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Showing papers on "Stochastic programming published in 2001"


Journal ArticleDOI
TL;DR: In this paper, a mathematical programming algorithm is proposed to obtain an optimum value insensitive to variations on design variables within a feasible region, where a multiobjective function is defined to have the mean and standard deviation of the original objective function, while the constraints are supplemented by adding a penalty term to the original constraints.

271 citations


Journal ArticleDOI
TL;DR: The results show that the performance of the multi-stage stochastic program could be improved drastically by choosing an appropriate scenario generation method.

266 citations


BookDOI
01 Jan 2001
TL;DR: In this article, real-time control of a container crane under state-dependent constraints using nonlinear nonlinear programming (NLP) and sensitivity analysis is used to find the optimal control solution for the nonlinear heat equation.
Abstract: I Optimal Control for Ordinary Differential Equations.- Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods.- Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints.- Real-Time Control of an Industrial Robot under Control and State Constraints.- Real-Time Optimal Control of Shape Memory Alloy Actuators in Smart Structures.- Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy.- Real-Time Optimization of DAE Systems.- Real-Time Solutions of Bang-Bang and Singular Optimal Control Problems.- Conflict Avoidance During Landing Approach Using Parallel Feedback Control.- II Optimal Control for Partial Differential Equations.- Optimal Control Problems with a First Order PDE System - Necessary and Sufficient Optimality Conditions.- Optimal Control Problems for the Nonlinear Heat Equation.- Fast Optimization Methods in the Selective Cooling of Steel.- Real-Time Optimization and Stabilization of Distributed Parameter Systems with Piezoelectric Elements.- Instantaneous Control of Vibrating String Networks.- Modelling, Stabilization, and Control of Flow in Networks of Open Channels.- Optimal Control of Distributed Systems with Break Points.- to Model Based Optimization of Chemical Processes on Moving Horizons.- Multiscale Concepts for Moving Horizon Optimization.- Real-Time Optimization for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column.- Towards Nonlinear Model-Based Predictive Optimal Control of Large-Scale Process Models with Application to Air Separation Plants.- IV Delay Differential Equations in Medical Decision Support Systems.- Differential Equations with State-Dependent Delays.- Biomathematical Models with State-Dependent Delays for Granulocytopoiesis.- Stochastic Optimization for Operating Chemical Processes under Uncertainty.- A Multistage Stochastic Programming Approach in Real-Time Process Control.- Optimal Control of a Continuous Distillation Process under Probabilistic Constraints.- Adaptive Optimal Stochastic Trajectory Planning.- Stochastic Optimization Methods in Robust Adaptive Control of Robots.- Multistage Stochastic Integer Programs: An Introduction.- Decomposition Methods for Two-Stage Stochastic Integer Programs.- Modeling of Uncertainty for the Real-Time Management of Power Systems.- Online Scheduling of Multiproduct Batch Plants under Uncertainty.- VIII Combinatorial Online Planning in Transportation.- Combinatorial Online Optimization in Real Time.- Online Optimization of Complex Transportation Systems.- Stowage and Transport Optimization in Ship Planning.- IX Real-Time Annealing in Image Segmentation.- Basic Principles of Annealing for Large Scale Non-Linear Optimization.- Multiscale Annealing and Robustness: Fast Heuristics for Large Scale Non-linear Optimization.- Author Index.

221 citations


Journal ArticleDOI
TL;DR: The Concave, Adaptive Value Estimation (CAVE) as discussed by the authors algorithm constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain.
Abstract: We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the process of deciding the inventory, and then realizing the demand, occurs repeatedly. The only information we use is the amount of inventory left over. Rather than attempting to estimate the demand distribution, we directly estimate the value function using a technique called the Concave, Adaptive Value Estimation CAVE algorithm. CAVE constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain. Since it is a sampling-based method, CAVE does not require knowledge of the underlying sample distribution. The result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi-gradient methods and more flexible than analytical techniques that require distribution information. In addition, we demonstrate near-optimal behavior of the CAVE approximation in experiments involving two different types of stochastic programs-the newsvendor stochastic inventory problem and two-stage distribution problems.

