The performance of an engine is one of the major concerns in the automotive industry. Increased emission restrictions on motor vehicles have led to the necessity of more accurate control on the engine performance. The...
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The performance of an engine is one of the major concerns in the automotive industry. Increased emission restrictions on motor vehicles have led to the necessity of more accurate control on the engine performance. The objective of this study is to optimize the injection and ignition system in an automobile internal-combustion engine. In this paper the engine torque, the fuel consumption and the hydrocarbon emissions are considered as the main performance metrics of the engine, and a mathematical model is proposed on the basis of response surface methodology and two-stage stochastic programming. The proposed model encompasses desirability functions with a maximum-minimum operator to convert several responses into a single response and also considers the probabilistic pattern of regression coefficients by some random scenarios. To illustrate application of the proposed approach, it was applied in a real case in an automotive company. The results of this test represent a reasonable performance of the proposed approach.
The location of multiple cross-docking centers (CDCs) and vehicle routing scheduling are two crucial choices to be made in strategic/tactical and operational decision levels for logistics companies. The choices lead t...
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The location of multiple cross-docking centers (CDCs) and vehicle routing scheduling are two crucial choices to be made in strategic/tactical and operational decision levels for logistics companies. The choices lead to more realistic problem under uncertainty by covering the decision levels in cross-docking distribution networks. This paper introduces two novel deterministic mixed-integer linear programming (MILP) models that are integrated for the location of CDCs and the scheduling of vehicle routing problem with multiple CDCs. Moreover, this paper proposes a hybrid fuzzy possibilistic-stochastic programming solution approach in attempting to incorporate two kinds of uncertainties into mathematical programming models. The proposed solving approach can explicitly tackle uncertainties and complexities by transforming the mathematical model with uncertain information into a deterministic model. m' imprecise constraints are converted into 2Rm' precise inclusive constraints that agree with R alpha-cut levels, along with the concept of feasibility degree in the objective functions based on expected interval and expected value of fuzzy numbers. Finally, several test problems are generated to appraise the applicability and suitability of the proposed new two-phase MILP model that is solved by the developed hybrid solution approach involving a variety of uncertainties and complexities. (C) 2013 Elsevier Inc. All rights reserved.
This paper provides necessary and sufficient optimality conditions for abstract-constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geom...
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This paper provides necessary and sufficient optimality conditions for abstract-constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of certain mappings, in particular their structure as difference of convex functions, and uses techniques of generalized differentiation (subdifferential and coderivative). It turns out that these tools can be used fruitfully out of the scope of Asplund spaces. Applications to infinite, stochastic and semi-definite programming are developed in separate sections.
We introduce a variant of Multicut Decomposition Algorithms, called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates a class of cut sel...
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We introduce a variant of Multicut Decomposition Algorithms, called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates a class of cut selection strategies to choose the most relevant cuts of the approximate recourse functions. This class contains Level 1 (Philpott et al. in J Comput Appl Math 290:196-208, 2015) and Limited Memory Level 1 (Guigues in Eur J Oper Res 258:47-57, 2017) cut selection strategies, initially introduced for respectively stochastic Dual Dynamic programming and Dual Dynamic programming. We prove the almost sure convergence of the method in a finite number of iterations and obtain as a by-product the almost sure convergence in a finite number of iterations of stochastic Dual Dynamic programming combined with our class of cut selection strategies. We compare the performance of Multicut Decomposition Algorithms, stochastic Dual Dynamic programming, and their variants with cut selection (using Level 1 and Limited Memory Level 1) on several instances of a portfolio problem. On these experiments, in general, stochastic Dual Dynamic programming is quicker (i.e., satisfies the stopping criterion quicker) than Multicut Decomposition Algorithms and cut selection allows us to decrease the computational bulk with Limited Memory Level 1 being more efficient (sometimes much more) than Level 1.
This paper extends the single-item single-stocking location nonstationary stochastic inventory problem to relax the assumption of independent demand. We present a mathematical programming-based solu-tion method built ...
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This paper extends the single-item single-stocking location nonstationary stochastic inventory problem to relax the assumption of independent demand. We present a mathematical programming-based solu-tion method built upon an existing piecewise linear approximation strategy under the receding horizon control framework. Our method can be implemented by leveraging off-the-shelf mixed-integer linear pro-gramming solvers. It can tackle demand under various assumptions: the multivariate normal distribution, a collection of time-series processes, and the Martingale Model of Forecast Evolution. We compare against exact solutions obtained via stochastic dynamic programming to demonstrate that our method leads to near-optimal plans.(c) 2022 Elsevier B.V. All rights reserved.
