• 충청수학회지
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• 제27권1호
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• pp.145-149
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• 2014

I consider the optimal consumption and portfolio selection problem with nonnegative wealth constraints using the dynamic programming approach. I use the constant relative risk aversion (CRRA) utility function and disutility to derive the closed-form solutions.

• 한국컴퓨터정보학회논문지
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• 제26권12호
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• pp.29-43
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• 2021

본 연구에서 제약식프로그래밍을 이용하여 제약식 있는 동적계획법 모형을 푸는 한 방법을 제시한다. 현재 제약식 있는 동적계획법을 다루는 방법은 각 단계별 제약식들의 상태를 일반적인 동적계획법의 상태공간에 추가하여 마치 제약식이 없는 동적계획법 방식을 적용하는데 반해, 이 연구에서 제시하는 방식은 제약식의 상태가 제약식프로그래밍의 변수 도메인으로 표현되고 저장된다. 계산에 있어서도 일반적인 동적계획법의 벨만방정식의 해법과 함께 제약식을 다루기 위한 제약식프로그래밍의 확산-추론 방법을 사용하는 하이브리드 방식을 따른다. 이 두가지 방식의 비교를 위해 특별히 장기 자동차 렌탈 문제를 제시하고 이 문제의 단순화된 모형을 중심으로 다른 방식으로 해결하는 과정을 보고 그 장단점을 논한다.

• Journal of Electrical Engineering and Technology
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• 제3권3호
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• pp.320-330
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• 2008

This paper presents an improved dynamic programming (IDP) approach to solve the economic power dispatch problem including transmission losses in power systems. A detailed mathematical derivation of recursive dynamic programming approach for the economic power dispatch problem with transmission losses is presented. The transmission losses are augmented with the objective function using price factor. The generalized expression for optimal scheduling of thermal generating units derived in this article can be implemented for the solution of the economic power dispatch problem of a large-scale system. Six-unit, fifteen-unit, and forty-unit sample systems with non-linear characteristics of the generator, such as ramp-rate limits and prohibited operating zones are considered to illustrate the effectiveness of the proposed method. The proposed method results have been compared with the results of genetic algorithm and particle swarm optimization methods reported in the literature. Test results show that the proposed IDP approach can obtain a higher quality solution with better performance.

• 한국컴퓨터정보학회논문지
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• 제21권9호
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• pp.91-100
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• 2016

In this research, emergency vehicle dispatching problems faced with in the wake of massive natural disasters are considered. Here, the emergency vehicle dispatching problems can be regarded as a single machine stochastic scheduling problems, where the processing times are independently and identically distributed random variables, are considered. The objective of minimizing the expected number of tardy jobs, with distinct job due dates that are independently and arbitrarily distributed random variables, is dealt with. For these problems, optimal static-list policies can be found by solving corresponding assignment problems. However, for the special cases where due dates are exponentially distributed random variables, using a proposed dynamic programming approach is found to be relatively faster than solving the corresponding assignment problems. This so-called Pivot Dynamic Programming approach exploits necessary optimality conditions derived for ordering the jobs partially.

• Water Engineering Research
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• 제1권4호
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• pp.279-291
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• 2000

A mathematical model using dynamic programming approach is applied to an optimal unit commitment problem. In this study, the units are treated as stages instead of as state dimension, and the time dimension corresponds to the state dimension instead of stages. A considerable amount of computer time is saved as compared to the normal approach if there are many units in the basin. A case study on the Lower Colorado River Basin System is presented to demonstrate the capabilities of the optimal scheduling of hydropower units.

• 대한산업공학회지
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• 제4권2호
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• pp.77-81
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• 1978

The assortment problem with deterministic demand has been formulated so that a dynamic programming can be applied to find optimal production lengths that will minimize the sum of cutting losses. The original minimization problem can be reformulated as the maximization problem with a different objective function. This problem can be solved by the dynamic programming technique. A numerical example illustrates this approach. The ratio of computation amount of emumeration method to that of this dynamic programming is approximately n to 1.

