Stochastic Dynamic Programming Formulation for a Wastewater Treatment Decision-Making Framework

Tsai, Julia C. C.; Chen, Victoria C. P.; Beck, M.B.; Chen, Jining

doi:10.1023/b:anor.0000045283.86576.62

Cited by 21 publications

(17 citation statements)

References 19 publications

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“…In several levels, the MAD values are quite high. We surmize that these levels require more discretization points to ensure a good MARS model, e.g., Tsai et al 9 utilized 12 167 discretization points. However, to reduce the computation needed to conduct the comparisons in the section, we chose to employ only 2209 discretization points.…”

Section: Computational Resultsmentioning

confidence: 99%

“…The primary objective function is to minimize economic cost, including capital and operating costs. More details of the decision-making framework within the wastewater treatment system can be found in Tsai et al 9 .…”

Section: Wastewater Treatment Systemmentioning

confidence: 99%

“…Chen et al 7,8 presented preliminary results for a 10-dimensional wastewater treatment SDP problem. The wastewater treatment SDP model studied in this paper was presented by Tsai et al 9 and is based on the work of Chen and Beck 10 . It involves an 11-level liquid line, and a six-level solid line, and up to 20 continuous state variables that monitor attributes of the liquid and solid.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic Program

Tsai¹,

Chen

2005

Quality & Reliability Eng

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This paper presents an automatic and more robust implementation of multivariate adaptive regression splines (MARS) within the orthogonal array (OA)/MARS continuous-state stochastic dynamic programming (SDP) method. MARS is used to estimate the future value functions in each SDP level. The default stopping rule of MARS employs the maximum number of basis functions (M max ), specified by the user. To reduce the computational effort and improve the MARS fit for the wastewater treatment SDP model, two automatic stopping rules, which automatically determine an appropriate value for M max , and a robust version of MARS that prefers lower-order terms over higher-order terms are developed. Computational results demonstrate the success of these approaches.

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Section: Computational Resultsmentioning

confidence: 99%

Section: Wastewater Treatment Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic Program

Tsai¹,

Chen

2005

Quality & Reliability Eng

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“…[21] studies several types of experimental designs for efficient state space discretization. This sampling scheme has been successfully used as a part of stochastic DP method to solve a high dimensional waste-water treatment planning problem [22].…”

Section: Pertinent Adp Literature Reviewmentioning

confidence: 99%

“…Approximating the value function surface with a linear function is often a gross simplification. More complex approximation schemes like multivariate adaptive regression splines [22] or radial basis functions (RBF) destroy the guarantee for the convergence of the value function approximation. As a general rule, there is no guarantee of convergence for any of these methods using continuous value function approximations aside from some very special cases [28] where it is assumed that the policy is fixed.…”

Section: Pertinent Adp Literature Reviewmentioning

confidence: 99%

Strategic capacity decision‐making in a stochastic manufacturing environment using real‐time approximate dynamic programming

Pratikakis

Park

Lee

2010

Naval Research Logistics

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Abstract:In this study, we illustrate a real-time approximate dynamic programming (RTADP) method for solving multistage capacity decision problems in a stochastic manufacturing environment, by using an exemplary three-stage manufacturing system with recycle. The system is a moderate size queuing network, which experiences stochastic variations in demand and product yield. The dynamic capacity decision problem is formulated as a Markov decision process (MDP). The proposed RTADP method starts with a set of heuristics and learns a superior quality solution by interacting with the stochastic system via simulation. The curse-of-dimensionality associated with DP methods is alleviated by the adoption of several notions including "evolving set of relevant states," for which the value function table is built and updated, "adaptive action set" for keeping track of attractive action candidates, and "nonparametric k nearest neighbor averager" for value function approximation. The performance of the learned solution is evaluated against (1) an "ideal" solution derived using a mixed integer programming (MIP) formulation, which assumes full knowledge of future realized values of the stochastic variables (2) a myopic heuristic solution, and (3) a sample path based rolling horizon MIP solution. The policy learned through the RTADP method turned out to be superior to polices of 2 and 3.

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Divergence Behaviour of the Successive Geometric Mean Method of Pairwise Comparison Matrix Generation for a Multiple Stage, Multiple Objective Optimization Problem

Tarun

Chen

Corley

2013

J. Multi-Crit. Decis. Anal.

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This paper focuses on the divergence behaviour of the successive geometric mean (SGM) method used to generate pairwise comparison matrices while solving a multiple stage, multiple objective (MSMO) optimization problem. The SGM method can be used in the matrix generation phase of our three-phase methodology to obtain pairwise comparison matrix at each stage of an MSMO optimization problem, which can be subsequently used to obtain the weight vector at the corresponding stage. The weight vectors across the stages can be used to convert an MSMO problem into a multiple stage, single objective (MSSO) problem, which can be solved using dynamic programming-based approaches.To obtain a practical set of non-dominated solutions (also referred to as Pareto optimal solutions) to the MSMO optimization problem, it is important to use a solution approach that has the potential to allow for a better exploration of the Pareto optimal solution space. To accomplish a more exhaustive exploration of the Pareto optimal solution space, the weight vectors that are used to scalarize the MSMO optimization problem into its corresponding MSSO optimization problem should vary across the stages. Distinct weight vectors across the stages are tied directly with distinct pairwise comparison matrices across the stages. A pairwise comparison matrix generation method is said to diverge if it can generate distinct pairwise comparison matrices across the stages of an MSMO optimization problem. In this paper, we demonstrate the SGM method's divergence behaviour when the three-phase methodology is used in conjunction with an augmented high-dimensional, continuous-state stochastic dynamic programming method to solve a large-scale MSMO optimization problem.

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Stochastic Dynamic Programming Formulation for a Wastewater Treatment Decision-Making Framework

Cited by 21 publications

References 19 publications

Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic Program

Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic Program

Strategic capacity decision‐making in a stochastic manufacturing environment using real‐time approximate dynamic programming

Divergence Behaviour of the Successive Geometric Mean Method of Pairwise Comparison Matrix Generation for a Multiple Stage, Multiple Objective Optimization Problem

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