217 citations


Journal ArticleDOI
TL;DR: In this article, an integrated fuzzy-stochastic linear programming model is developed and applied to municipal solid waste management, with the objective of minimizing system costs over the planning horizon.
Abstract: In this study, an integrated fuzzy-stochastic linear programming model is developed and applied to municipal solid waste management. Methods of chance-constrained programming and fuzzy linear programming are incorporated within a general interval-parameter mixed-integer linear programming framework. It improves upon the existing optimization methods with advantages in uncertainty reflection, data availability, and computational requirement. The model can be used for answering questions related to types, times and sites of solid waste management practices, with the objective of minimizing system costs over the planning horizon. The model can effectively reflect dynamic, interactive, and uncertain characteristics of municipal waste management systems. In its solution process, the model is transformed into two deterministic submodels, corresponding to upper and lower bounds of the desired objective function values under a given significance level, based on an interactive algorithm. Results of the method's application to a hypothetical case indicate that reasonable outputs have been obtained. It demonstrates the practical applicability of the proposed methodology.

202 citations


Journal ArticleDOI
TL;DR: The proposed evolutionary optimization algorithm is suggested to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem and is suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region.
Abstract: Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. This procedure has a number of known difficulties. First, the obtained solution to the goal programming problem is sensitive to the chosen weight vector. Second, the conversion to a single-objective optimization problem involves additional constraints. Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods. In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals and then suggest an evolutionary optimization algorithm to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem. The proposed approach alleviates all the above difficulties. It does not need any weight vector. It eliminates the need of having extra constraints needed with the classical formulations. The proposed approach is also suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region. The efficacy of the proposed approach is demonstrated by solving a number of nonlinear goal programming test problems and an engineering design problem. In all problems, multiple solutions (each corresponding to a different weight vector) to the goal programming problem are found in one single simulation run. The results suggest that the proposed approach is an effective and practical tool for solving real-world goal programming problems.

155 citations


Journal ArticleDOI
TL;DR: This work considers the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory, and proposes a heuristic, establishes conditions under which the heuristic finds an optimal solution, and reports results of the application at a catalog retailer.
Abstract: We consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution, and report results of the application of our procedure at a catalog retailer. Our procedure improves on the existing method by enough to double profits. In addition, our method can be used to choose the optimal reorder time, to quantify the benefit of leadtime reduction, and to choose the best replenishment contract.

150 citations


Journal ArticleDOI
TL;DR: By applying stochastic dynamic programming to the minimization of a mean-squared error loss function under Markov-state dynamics, recursive expressions for the optimal-replication strategy are derived that are readily implemented in practice.
Abstract: Given a European derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based, we solve the optimal-replication problem: Find a self-financing dynamic portfolio strategy--involving only the underlying securities--that most closely approximates the payoff function at maturity. By applying stochastic dynamic programming to the minimization of a mean-squared error loss function under Markov-state dynamics, we derive recursive expressions for the optimal-replication strategy that are readily implemented in practice. The approximation error or "e" of the optimal-replication strategy is also given recursively and may be used to quantify the "degree" of market incompleteness. To investigate the practical significance of these e-arbitrage strategies, we consider several numerical examples, including path-dependent options and options on assets with stochastic volatility and jumps.