• International Journal of Control, Automation, and Systems
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• 제5권2호
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• pp.192-199
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• 2007

This paper proposes a new printed circuit board (PCB) assembly planning method for multi-head surface mounters. We present an integer programming formulation for the optimization problem, and propose a heuristic method to solve the large NP-complete problem within a reasonable time. A dynamic programming technique is then applied to the feeder arrangement optimization and placement sequence optimization to reduce the overall assembly time. Comparative simulation results are finally presented to verify the usefulness of the proposed method.

• Journal of Electrical Engineering and Technology
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• 제11권2호
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• pp.329-337
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• 2016

With the increasing deployment of distributed generators in the distribution system, a very large search space is required when dynamic programming (DP) is applied for the optimized dispatch schedules of voltage and reactive power controllers such as on-load tap changers, distributed generators, and shunt capacitors. This study proposes a new optimal voltage and reactive power scheduling method based on dynamic programming with a heuristic searching space reduction approach to reduce the computational burden. This algorithm is designed to determine optimum dispatch schedules based on power system day-ahead scheduling, with new control objectives that consider the reduction of active power losses and maintain the receiving power factor. In this work, to reduce the computational burden, an advanced voltage sensitivity index (AVSI) is adopted to reduce the number of load-flow calculations by estimating bus voltages. Moreover, the accumulated switching operation number up to the current stage is applied prior to the load-flow calculation module. The computational burden can be greatly reduced by using dynamic programming. Case studies were conducted using the IEEE 30-bus test systems and the simulation results indicate that the proposed method is more effective in terms of saving electric charges and improving the voltage profile than loss minimization.

• 산업경영시스템학회지
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• 제35권2호
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• pp.57-63
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• 2012

소프트웨어 개발에 있어서 소프트웨어를 시장에 출시하는 계획을 수립하는 것은 소프트웨어를 이루고 있는 기능들을 구현하는 데 제약이 되는 조건들(기술, 자원, 위험, 예산 등)을 만족하면서 계획된 출시기간에 이들 기능들을 할당하는 일이다. 이와 같이 소프트웨어 출시를 계획하는 것은 소프트웨어 제품라인에 대해서 고려할 때 더욱 복잡해진다. 본 연구에서는 소프트웨어 제품라인에 있어서 소프트웨어 출시 계획을 수립하기 위한 문제를 우선순위 제약하의 다수 0-1 배낭문제로 수리 모형화하고, 이를 풀기 위한 최적해법이 개발된다. 최적해법은 동적 계획법이 주가 되고, 문제의 크기를 줄이기 위하여 휴리스틱과 축소방법이 이용된다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.2617-2622
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• 2003

The pH neutralization process has long been taken as a representative benchmark problem of nonlinear chemical process control due to its nonlinearity and time-varying nature. For general nonlinear processes, it is difficult to control with a linear model-based control method so nonlinear controls must be considered. Among the numerous approaches suggested, the most rigorous approach is the dynamic optimization. However, as the size of the problem grows, the dynamic programming approach is suffered from the curse of dimensionality. In order to avoid this problem, the Neuro-Dynamic Programming (NDP) approach was proposed by Bertsekas and Tsitsiklis (1996). The NDP approach is to utilize all the data collected to generate an approximation of optimal cost-to-go function which was used to find the optimal input movement in real time control. The approximation could be any type of function such as polynomials, neural networks and etc. In this study, an algorithm using NDP approach was applied to a pH neutralization process to investigate the feasibility of the NDP algorithm and to deepen the understanding of the basic characteristics of this algorithm. As the global approximator, the neural network which requires training and k-nearest neighbor method which requires querying instead of training are investigated. The global approximator requires optimal control strategy. If the optimal control strategy is not available, suboptimal control strategy can be used even though the laborious Bellman iterations are necessary. For pH neutralization process it is rather easy to devise an optimal control strategy. Thus, we used an optimal control strategy and did not perform the Bellman iteration. Also, the effects of constraints on control moves are studied. From the simulations, the NDP method outperforms the conventional PID control.