This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem....
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This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem. Extensive computational experiments were carried out to evaluate the performance of the proposed approach, both in terms of computational efficiency and efficacy. The analysis of the results shows that the clustering approach exhibits good performance also when compared with other reduction approaches.
We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C2 objectives. Upper-C2 functions can be viewed as ...
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This paper proposes a stochastic hydro unit commitment (SHUC) model for a price-taker hydropower producer in a liberalized market. The objective is to maximize the total revenue of the hydropower producer, including t...
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This paper proposes a stochastic hydro unit commitment (SHUC) model for a price-taker hydropower producer in a liberalized market. The objective is to maximize the total revenue of the hydropower producer, including the immediate revenue, future revenue (i.e., opportunity cost), and startup and shutdown cost. The market price uncertainty is taken into account through the scenario tree. The solution of the model is a challenging task due to its non-convex and high-dimensional characteristics. A solution method based on the Benders Decomposition (BD) and Modified stochastic Dual Dynamic programming (MSDDP) is proposed to solve the problem efficiently. Firstly, the BD is applied to decompose the original problem into a Benders master problem representing the hydro unit commitment and a Benders subproblem representing the optimal operation of the hydropower plants. The Benders subproblem, which contains a large number of integer variables, is further decomposed by the period and solved by the MSDDP proposed in this paper. Finally, we verify the effectiveness of the SHUC model and the performance of the proposed solution method in case studies.
Storage systems and demand-response programs will play a vital role in future energy systems. Batteries, hydrogen or pumped hydro storage systems can be combined to form hybrid storage facilities to not only manage th...
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Storage systems and demand-response programs will play a vital role in future energy systems. Batteries, hydrogen or pumped hydro storage systems can be combined to form hybrid storage facilities to not only manage the intermittent behavior of renewable sources, but also to store surplus renewable energy in a practice known as 'green' storage. On the other hand, demand-response programs are devoted to encouraging a more active participation of consumers by pursuing a more efficient operation of the system. In this context, proper scheduling tools able to coordinate different storage systems and demand-response programs are essential. This paper presents a stochastic mixed-integer-lineal-logical framework for optimal scheduling of isolated microgrids. In contrast to other works, the present model includes a logical-based formulation to explicitly coordinate batteries and pumped hydro storage units. A case study on a benchmark isolated microgrid serves to validate the developed optimization model and analyze the effect of applying demand-response premises in microgrid operation. The results demonstrate the usefulness of the developed method, and it is found that operation cost and fuel consumption can be reduced by similar to 38% and similar to 82% by applying demand-response initiatives.
This thesis addresses two challenging problems. The first part is focused on developing algorithms and software for two-stage stochastic mixed-integer nonlinear programming problems (SMINLPs). The second part is on th...
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This thesis addresses two challenging problems. The first part is focused on developing algorithms and software for two-stage stochastic mixed-integer nonlinear programming problems (SMINLPs). The second part is on the long term planning of power systems. stochastic programming, also known as stochastic optimization, is a mathematical framework to model decision-making under uncertainty that has been widely applied in process systems engineering (PSE). Two-stage stochastic mixed-integer programming (SMIPs) is a special case of stochastic programming that considers first and second stage decisions made sequentially with both discrete and continuous variables. Although there have been algorithmic advances in linear SMIPs, the decomposition algorithms to address the nonlinear counterpart, stochastic mixed-integer nonlinear programs (SMINLPs), are few. In Part I of this thesis, we propose four decomposition algorithms for different classes of SMINLPs. For SMINLPs with convex nonlinear constraints, mixed-binary first and second variables, and discrete probability distributions, we propose an improved L-shaped algorithm that combines strengthened Benders cuts and Lagrangean cuts. This algorithm has no guarantee of global optimality. To close the optimality gap, we propose a generalized Benders decomposition-based branch-and-bound algorithm where the stage two problems are convexified sequentially by performing basic steps. For SMINLPs with nonconvex constraints, mixed-binary first and second variables, and discrete probability distributions, we propose a generalized Benders decomposition-based branch-and-cut algorithm where we combine the Benders cuts derived from convexification of the stage two problems and the Lagrangean cuts. A spatial branch-and-cut algorithm is performed to guarantee convergence to global optimality. Last but not least, a sample-average approximation-based outer approximation algorithm is proposed for nonconvex SMINLPs with continuous probability di
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