtained in the form of the nonlinear state equation and is designed by using the nonlinear optimal control theory, which means the design of the integral nonlinear sliding surface and equivalent control input. The homogeneous $2{\upsilon}(\kappa)$ form is defined in order to easily select the $2{\upsilon}$ or even $(\kappa)-form$ higher order nonlinear terms in the suggested sliding surface. The corresponding nonlinear control input is designed in order to generate the sliding mode on the predetermined transformed new surface by means of diagonalization method. As a result, the whole sliding output from a given initial state to origin is completely guaranteed against persistent disturbances. The prediction/predetermination of output is enable. Moreover, the better performance by the nonlinear sliding surface than that of the linear sliding surface can be obtained. Through an illustrative example, the usefulness of the algorithm is shown.

• Journal of Power Electronics
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• v.15 no.1
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• pp.160-176
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• 2015

This paper presents a method of designing optimal integer- and fractional-order proportional-integral-derivative (FOPID) controllers for a boost converter to gain a set of favorable characteristics at various operating points. A Pareto-based multi-objective optimization approach called strength Pareto evolutionary algorithm (SPEA) is used to obtain fast and low overshoot start-up and dynamic responses and switching stability. The optimization approach generates a set of optimal gains called Pareto set, which corresponds to a Pareto front. The Pareto front is a set of optimal results for objective functions. These results provide designers with a trade-off look-up table, in which they can easily choose any of the optimal gains based on design requirements. The SPEA also overcomes the difficulties of tuning the FOPID controller, which is an extension to the classic integer-order PID controllers and potentially promises better results. The proposed optimized FOPID controller provides an excellent start-up response and the desired dynamic response. This paper presents a detailed comparison of the optimum integer- and the fractional-order PID controllers. Extensive simulation and experimental results prove the superiority of the proposed design methodology to achieve a wide set of desired technical goals.

• Industrial Engineering and Management Systems
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• v.14 no.2
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• pp.129-158
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• 2015

It is necessary for retailers to determine the optimal ordering policy of products considering supply disruptions due to a natural disaster and a production process failure as quality and machine breakdowns. Under the situation, a dualsourcing supply chain (DSSC) is one of effective SC for retailers to order products reliably. This paper proposes the optimal ordering policy of a product in a DSSC with a retailer and two manufacturers. Two manufacturers may face supply disruptions due to a natural disater and a production process failure after they received the retailer's order of products. Here, two scenarios of demand information of products are assumed: (i) the demand distribution is known (ii) mean and variance of the demand are known. Under above situations, two types of DSSC are discussed. Under a decentralized DSSC (DSC), a retailer determines the optimal ordering policy to maximize his/her total expected profit. Under the integrated DSSC (ISC), the optimal ordering policy is determined to maximize the whole system's total expected profit. Numerical analysis investigates how demand information and supply disruptions affect the optimal decisions under DSC and ISC. Besides, profitability of supply chain coordination adjusting the wholesale price is evaluated to encourage the optimal decision under ISC.

• Computers and Concrete
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• v.25 no.4
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• pp.303-310
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• 2020

In this research, a hybrid mathematical model is derived using the higher-order polynomial kinematic model in association with soft computing technique for the prediction of best fiber volume fractions and the minimal mass of the layered composite structure. The optimal values are predicted further by taking the frequency parameter as the constraint and the projected values utilized for the computation of the eigenvalue and deflections. The optimal mass of the total layered composite and the corresponding optimal volume fractions are evaluated using the particle swarm optimization by constraining the arbitrary frequency value as mass/volume minimization functions. The degree of accuracy of the optimal model has been proven through the comparison study with published well-known research data. Further, the predicted values of volume fractions are incurred for the evaluation of the eigenvalue and the deflection data of the composite structure. To obtain the structural responses i.e. vibrational frequency and the central deflections the proposed higher-order polynomial FE model adopted. Finally, a series of numerical experimentations are carried out using the optimal fibre volume fraction for the prediction of the optimal frequencies and deflections including associated structural parameter.

• Proceedings of the Safety Management and Science Conference
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• 2000.05a
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• pp.77-86
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• 2000

This paper deals with the problem of determining the retailer's optimal price and order size under the condition of order-size-dependent delay in payments. It is assumed that the length of delay is a function of the retailer's total amount of purchase. The constant price elasticity demand function is adopted which is a decreasing function of retail price. Investigation of the properties of an optimal solution allows us to develop an algorithm whose validity is illustrated through an example problem.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.701-716
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• 1998

In this paper we develop algorithms in programming lan-guage SCHEME for implementation of the main first order gradient techniques for unconstrained optimization. Implementation of the de-scent techniques which use non-optimal descent steps as well as imple-mentation of the optimal descent techniques are described. Also we investigate implementation of the global problem called optimization along a line. Developed programs are effective and simpler with re-spect to the corresponding in the procedural programming languages. Several numerical examples are reported.

• Journal of Korean Society for Quality Management
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• v.19 no.2
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• pp.133-137
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• 1991

In this paper, the queueing system in series is studied. The system is a tandem queueing system which has three stations. In system, one service station has a general distributions and two service stations have exponential distribution. Each station has a single server. The customer arrives with Poisson process and is serviced sequentially. It is assumed that the order of stations does not affect the quality of services. Using the light traffic approximations, the optimal order of the system which has the three stations is decided.

• Journal of Korean Institute of Industrial Engineers
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• v.4 no.1
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• pp.49-55
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• 1978

This paper presents a new method, called a modified economic order quantity method, for determining the optimal inventory policy, which uses the rate of return as its decision criterion. Especially for the simplest possible inventory system with constant demand rate, no backlogging, no lead time, etc., the formula for the optimal order policy is derived. Also mentioned are the relative merits and shortcomings of this method compared to the conventional EOQ model.

• Journal of Advanced Marine Engineering and Technology
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• v.18 no.4
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• pp.77-83
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• 1994

In this paper, an optimal control of first order systems is discussed. The control system comprises a main controller and an auxiliary controller. The main controller is designed based on the LQ control scheme including an integrator to remove the off-set. The non-linear auxiliary controller is added parallely to the main controller to obtain a finite time settling control. The control parameters under variation of the system and various coefficients of the performance indices are computed numerically, and the control responses for the system with the proposed controllers demonstrated the usefulness of the control method.