149 citations


Journal ArticleDOI
TL;DR: The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.
Abstract: This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks. These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach, although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

149 citations


Journal ArticleDOI
TL;DR: The paper describes the implementation of a new integrated tool for risk management in hydropower systems where operation scheduling and hedging by future contacts are integrated in one model and the resulting large stochastic dynamic optimization problem is solved.
Abstract: The paper describes the implementation of a new integrated tool for risk management in hydropower systems. Earlier practice in Scandinavia has been to separate operations scheduling and contract management. In the present approach operation scheduling and hedging by future contacts are integrated in one model. The risk level is controlled by setting revenue targets. Revenues below target are penalized; this implicitly defines a revenue utility function to reduce risk. The possibility of dynamically changing the future contract portfolio is now represented. The resulting large stochastic dynamic optimization problem is solved using a combination of stochastic dynamic programming and stochastic dual dynamic programming. Simulations for a test case show that the profit in the lower range is considerably improved with the new tool. The approach can be useful for hydropower companies that face price risks in addition to the inflow uncertainty, as is the case in a deregulated system.

144 citations


Journal ArticleDOI
TL;DR: In this article, a stochastic averaging-based nonlinear feedback control strategy was proposed for a randomly excited structural system and the control forces were divided into conservative and dissipative parts.
Abstract: A strategy for optimal nonlinear feedback control of randomlyexcited structural systems is proposed based on the stochastic averagingmethod for quasi-Hamiltonian systems and the stochastic dynamicprogramming principle. A randomly excited structural system isformulated as a quasi-Hamiltonian system and the control forces aredivided into conservative and dissipative parts. The conservative partsare designed to change the integrability and resonance of the associatedHamiltonian system and the energy distribution among the controlledsystem. After the conservative parts are determined, the system responseis reduced to a controlled diffusion process by using the stochasticaveraging method. The dissipative parts of control forces are thenobtained from solving the stochastic dynamic programming equation. Boththe responses of uncontrolled and controlled structural systems can bepredicted analytically. Numerical results for a controlled andstochastically excited Duffing oscillator and a two-degree-of-freedomsystem with linear springs and linear and nonlinear dampings, show thatthe proposed control strategy is very effective and efficient.

BookDOI
01 Jan 2001
TL;DR: A Finite-Dimensional Approach to Infinite-Ddimensional Constraints in Stochastic Programming Duality and Hierarchical Sparsity in Multistage Convex Stochastics Programs M. Steinbach.
Abstract: Preface. Output analysis for approximated stochastic programs J. Dupacova. Combinatorial Randomized Rounding: Boosting Randomized Rounding with Combinatorial Arguments P. Efraimidis, P.G. Spirakis. Statutory Regulation of Casualty Insurance Companies: An Example from Norway with Stochastic Programming Analysis A. Gaivoronski, et al. Option pricing in a world with arbitrage X. Guo, L. Shepp. Monte Carlo Methods for Discrete Stochastic Optimization T. Homem-de-Mello. Discrete Approximation in Quantile Problem of Portfolio Selection A. Kibzun, R. Lepp. Optimizing electricity distribution using two-stage integer recourse models W.K. Klein Haneveld, M.H. van der Vlerk. A Finite-Dimensional Approach to Infinite-Dimensional Constraints in Stochastic Programming Duality L. Korf. Non-Linear Risk of Linear Instruments A. Kreinin. Multialgorithms for Parallel Computing: A New Paradigm for Optimization J. Nazareth. Convergence Rate of Incremental Subgradient Algorithms A. Nedic, D. Bertsekas. Transient Stochastic Models for Search Patterns E. Pasiliao. Value-at-Risk Based Portfolio Optimization A. Puelz. Combinatorial Optimization, Cross-Entropy, Ants and Rare Events R.Y. Rubinstein. Consistency of Statistical Estimators: the Epigraphical View G. Salinetti. Hierarchical Sparsity in Multistage Convex Stochastic Programs M. Steinbach. Conditional Value-at-Risk: Optimization Approach S. Uryasev, R.T. Rockafellar.

