Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. computationally costly, global black-box nonconvex optimization problems....
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Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. computationally costly, global black-box nonconvex optimization problems. In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) are described. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvex problems with linear and nonlinear constraints, and mixed-integernonlinear problems (MINLP). Solvers in the TOMLAB Optimization Environment (http://***/tomlab/) have been compared, specifically the three deterministic derivative-free solvers rbfSolve, ARBFMIP and EGO with three derivative-based mixed-integernonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENO solver implementing a stochastic genetic algorithm. Results show that the deterministic derivative-free methods compare well with the derivative-based ones, but the stochastic genetic algorithm solver is several orders of magnitude too slow for practical use. When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior.
We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integernonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Sin...
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We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integernonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Since we do not require an algebraic representation of the problem, reformulation techniques for the construction of the convex relaxation cannot be applied, and we are restricted to sampling techniques in case of nonquadratic nonconvex functions. The linear relaxation is further improved by mixed-integer-rounding cuts. Also box reduction techniques are applied to improve efficiency. Numerical results on medium size test problems are presented to show the efficiency of the method.
We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integernonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Sin...
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We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integernonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Since we do not require an algebraic representation of the problem, reformulation techniques for the construction of the convex relaxation cannot be applied, and we are restricted to sampling techniques in case of nonquadratic nonconvex functions. The linear relaxation is further improved by mixed-integer-rounding cuts. Also box reduction techniques are applied to improve efficiency. Numerical results on medium size test problems are presented to show the efficiency of the method.
The design of optimal separation flow sheets for multi-component mixtures is still not a solved problem. This is especially the case when non-ideal or azeotropic mixtures or hybrid separation processes are considered....
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The design of optimal separation flow sheets for multi-component mixtures is still not a solved problem. This is especially the case when non-ideal or azeotropic mixtures or hybrid separation processes are considered. We review recent developments in this field and present a systematic framework for the design of separation flow sheets. This framework proposes a three-step approach. In the first step different flow sheets are generated. In the second step these alternative flow sheet structures are evaluated with shortcut methods. In the third step a rigorous mixed-integer nonlinear programming (MINLP) optimization of the entire flow sheet is executed to determine the best alternative. Since a number of alternative flow sheets have already been eliminated, only a few optimization runs are necessary in this final step. The whole framework thus allows the systematic generation and evaluation of separation processes and is illustrated with the case study of the separation of ethanol and water.
The design of optimal separation flow sheets for multi-component mixtures is still not a solved problem This is especially the case when non-ideal or azeotropic mixtures or hybrid separation processes are considered. ...
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The design of optimal separation flow sheets for multi-component mixtures is still not a solved problem This is especially the case when non-ideal or azeotropic mixtures or hybrid separation processes are considered. We review recent developments in this field and present a systematic framework for the design of separation flow sheets. This framework proposes a three-step approach. In the first step different flow sheets are generated. In the second step these alternative flow sheet structures are evaluated with shortcut methods. In the third step a rigorous mixed-integer nonlinear programming （MINLP） optimization of the entire flow sheet is executed to determine the best alternative. Since a number of alternative flow sheets have already been eliminated, only a few optimization runs are necessary in this final step. The whole framework thus allows the systematic generation and evaluation of separation processes and is illustrated with the case study of the separation of ethanol and water.
We develop a new mixedintegernonlinear model to maximize a manufacturer's expected profit by combining strategic acquisition decisions with inventory management, where the manufacturer produces multiple products...
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We develop a new mixedintegernonlinear model to maximize a manufacturer's expected profit by combining strategic acquisition decisions with inventory management, where the manufacturer produces multiple products but faces uncertain demand for each product. This model also considers that suppliers provide competitive discount schemes. An iterative algorithm is developed to solve the problem. The preliminary computational results for a numerical example are reported.
According to multiproduct/multipurpose batch and continuous processes scheduling, an overview of developments in the chemical processes scheduling is presented. Two scheduling methodologies based on time representatio...
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ISBN:
(纸本)9781424421138
According to multiproduct/multipurpose batch and continuous processes scheduling, an overview of developments in the chemical processes scheduling is presented. Two scheduling methodologies based on time representation are introduced: one is discrete-time approaches the other is various continuous-time approaches, and the strengths and limitations of these approaches are examined. Also, important characteristics of chemical processes challenging to the scheduling problem are discussed, further research area and possible directions in the production scheduling problem are pointed out.
We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO probl...
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We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a mixed-integer nonlinear programming (MINLP) program. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimization approach. We also develop three MINLP formulations based on a nonconvex formulation, the conventional Big.-M formulation and generalized disjunctive programming (GDP). In addition, we compare the outer approximation and NLP branch and bound algorithms on these formulations. This problem is applied to a system of two series connected continuous stirred tank reactors where a first-order reaction takes place. Our results demonstrate that the simultaneous MIDO approach is able to efficiently address the solution of the integrated design and control problem in a systematic way. (c) 2006 Elsevier Ltd. All rights reserved.
Quality-of-service (QoS) is essential for multimedia applications, such as video-conferencing and voice over IP (VoIP) services, in wireless mesh networks (WMNs). A consequence of many clients accessing the Internet v...
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Quality-of-service (QoS) is essential for multimedia applications, such as video-conferencing and voice over IP (VoIP) services, in wireless mesh networks (WMNs). A consequence of many clients accessing the Internet via the same backhaul is that throughput depends on the number of hops from the backhaul. This spatial bias problem is formulated as a mixed-integer nonlinear programming problem that considers end-to-end delay in terms of gateway selection, least-hop and load-balanced routing, and link capacity constraints. In this paper, we propose a routing algorithm for the network layer and a bandwidth allocation scheme for the medium access control (MAC) layer. The latter achieves fairness in both throughput and end-to-end delay in orthogonal mesh backbone networks with a distributed scheme, thereby minimizing the objective function. Our experiment results show that the proposed algorithm achieves throughput fairness, reduces end-to-end delay, and outperforms other general schemes and algorithms by at least 10.19%.
The paper describes a new computerized collection of test models for mixed-integer nonlinear programming. Because there is no standard format for nonlinear models, the model collection is augmented with a translation ...
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The paper describes a new computerized collection of test models for mixed-integer nonlinear programming. Because there is no standard format for nonlinear models, the model collection is augmented with a translation server that can transform the models from their basic GAMS format into other formats, including AMPL, BARON, LGO, LINGO, and MINOPT. The translation server can also be used to transform industrial models that contain confidential information. Such transformations allow many of these models to be distributed to the research community as highly relevant algorithmic test models.
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