Incorporating uncertainty in optimization models gives rise to large, structured mathematical programs. Decomposition procedures are well-suited for parallelization, thus providing a promising venue for solving large ...
详细信息
Incorporating uncertainty in optimization models gives rise to large, structured mathematical programs. Decomposition procedures are well-suited for parallelization, thus providing a promising venue for solving large stochastic programs arising in diverse practical applications. This paper presents an adaptation of decomposition methods for execution on distributed computing systems. A regularized decomposition, as well as the linear decomposition algorithm, are implemented for execution on distributed multiprocessors. Computational results on an IBM SP2 multiprocessor system are reported to demonstrate the comparative performance of the methods on a number of test cases. (C) 1998 Elsevier Science B.V.
We present a constant-potential infeasible-start interior-point (INFCP) algorithm for linear programming (LP) problems with a worst-case iteration complexity analysis as well as some computational results. The perform...
详细信息
We present a constant-potential infeasible-start interior-point (INFCP) algorithm for linear programming (LP) problems with a worst-case iteration complexity analysis as well as some computational results. The performance of the INFCP algorithm is compared to those of practical interior-point algorithms. New features of the algorithm include a heuristic method for computing a "good" starting point and a procedure for solving the augmented system arising from stochastic programming with simple recourse. We also present an application to large scale planning problems under uncertainty.
This paper describes two variants of the Indian MARKAL model: a long-term technology oriented optimisation model for energy-environment planning for India. The first variant uses stochastic programming to include futu...
详细信息
This paper describes two variants of the Indian MARKAL model: a long-term technology oriented optimisation model for energy-environment planning for India. The first variant uses stochastic programming to include future uncertainties in the analysis. Details of model formulation, results and sensitivity analysis are described here. The second variant uses an innovative approach to simulate price sensitive demands within a linear formulation. The analysis incorporating future uncertainties suggests that it is prudent to reduce carbon emission in anticipation of a global regime in future. Modelling with price elastic demands estimates up to 10% reduction in carbon emission due to reduced demands, under a severe carbon tax. (C) 1998 Elsevier Science Ltd. All rights reserved.
We present a technique for approximating sequences of linear programs with varying right-hand sides and study the geometric properties of this approximation. Our approximation has an efficiency advantage over optimal ...
详细信息
We present a technique for approximating sequences of linear programs with varying right-hand sides and study the geometric properties of this approximation. Our approximation has an efficiency advantage over optimal solutions. When applied to deterministic control problems, the suggested technique outperforms the linear feedback model and provides accurate results (error of 5.8% in our numerical example). Numerical experience with stochastic models indicates that this approach may outperform the limited lookahead policies while maintaining low computational requirements.
This paper presents a mixed integer programming model for optimal development of an oil field under uncertain future oil prices. Based on a two-dimensional reservoir description, the model suggests decisions concernin...
详细信息
This paper presents a mixed integer programming model for optimal development of an oil field under uncertain future oil prices. Based on a two-dimensional reservoir description, the model suggests decisions concerning both design and operation, and the objective is to maximise the expected net present value of the oil field. A finite set of oil price scenarios with associated probabilities is given, and the scenario and policy aggregation technique developed by Rockafellar and Wets is used for solving the problem. This technique is developed for the case of continuous variables, and in this paper, we discuss different methods for adapting the scenario aggregation approach to the case of mixed integer problems. This is done by utilizing the interaction between the continuous (production) and integer (design) variables. We present numerical experiments and conclude that scenario aggregation may be a suitable technique also for mixed integer problems.
Future patterns of climate change and economic growth are critical parameters in long-term energy planning. This paper describes a multi-stage stochastic programming approach to formulate a flexible energy plan. The p...
详细信息
Future patterns of climate change and economic growth are critical parameters in long-term energy planning. This paper describes a multi-stage stochastic programming approach to formulate a flexible energy plan. The plan incorporates multiple future scenarios and provides for mid-course corrections depending upon the actual realizations of future uncertainties. Results are derived from the stochastic version of Extended MARKAL (MARKet ALlocation) model for Quebec, developed for this purpose. The analysis indicates significant savings of overall system cost in using a hedging strategy over any of the perfect foresight ones. With a 50% probability of implementing stringent carbon mitigation measures after 15 years, the emission trajectory takes the middle path till this uncertainty is resolved. Prior to resolution, electricity supply follows the middle path, natural gas and renewable energy tend to follow the low mitigation trajectory, and oil supply approaches the high mitigation trajectory. A set of specialized hedging technologies has been identified, which emerges more competitive in the hedging strategy than in any of the perfect foresight ones. The paper concludes that such treatment of future uncertainties can give insights that are beyond the scope of an analysis based on deterministic scenarios. (C) 1998 Elsevier Science B.V. All rights reserved.
In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function f: R-n--> R boolean OR {infinity}. Instead of the original objective function f, we employ a...
详细信息
In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function f: R-n--> R boolean OR {infinity}. Instead of the original objective function f, we employ a convex approximation f(k+1) at the kth iteration. Some global convergence rate estimates are obtained. We illustrate our approach by proposing (i) a new family of proximal point algorithms which possesses the global convergence rate estimate f(x(k)) - min(x is an element of Rn) f(x) = O(1/(Sigma(j=0)(k-1)root lambda(j))(2)) even if the iteration points are calculated approximately, where {lambda(k)}(k=0)(infinity) are the proximal parameters, and (ii) a variant proximal bundle method. Applications to stochastic programs are discussed.
This paper outlines the general framework of uncertain programming. The main purpose is to provide a unifying principle of stochastic programming and fuzzy programming and lay a foundation for optimization theory in g...
详细信息
This paper outlines the general framework of uncertain programming. The main purpose is to provide a unifying principle of stochastic programming and fuzzy programming and lay a foundation for optimization theory in generally-uncertain (random, fuzzy, fuzzy random, grey, etc.) environments. Three broad classes of uncertain programming are expected value models and chance constrained programming as well as dependent-chance programming. In order to solve general uncertain programming models, a simulation based genetic algorithm is also documented. Finally, some applications and further research problems appearing in this area are posed.
In many decision problems, some of the factors considered are subject to significant uncertainty, randomness, or statistical fluctuations: these circumstances motivate the study of stochastic models. The paper is inte...
详细信息
In many decision problems, some of the factors considered are subject to significant uncertainty, randomness, or statistical fluctuations: these circumstances motivate the study of stochastic models. The paper is intended to provide an overview of modelling tools available for the development, analysis, solution and maintenance of stochastic programs. A brief introduction to some important model forms is followed by a review of suitable modelling and computational environments, including algebraic modelling languages. Aspects of problem description, solution methodology, report generation, and visual problem representation, as well as certain auxiliary tools and diagnostics are discussed. An extensive list of references is provided, to give further pointers into a challenging field of great practical importance.
In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Grobner basis methods from computational algebra to solve th...
详细信息
In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Grobner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed. (C) 1998 The Mathematical programming Society, Inc. Published by Elsevier Science B.V.
暂无评论