Book ChapterDOI
01 Jan 2001
TL;DR: The suggested methodology can be used for optimizing of portfolios by investment companies, brokerage firms, mutual funds, and any businesses that evaluate risks, and can be applied to any financial or non-financial problems involving optimization of percentiles.
Abstract: A new approach for optimization or hedging of a portfolio of finance instruments to reduce the risks of high losses is suggested and tested with several applications. As a measure of risk, Conditional Value-at-Risk (CVaR) is used. For several important cases, CVaR coincides with the expected shortfall (expected loss exceeding Values-at-Risk). However, generally, CVaR and the expected shortfall are different risk measures. CVaR is a coh erent risk measure both for continuous and discrete distributions. CVaR is a more consistent measure of risk than VaR. Portfolios with low CVaR also have low VaR because CVaR is greater than VaR. The approach is based on a new representation of the performance function, which allows simultaneous calculation of VaR and minimization of CVaR. It can be used in conjunction with analytical or scenario based optimization algorithms If the number of scenarios is fixed, the problem is reduced to a Linear Programming or Nonsmooth Optimization Problem. These techniques allow optimizing portfolios with large numbers of instruments. The approach is tested with two examples: (1) portfolio optimization and comparison with the Minimum Variance approach; (2) hedging of a portfolio of options. The suggested methodology can be used for optimizing of portfolios by investment companies, brokerage firms, mutual funds, and any businesses that evaluate risks. Although the approach is used for portfolio analysis, it is very general and can be applied to any financial or non-financial problems involving optimization of percentiles.

Journal ArticleDOI
TL;DR: This paper reports on the solution of an asset-liability management model for an actual Dutch pension fund with 4,826,809 scenarios; 12,469,250 constraints; and 24,938,502 variables; which is the largest stochastic linear program ever solved.
Abstract: Financial institutions require sophisticated tools for risk management. For companywide risk management, both sides of the balance sheet should be considered, resulting in an integrated asset-liability management approach. Stochastic programming models suit these needs well and have already been applied in the field of asset-liability management to improve financial operations and risk management. The dynamic aspect of the financial planning problems inevitably leads to multiple decision stages trading dates in the stochastic program and results in an explosion of dimensionality. In this paper we show that dedicated model generation, specialized solution techniques based on decomposition and high-performance computing, are the essential elements to tackle these large-scale financial planning problems. It turns out that memory management is a major bottleneck when solving very large problems, given an efficient solution approach and a parallel computing facility. We report on the solution of an asset-liability management model for an actual Dutch pension fund with 4,826,809 scenarios; 12,469,250 constraints; and 24,938,502 variables; which is the largest stochastic linear program ever solved. A closer look at the optimal decisions reveals that the initial asset mix is more stable for larger models, demonstrating the potential benefits of the high-performance computing approach for ALM.

Book
01 Jan 2001
TL;DR: In this article, the authors present a survey on the history of semi-infinite programming and its application in probability and statistics, as well as a discussion of some applications of LSIP to Probability and Statistics.
Abstract: Preface. Contributing Authors. Part I: History. 1. On the 1962-1972 Decade of Semi-Infinite Programming: A Subjective View K.O. Kortanek. Part II: Theory. 2. About Disjunctive Optimization I.I. Eremin. 3. On Regularity and Optimality in Nonlinear Semi-Infinite Programming A. Hassouni, W. Oettli. 4. Asymptotic Constraint Qualifications and Error Bounds for Semi-Infinite Systems of Convex Inequalities W. Li, I. Singer. 5. Stability of the Feasible Set Mapping in Convex Semi-Infinite Programming M.A. Lopez, et al. 6. On Convex Lower Level Problems in Generalized Semi-Infinite Optimization J.-J. Ruckmann, O. Stein. 7. On Duality Theory of Conic Linear Problems A. Shapiro. Part III: Numerical Methods. 8. Two Logarithmic Barrier Methods for Convex Semi-Infinite Problems L. Abbe. 9. First-Order Algorithms for Optimization Problems with a Maximum Eigenvalue/Singular Value Cost and or Constraints E. Polak. 10. Analytic Center Based Cutting Plane Method for Linear Semi-Infinite Programming S.-Y. Wu, et al. Part IV: Modeling and Applications. 11. On Some Applications of LSIP to Probability and Statistics M. Dall'Aglio. 12. Separation by Hyperplanes: A Linear Semi-Infinite Programming Approach M.A. Goberna, et al. 13. A Semi-Infinite Optimization Approach to Optimal Spline Trajectory Planning of Mechanical Manipulators C. Guarino Lo Bianco, A. Piazzi. 14. On Stability of Guaranteed Estimation Problems: Error Bounds for Information Domains and Experimental Design M.I. Gusev, S.A.Romanov. 15. Optimization under Uncertainty and Linear Semi-Infinite Programming: A Survey T. Leon, E. Vercher. 16. Semi-Infinite Assignment and Transportation Games J. Sanchez-Soriano, et al. 17. The Owen Set and the Core of Semi-Infinite Linear Production Situations S. Tijs, et al.

