Advances in Fuzzy Dynamic Programming

2021 ◽  
pp. 166-186
Author(s):  
Felix Mora-Camino ◽  
Elena Capitanul Conea ◽  
Fabio Krykhtine ◽  
Walid Moudani ◽  
Carlos Alberto Nunes Cosenza
Keyword(s):  
Dynamic Programming ◽  
Cumulative Risk ◽  
Planning Problem ◽  
Dual Numbers ◽  
Sequential Decision ◽  
Investment Planning ◽  
Deterministic Dynamic ◽  
Programming Process ◽  
Mathematical Programming Problems ◽  
Under Construction

This chapter considers the use of fuzzy dual numbers to model and solve through dynamic programming process mathematical programming problems where uncertainty is present in the parameters of the objective function or of the associated constraints. It is only supposed that the values of the uncertain parameters remain in known real intervals and can be modelled with fuzzy dual numbers. The interest of adopting the fuzzy dual formalism to implement the sequential decision-making process of dynamic programming is discussed and compared with early fuzzy dynamic programming. Here, the comparison between two alternatives is made considering not only the cumulative performance but also the cumulative risk associated with previous steps in the dynamic process, displaying the traceability of the solution under construction as it is effectively the case with the classical deterministic dynamic programming process. The proposed approach is illustrated in the case of a long-term airport investment planning problem.

Advances in Fuzzy Dynamic Programming

2018 ◽  
pp. 116-139
Author(s):  
Felix Mora-Camino ◽  
Elena Capitanul Conea ◽  
Fabio Krykhtine ◽  
Walid Moudani ◽  
Carlos Alberto Nunes Cosenza
Keyword(s):  
Dynamic Programming ◽  
Cumulative Risk ◽  
Planning Problem ◽  
Dual Numbers ◽  
Sequential Decision ◽  
Investment Planning ◽  
Deterministic Dynamic ◽  
Programming Process ◽  
Mathematical Programming Problems ◽  
Under Construction

This chapter considers the use of fuzzy dual numbers to model and solve through dynamic programming process mathematical programming problems where uncertainty is present in the parameters of the objective function or of the associated constraints. It is only supposed that the values of the uncertain parameters remain in known real intervals and can be modelled with fuzzy dual numbers. The interest of adopting the fuzzy dual formalism to implement the sequential decision-making process of dynamic programming is discussed and compared with early fuzzy dynamic programming. Here, the comparison between two alternatives is made considering not only the cumulative performance but also the cumulative risk associated with previous steps in the dynamic process, displaying the traceability of the solution under construction as it is effectively the case with the classical deterministic dynamic programming process. The proposed approach is illustrated in the case of a long-term airport investment planning problem.

Role of Trip Information Preview in Fuel Economy of Plug-In Hybrid Vehicles

2009 ◽  
Author(s):  
Chen Zhang ◽  
Ardalan Vahidi ◽  
Xiaopeng Li ◽  
Dean Essenmacher
Keyword(s):  
Dynamic Programming ◽  
Fuel Economy ◽  
Substantial Reduction ◽  
Hybrid Vehicles ◽  
Hilly Terrain ◽  
Additional Increase ◽  
Charging Station ◽  
Complete Knowledge ◽  
Deterministic Dynamic

This paper investigates the role of partial or complete knowledge of future driving conditions in fuel economy of Plug-in Hybrid Vehicles (PHEVs). We show that with the knowledge of distance to the next charging station only, substantial reduction in fuel use, up to 18%, is possible by planning a blended utilization of electric motor and the engine throughout the entire trip. To achieve this we formulate a modified Equivalent Consumption Minimization Strategy (ECMS) which takes into account the traveling distance. We show further fuel economy gain, in the order of 1–5%, is possible if the future terrain and velocity are known; we quantify this additional increase in fuel economy for a number of velocity cycles and a hilly terrain profile via deterministic dynamic programming.

scholarly journals A dynamic programming process

1964 ◽  
Vol 7 (1) ◽  
pp. 36-39
Author(s):  
L. J. Slater
Keyword(s):  
Dynamic Programming ◽  
Programming Process

scholarly journals Dynamic Network Planning of Underground Logistics System on Uncertainty Graph

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
YiHua Zhong ◽  
ShiMing Luo ◽  
Min Bao ◽  
XiaoDie Lv
Keyword(s):  
Dynamic Programming ◽  
Programming Model ◽  
Network Planning ◽  
Dynamic Network ◽  
Planning Problem ◽  
Uncertainty Measure ◽  
Uncertain Graph ◽  
Logistics System ◽  
Nanjing City ◽  
Dynamic Programming Model

When designing the underground logistics system, it is necessary to consider the uncertainty of logistics nodes, high cost, and high risk. This paper employed the theories of uncertain graph and dynamic programming to solve the network planning problem of underground logistics system. Firstly, we proposed the concepts of uncertainty measure matrix and vertices structure uncertainty graph by using uncertainty measure and uncertainty graph. Secondly, vertices structure uncertainty graph of the underground logistics system was constructed based on our proposed vertices structure uncertainty graph and the uncertainty of logistics nodes. Thirdly, the dynamic programming model of the underground logistics system was established, and its solution algorithm was also designed by improving simulated annealing. Finally, the correctness and feasibility of the method was validated by using a numerical example of the underground logistics system in Xianlin district, Nanjing City in China.

