Explore the vast range of titles available.

Long‐term multireservoir operations optimization is challenging for existing optimization methods such as stochastic dynamic programming (SDP) and implicit stochastic programming (ISP) suffering from excessive computing time requirements. More difficult is to tackle a risk‐based optimization problem and provide an efficient frontier of the objective function for multireservoir systems. The Fletcher–Ponnambalam (FP) method is an explicit stochastic optimization method suitable for multireservoir operations optimization which faces no curse of dimensionality of SDP and has no need for scenario generations of ISP, thus is extremely fast. Earlier implementations have developed expressions for mean and variance of storages and releases, including deficits and surpluses, to estimate fairly accurate values of the linear and quadratic objective functions when compared with other well‐known methods. This paper introduces analytical derivations of hydropower equations to be used in the recent extension of the FP method and applies it to a long‐term operations optimization problem of a three‐reservoir system in Iran. The objective function is to maximize the expected value of the annual energy, which is a multiplicative nonlinear function of both releases and storage levels. The computational results from simulations for the 60 years of available inflow data for the chosen multireservoir system using the policies derived by the FP, ISP, and SDP methods were compared. The solution qualities were nearly the same, but the FP method has tremendous speedups over the other methods. Secondly, expressions for the variances of monthly energy productions were derived to compute efficient frontier for risk‐return tradeoffs of annual energy to guide decision makers. Plain Language Summary Optimizing long‐term operations for multiple reservoirs is difficult with traditional methods like stochastic dynamic programming (SDP) and implicit stochastic programming (ISP) because they require a lot of computing time. It's even harder to address risk‐based optimization and to create an efficient frontier, which shows the best trade‐offs between different goals. The Fletcher–Ponnambalam (FP) method is a fast and effective solution that doesn't suffer from the complexity issues of SDP and doesn't need scenario generations like ISP. Previous versions of the FP method could accurately estimate values using mean and variance of storage and releases. This paper improves the FP method by introducing new hydropower equations and applies it to optimize a three‐reservoir system in Iran over 60 years of inflow data. The goal is to maximize annual energy, a complex function of water releases and storage levels. The FP method produced solutions comparable in quality to SDP and ISP but was much faster. Additionally, new calculations for monthly energy variance were developed to help make better risk‐return decisions for annual energy production. Key Points Analytic expressions are derived for the moments of energy function to be used in hydropower multireservoir operations optimization, not considered before The derived expressions for the second moment of the generated energy is used to produce efficient frontier easily for annual hydroenergy production function The Fletcher–Ponnambalam (FP) results are better than stochastic dynamic programming and comparable to implicit stochastic programming but much faster than these methods

Reinforcement learning algorithms are central to the cognition and decision-making of embodied intelligent agents. A bilevel optimization (BO) modeling approach, along with a host of efficient BO algorithms, has been proven to be an effective means of addressing actor-critic (AC) policy optimization problems. In this work, based on a bilevel-structured AC problem model, an implicit zeroth-order stochastic algorithm is developed. A locally randomized spherical smoothing technique, which can be applied to nonsmooth nonconvex implicit AC formulations and avoid the closed-form lower-level mapping, is introduced. In the proposed zeroth-order scheme, the gradient of the implicit function can be approximated through inexact lower-level value estimations that are practically available. Under suitable assumptions, the algorithmic framework designed for the bilevel AC method is characterized by convergence guarantees under a fixed stepsize and smoothing parameter. Moreover, the proposed algorithm is equipped with the overall iteration complexity of O ( n 2 L 0 2 L ~ 0 2 ϵ − 1 ) . The convergence performance of the proposed algorithm is verified through numerical simulations.

Uncertainty modelling is key to obtain a realistically feasible solution for large-scale optimization problems. In this study, we consider two-stage stochastic programming to model discrete-time batch process operations with a type II endogenous (decision dependent) uncertainty, where time of uncertainty realizations are dependent on the model decisions. We propose an integer programming model to solve the problem, whose key feature is that it does not require auxiliary binary variables or explicit non-anticipativity constraints to ensure non-anticipativity. To the best of our knowledge this is the first model dealing with such type II uncertainties that has these characteristics, which makes it a much more computationally attractive model. We present a proof that non-anticipativity is enforced implicitly as well as computational results using a large-scale scientific services industrial plant. The computational results from the case study depicts significant benefits in using the proposed stochastic programming approach.