Journal ArticleDOI
TL;DR: In this article, the authors investigate market power issues in bid-based hydrothermal scheduling, where market power is simulated with a single-stage Nash-Cournot equilibrium model and market power assessment for multiple stages is carried through a stochastic dynamic programming scheme.
Abstract: The objective of this paper is to investigate market power issues in bid-based hydrothermal scheduling. Initially, market power is simulated with a single-stage Nash-Cournot equilibrium model. Market power assessment for multiple stages is then carried through a stochastic dynamic programming scheme. The decision in each stage and state is the equilibrium of a multi-agent game. Thereafter, mitigation measures, specially bilateral contracts, are investigated. Case studies with data taken from the Brazilian system are presented and discussed.

Journal ArticleDOI
TL;DR: In this article, formal optimal decision approaches for a multi-period asset/liability management model for a pension fund are studied. But the authors focus on the problem of finding the optimal allocation proportions for a large number of instruments and scenarios.
Abstract: This article studies formal optimal decision approaches for a multi‐period asset/liability management model for a pension fund. The authors use Conditional Value‐at‐Risk (CVaR) as a risk measure, the weighted average of the Value‐at‐Risk (VaR) and those losses exceeding VaR. The model is based on sample‐path simulation of the liabilities and returns of financial instruments in the portfolio. The same optimal decisions are made for groups of sample‐paths, which exhibit similar performance characteristics. Since allocation proportions are time‐dependent, these techniques are more flexible than more standard allocation procedures, e.g. “constant proportions.” Optimization is conducted using linear programming. Compared with traditional stochastic programming algorithms (for which the problem dimension increases exponentially in the number of time stages), this approach exhibits a linear growth of the dimension. Therefore, this approach allows the solution of problems with very large numbers of instruments and scenarios.

Journal ArticleDOI
TL;DR: An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs and is shown to converge globally and to run in polynomial-time.
Abstract: An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a finite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time.

Journal ArticleDOI
TL;DR: In this article, the authors consider the mathematical modeling and solution of robust and cost-optimizing structural (topology) design problems and provide results on the existence of optimal solutions which allow for zero lower design bounds.
Abstract: We consider the mathematical modelling and solution of robust and cost-optimizing structural (topology) design problems. The setting is the optimal design of a linear-elastic structure, for example a truss topology, under unilateral frictionless contact, and under uncertainty in the data describing the load conditions, the material properties, and the rigid foundation. The resulting stochastic bilevel optimization model finds a structural design that responds the best to the given probability distribution in the data. This model is of special interest when a structural failure will lead to a reconstruction cost, rather than loss of life. For the mathematical model, we provide results on the existence of optimal solutions which allow for zero lower design bounds. We establish that the optimal solution is continuous in the lower design bounds, a result which validates the use of small but positive values of them, and for such bounds we also establish the locally Lipschitz continuity and directional differentiability of the implicit upper-level objective function. We also provide a heuristic algorithm for the solution of the problem, which makes use of its differentiability properties and parallelization strategies across the scenarios. A small set of numerical experiments illustrates the behaviour of the stochastic solution compared to an average-case deterministic one, establishing an increased robustness.