scholarly journals Benders decomposition with adaptive oracles for large scale optimization

2020 ◽  
Author(s):  
Nicolò Mazzi ◽  
Andreas Grothey ◽  
Ken McKinnon ◽  
Nagisa Sugishita
Keyword(s):  
Large Scale ◽  
Benders Decomposition ◽  
Optimization Problems ◽  
Cutting Plane ◽  
Computational Effort ◽  
Planning Problem ◽  
Illustrative Case ◽  
Investment Planning ◽  
Cutting Plane Algorithms ◽  
Inexact Information

AbstractThis paper proposes an algorithm to efficiently solve large optimization problems which exhibit a column bounded block-diagonal structure, where subproblems differ in right-hand side and cost coefficients. Similar problems are often tackled using cutting-plane algorithms, which allow for an iterative and decomposed solution of the problem. When solving subproblems is computationally expensive and the set of subproblems is large, cutting-plane algorithms may slow down severely. In this context we propose two novel adaptive oracles that yield inexact information, potentially much faster than solving the subproblem. The first adaptive oracle is used to generate inexact but valid cutting planes, and the second adaptive oracle gives a valid upper bound of the true optimal objective. These two oracles progressively “adapt” towards the true exact oracle if provided with an increasing number of exact solutions, stored throughout the iterations. These adaptive oracles are embedded within a Benders-type algorithm able to handle inexact information. We compare the Benders with adaptive oracles against a standard Benders algorithm on a stochastic investment planning problem. The proposed algorithm shows the capability to substantially reduce the computational effort to obtain an $$\epsilon $$ ϵ -optimal solution: an illustrative case is 31.9 times faster for a $$1.00\%$$ 1.00 % convergence tolerance and 15.4 times faster for a $$0.01\%$$ 0.01 % tolerance.

ONLINE CAPACITY PLANNING FOR REHABILITATION TREATMENTS: AN APPROXIMATE DYNAMIC PROGRAMMING APPROACH

2018 ◽  
Vol 34 (3) ◽  
pp. 381-405
Author(s):  
Ingeborg A. Bikker ◽  
Martijn R.K. Mes ◽  
Antoine Sauré ◽  
Richard J. Boucherie
Keyword(s):  
Dynamic Programming ◽  
Capacity Planning ◽  
Approximate Dynamic Programming ◽  
Capacity Allocation ◽  
Access Time ◽  
Programming Approach ◽  
Planning Problem ◽  
Dynamic Programming Approach ◽  
Negative Effect ◽  
Long Access

AbstractWe study an online capacity planning problem in which arriving patients require a series of appointments at several departments, within a certain access time target.This research is motivated by a study of rehabilitation planning practices at the Sint Maartenskliniek hospital (the Netherlands). In practice, the prescribed treatments and activities are typically booked starting in the first available week, leaving no space for urgent patients who require a series of appointments at a short notice. This leads to the rescheduling of appointments or long access times for urgent patients, which has a negative effect on the quality of care and on patient satisfaction.We propose an approach for allocating capacity to patients at the moment of their arrival, in such a way that the total number of requests booked within their corresponding access time targets is maximized. The model considers online decision making regarding multi-priority, multi-appointment, and multi-resource capacity allocation. We formulate this problem as a Markov decision process (MDP) that takes into account the current patient schedule, and future arrivals. We develop an approximate dynamic programming (ADP) algorithm to obtain approximate optimal capacity allocation policies. We provide insights into the characteristics of the optimal policies and evaluate the performance of the resulting policies using simulation.

Has Dynamic Programming Improved Decision Making?

2019 ◽  
Vol 11 (1) ◽  
pp. 833-858 ◽  
Author(s):  
John Rust
Keyword(s):  
Decision Making ◽  
Dynamic Programming ◽  
Real World ◽  
Operations Research ◽  
Decision Rules ◽  
Decision Problems ◽  
Optimal Decision ◽  
Sequential Decision ◽  
Success Stories ◽  
Real World Applications

Dynamic programming (DP) is a powerful tool for solving a wide class of sequential decision-making problems under uncertainty. In principle, it enables us to compute optimal decision rules that specify the best possible decision in any situation. This article reviews developments in DP and contrasts its revolutionary impact on economics, operations research, engineering, and artificial intelligence with the comparative paucity of its real-world applications to improve the decision making of individuals and firms. The fuzziness of many real-world decision problems and the difficulty in mathematically modeling them are key obstacles to a wider application of DP in real-world settings. Nevertheless, I discuss several success stories, and I conclude that DP offers substantial promise for improving decision making if we let go of the empirically untenable assumption of unbounded rationality and confront the challenging decision problems faced every day by individuals and firms.

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