We propose and investigate a queueing model of a battery swapping and charging station (BSCS) for electric vehicles (EVs). A new approach to the analysis of the queueing model is developed, which combines the representation of the model as a stochastic dynamic system with the use of the methods and results of tropical algebra, which deals with the theory and applications of algebraic systems with idempotent operations. We describe the dynamics of the queueing model by a system of recurrence equations that involve random variables (RVs) to represent the interarrival time of incoming EVs. A performance measure for the model is defined as the mean operation cycle time of the station. Furthermore, the system of equations is represented in terms of the tropical algebra in vector form as an implicit linear state dynamic equation. The performance measure takes on the meaning of the mean growth rate of the state vector (the Lyapunov exponent) of the dynamic system. By applying a solution technique of vector equations in tropical algebra, the implicit equation is transformed into an explicit one with a state transition matrix with random entries. The evaluation of the Lyapunov exponent reduces to finding the limit of the expected value of norms of tropical matrix products. This limit is then obtained using results from the tropical spectral theory of deterministic and random matrices. With this approach, we derive a new exact formula for the mean cycle time of the BSCS, which is given in terms of the expected value of the RVs involved. We present the results of the Monte Carlo simulation of the BSCS’s operation, which show a good agreement with the exact solution. The application of the obtained solution to evaluate the performance of one BSCS and to find the optimal distribution of battery packs between stations in a network of BSCSs is discussed. The solution may be of interest in the case when the details of the underlying probability distributions are difficult to determine and, thus, serves to complement and supplement other modeling techniques with the need to fix a distribution.

In the long-term operation of hydropower reservoirs, operating rules have been used widely to decide reservoir operation because they can help operators make an approximately optimal decision with limited runoff information. However, the problems faced by reservoir managers is how to make and select an efficient operating rule properly. This study focuses on identifying efficient and reliable operating rules for the long-term operation of hydropower reservoirs using system dynamics (SD) approach. A stochastic hydrological model of reservoir inflow time series was established and used to generate a large number of inflow scenarios. A deterministic optimization operation model of hydropower reservoirs was constructed and then resolved using dynamic programming (DP) algorithm. Simultaneously, within implicit stochastic optimization (ISO) framework, different operating rules were derived using linear fitting methods. Finally, the most efficient one of the existing operating rules was identified based on SD simulation coupled with the operating rules. The Three Gorges Reservoir (TGR) in central China was used as a case study. The results show that the SD simulation is an efficient way to simulate a complicated reservoir system using feedback and causal loops. Moreover, it can directly and efficiently guide reservoir managers to make and identify efficient operating rules for the long-term operation of hydropower reservoirs.

In this paper, we consider the stochastic mathematical programs with linear complementarity constraints, which include two kinds of models called here-and-now and lower-level wait-and-see problems. We present a combined smoothing implicit programming and penalty method for the problems with a finite sample space. Then, we suggest a quasi-Monte Carlo approximation method for solving a problem with continuous random variables. A comprehensive convergence theory is included as well. We further report numerical results with the so-called picnic vender decision problem.

The purpose of this paper is to consider a class of mathematical programs with fuzzy implicit variational inequality constraints in finite dimension real spaces. By using the “tolerance approach” and the fuzzy set theory, we also show that solving the fuzzy mathematical program problem with fuzzy implicit variational inequality constraints is equivalent to solving a fuzzy implicit complementarity constrained optimization problem, and the fuzzy implicit complementarity constrained optimization problem can be converted to a regular nonlinear parametric programming problem. Further, a new smoothing approach based on a version of the “method of centres” with entropic regularization for solving the resulting optimization problem and our main results are presented and a numerical example is provided to illustrate our main results applying quasi-Newton line search of MATLAB software.

In this paper we discuss the sample average approximation (SAA) method for a class of stochastic programs with nonsmooth equality constraints. We derive a uniform Strong Law of Large Numbers for random compact set-valued mappings and use it to investigate the convergence of Karush-Kuhn-Tucker points of SAA programs as the sample size increases. We also study the exponential convergence of global minimizers of the SAA problems to their counterparts of the true problem. The convergence analysis is extended to a smoothed SAA program. Finally, we apply the established results to a class of stochastic mathematical programs with complementarity constraints and report some preliminary numerical test results.

We consider a stochastic version of the classical shortest path problem whereby for each node of a graph, we must choose a probability distribution over the set of successor nodes so as to reach a certain destination node with minimum expected cost. The costs of transition between successive nodes can be positive as well as negative. We prove natural generalizations of the standard results for the deterministic shortest path problem, and we extend the corresponding theory for undiscounted finite state Markovian decision problems by removing the usual restriction that costs are either all nonnegative or all nonpositive.

This paper considers the stochastic, single-item, periodic review inventory problem. Most importantly we assume a finite production capacity per period and a production cost function containing a fixed (as well as a variable) component. With stationary data, a convex expected holding and shortage cost function, we show that generally the modified ( s , S ) policy is not optimal to the finite horizon problems. The optimal policy does, however, show a systematic pattern which we call the X-Y band structure. This X-Y band policy is interpreted as follows: whenever the inventory level drops below X , order up to capacity; when the inventory level is above Y , do nothing; if the inventory level is between X and Y , however, the ordering pattern is different from problem to problem. Although the X and Y bounds may change from period to period, we prove the existence of a pair of finite X and Y values that can apply for all the periods (i.e., bounds on individual bounds). One calculation for such X and Y bounds that are tight in some cases is also provided. By exploring the X-Y band structure, we can drastically reduce the computation effort for finding the optimal policies.