Journal ArticleDOI
TL;DR: This work casts the progressive hedging algorithm (PHA) of Rockafellar and Wets in a meta-heuristic framework with the sub-problems generated for each scenario solved heuristically, and uses an algorithm for sub-Problems that is exact in its usual context but serves as a heuristic for the meta- heuristic.

Journal ArticleDOI
TL;DR: In this paper, different concepts of efficient solutions to problems of stochastic multiple-objective programming are analyzed and relationships between the different concepts are established, which enables us to determine what type of efficient solution are obtained by each of these concepts.
Abstract: In this work, different concepts of efficient solutions to problems of stochastic multiple-objective programming are analyzed. We center our interest on problems in which some of the objective functions depend on random parameters. The existence of different concepts of efficiency for one single stochastic problem, such as expected-value efficiency, minimum-risk efficiency, etc., raises the question of their quality. Starting from this idea, we establish some relationships between the different concepts. Our study enables us to determine what type of efficient solutions are obtained by each of these concepts.

Journal ArticleDOI
TL;DR: An industrial gases tanker vehicle visitsn customers on a tour, with a possible ( n + 1)st customer added at the end, to adjust dynamically the amount of product provided on scene to each customer so as to minimize total expected costs, comprising costs of earliness, lateness, product shortfall, and returning to the depot nonempty.
Abstract: An industrial gases tanker vehicle visitsn customers on a tour, with a possible ( n + 1)st customer added at the end. The amount of needed product at each customer is a known random process, typically a Wiener process. The objective is to adjust dynamically the amount of product provided on scene to each customer so as to minimize total expected costs, comprising costs of earliness, lateness, product shortfall, and returning to the depot nonempty. Earliness costs are computed by invocation of an annualized incremental cost argument. Amounts of product delivered to each customer are not known until the driver is on scene at the customer location, at which point the customer is either restocked to capacity or left with some residual empty capacity, the policy determined by stochastic dynamic programming. The methodology has applications beyond industrial gases.

Journal ArticleDOI
TL;DR: A modified stochastic ruler method for finding a global optimal solution to a discrete optimization problem in which the objective function cannot be evaluated analytically but has to be estimated or measured, which is guaranteed to converge almost surely to the set of global optimal solutions.

Journal ArticleDOI
TL;DR: The state-of-the-art on application of optimisation techniques in groundwater quality and quantity management is presented.
Abstract: This paper presents the state-of-the-art on application of optimisation techniques in groundwater quality and quantity management. In order to solve optimisation-based groundwater management models, researchers have used various mathematical programming techniques such as linear programming (LP), nonlinear programming (NLP), mixed-integer programming (MIP), optimal control theory-based mathematical programming, differential dynamic programming (DDP), stochastic programming (SP), combinatorial optimisation (CO), and multiple objective programming for multipurpose management. Studies reported in the literature on the application of these methods are reviewed in this paper.

Journal ArticleDOI
TL;DR: An approach to analyzing demand scenarios in technology-driven markets where product demands are volatile, but follow a few identifiable lifecycle patterns, which provides a practical scenario analysis method for manufacturing demand in a technology market.
Abstract: This paper proposes an approach to analyzing demand scenarios in technology-driven markets where product demands are volatile, but follow a few identifiable lifecycle patterns. After examining a large amount of semiconductor data, we found that not only can products be clustered by lifecycle patterns, but in each cluster there exists a leading indicator product that provides advanced indication of changes in demand trends. Motivated by this finding, we propose a scenario analysis structure in the context of stochastic programming. Specifically, the demand model that results from this approach provides a mechanism for building a scenario tree for semiconductor demand. Using the Bass growth model and a Bayesian update structure, the approach streamlines scenario analysis by focusing on parametric changes of the demand growth model over time. The Bayesian structure allows expert judgment to be incorporated into scenario generation while the Bass growth model allows an efficient representation of time varying demands. Further, by adjusting a likelihood threshold, the method generates scenario trees of different sizes and accuracy. This structure provides a practical scenario analysis method for manufacturing demand in a technology market. We demonstrate the applicability of this method using real semiconductor data.

Journal ArticleDOI
TL;DR: The performance of the best T7f plan falls short of the benchmark on several counts, reflecting the need to account for variability in the highly stochastic system of traffic operations, which is not possible under the deterministic conditions intrinsic to T7F.
Abstract: A stochastic signal optimization method based on a genetic algorithm (GA-SOM) that interfaces with the microscopic simulation program CORSIM is assessed. A network in Chicago consisting of nine signalized intersections is used as an evaluation test bed. Taking CORSIM as the best representation of reality, the performance of the GA-SOM plan sets a ceiling on how good any (fixed) signal plan can be. An important aspect of this approach is its accommodations of variability. Also discussed is the robustness of an optimal plan under changes in demand. This benchmark is used to assess the best signal plan generated by TRANSYT-7F (T7F), Version 8.1, from among 12 reasonable strategies. The performance of the best T7F plan falls short of the benchmark on several counts, reflecting the need to account for variability in the highly stochastic system of traffic operations, which is not possible under the deterministic conditions intrinsic to T7F. As a sidelight, the performance of the GA-SOM plan within T7F is also computed and it is found to perform nearly as well as the optimum T7F plan.

Journal ArticleDOI
TL;DR: Comparison of the results with those from a robust deterministic modeling/optimization strategy suggests that the hybrid methodologies can be gainfully employed for process optimization.
Abstract: This article presents two hybrid robust process optimization approaches integrating artificial neural networks (ANN) and stochastic optimization formalisms - genetic algorithms (GAs) and simultaneous perturbation stochastic approximation (SPSA). An ANN-based process model was developed solely from process input-output data and then its input space comprising design and operating variables was optimized by employing either the GA or the SPSA methodology. These methods possess certain advantages over widely used deterministic gradient-based techniques. The efficacy of ANN-GA and ANN-SPSA formalisms in the presence of noise-free as well as noisy process data was demonstrated for a representative system involving a nonisothermal CSTR. The case study considered a nontrivial optimization objective, which, in addition to the conventional parameter design, also addresses the issue of optimal tolerance design. Comparison of the results with those from a robust deterministic modeling/optimization strategy suggests that the hybrid methodologies can be gainfully employed for process optimization.

Proceedings ArticleDOI
09 Dec 2001
TL;DR: It is argued that the SAA method is easily implementable and can be surprisingly efficient for some classes of stochastic programming problems, particularly for optimization of an expected value function.
Abstract: Various stochastic programming problems can be formulated as problems of optimization of an expected value function. Quite often the corresponding expectation function cannot be computed exactly and should be approximated, say by Monte Carlo sampling methods. In fact, in many practical applications, Monte Carlo simulation is the only reasonable way of estimating the expectation function. In this paper we discuss convergence properties of the sample average approximation (SAA) approach to stochastic programming. We argue that the SAA method is easily implementable and can be surprisingly efficient for some classes of stochastic programming problems.

Book ChapterDOI
26 Mar 2001
TL;DR: An introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization is given.
Abstract: Mathematical optimization techniques are on their way to becoming a standard tool in chemical process engineering. While such approaches are usually based on deterministic models, uncertainties such as external disturbances play a significant role in many real-life applications. The present article gives an introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization.

Journal ArticleDOI
TL;DR: The proposed interactive satisficing method can be used to solve linear as well as a class of nonlinear multiobjective problems in mixed fuzzy-stochastic environment wherein various kinds of uncertainties related to fuzziness and/or randomness are present.