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optimization of Multiple-Fan Air-Cooler Control in a Distillation Column

KAGAKU KOGAKU RONBUNSHU 2022年第3期48卷 93-98页

作者： Daiguji, Masaharu Yamashita, Yoshiyuki Tokyo Univ Agr & Technol Grad Sch Engn Dept Chem Engn 2-24-16 Naka Cho Koganei Tokyo 1848588 Japan

Air coolers are often used in refineries and petrochemical plants to cool process fluid or circulating cooling water. In general, an overhead air-cooler of atmospheric distillation columns consists of multiple fans including fixed fans and variable flowrate fans that can change flowrate by controlling the pitch angle or the rotation speed. Even when the air-coolers are affected by disturbances on the process side or cooling side, the influence of the disturbances can usually be suppressed by variable fans which control the column overhead pressure or the outlet temperature. However, when the controller output exceeds the operating range of the variable fans, it is necessary to return the controller output into the operating range by starting or stopping the fixed fan in order to restart control. There are two issues to consider in the operation of an air-cooler with multiple fans. One is that the air-flow rate fluctuates when the fixed fan is started or stopped, and the other is that the power consumption of the fans cannot be minimized. In this paper, first, in order to suppress the start/stop disturbance of the fixed fan, a cascade control method which estimates total air flowrate and defines this as an intermediate variable is proposed. On the process dynamic simulator Aspen HYSYS (R)` Dynamics, it was shown that when starting and stopping the fixed fan, the proposed control system immediately manipulates the variable fans to stabilize the air flowrate and the tower overhead pressure. Next, we propose a method for optimizing the number of fixed fans in operation so as to minimize the power consumption while reducing the frequency of starting and stopping of fixed fans. As a result of applying the proposed method to the simulation data, it was elucidated that the power consumption can be expected to be reduced without changing the frequency of changing the number of fixed fans compared to the conventional method.

关键词： Process Control mixed-integer non-linear optimization Air-Cooler Optimal Operation

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A proximal-point outer approximation algorithm

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COMPUTATIONAL optimization AND APPLICATIONS 2020年第3期77卷 755-777页

作者： De Mauri, Massimo Gillis, Joris Swevers, Jan Pipeleers, Goele Katholieke Univ Leuven Dept Mech Engn MECO Res Team Leuven Belgium Flanders Make DMMS M Leuven Belgium

Many engineering and scientific applications, e.g. resource allocation, control of hybrid systems, scheduling, etc., require the solution of mixed-integer non-linear problems (MINLPs). Problems of such class combine the high computational burden arising from considering discrete variables with the complexity of non-linear functions. As a consequence, the development of algorithms able to efficiently solve medium-large MINLPs is still an interesting field of research. In the last decades, several approaches to tackle MINLPs have been developed. Some of such approaches, usually defined as exact methods, aim at finding a globally optimal solution for a given MINLP at expense of a long execution time, while others, generally defined as heuristics, aim at discovering suboptimal feasible solutions in the shortest time possible. Among the various proposed paradigms, outer approximation (OA) and feasibility pump (FP), respectively as exact method and as heuristic, deserve a special mention for the number of relevant publications and successful implementations related to them. In this paper we present a new exact method for convex mixed-integer non-linear programming called proximal outer approximation (POA). POA blends the fundamental ideas behind FP into the general OA scheme that attepts to yield faster and more robust convergence with respect to OA while retaining the good performances in terms of fast generation of feasible solutions of FP.

关键词： Feasibility pump linear outer approximation mixed-integer non-linear optimization mixed-integer programming

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Volume computation for sparse Boolean quadric relaxations

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DISCRETE APPLIED MATHEMATICS 2020年 275卷 79-94页

作者： Lee, Jon Skipper, Daphne Univ Michigan Dept I&OE Ann Arbor MI 48109 USA US Naval Acad Dept Math Annapolis MD 21402 USA

Motivated by understanding the quality of tractable convex relaxations of intractable polytopes, Ko et al. gave a closed-form expression for the volume of a standard relaxation L(G) of the Boolean quadric polytope (also known as the (full) correlation polytope) P(G) of the complete graph G = K-n. We extend this work to structured sparse graphs. In particular, we (i) demonstrate the existence of an efficient algorithm for vol(L(G)) when G has bounded treewidth, (ii) give closed-form expressions (and asymptotic behaviors) for vol(L(G)) for all stars, paths, and cycles, and (iii) give a closed-form expression for vol(P(G)) for all cycles. Further, we demonstrate that when G is a cycle, the simple relaxation L(G) is a very close model for the much more complicated P(G). Additionally, we give some computational results demonstrating that this behavior of the cycle seems to extend to more complicated graphs. Finally, we speculate on the possibility of extending some of our results to cactii or even series-parallel graphs. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Volume Boolean quadric polytope Correlation polytope mixed-integer non-linear optimization Order polytope Counting linear extensions Bounded treewidth Cut polytope

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System-Level optimization in Poisson Cellular Networks: An Approach Based on the Generalized Benders Decomposition

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IEEE WIRELESS COMMUNICATIONS LETTERS 2020年第10期9卷 1773-1777页

作者： Song, Jian Di Renzo, Marco Zappone, Alessio Sciancalepore, Vincenzo Perez, Xavier Costa Univ Paris Saclay Lab Signaux & Syst Cent Supelec CNRS F-91192 Gif Sur Yvette France Univ Cassino & Southern Lazio DAEIMI Dept I-03043 Cassino Italy NEC Labs Europe D-69115 Heidelberg Germany

During the last decade, stochastic geometry has been widely employed for system-level analysis in cellular networks. The resulting analytical frameworks are, however, not always amenable for system-level optimization. This is due to three main reasons: (i) the performance metric of interest may not be formulated in closed-form;(ii) under some analytically tractable modeling assumptions, important system parameters may not explicitly appear in the analytical frameworks;and (iii) the optimization problem may not possess any structural properties, e.g., convexity, that facilitate the development of numerical algorithms for optimizing multiple (continuous- and discrete-valued) parameters at an affordable computational complexity and with performance-guarantee, e.g., the convergence to the global optimum is provable. In this letter, by leveraging a recently proposed definition of coverage probability, we formulate mixed-integer non-linear system-level resource allocation problems in Poisson cellular networks and prove that their global optimum can be efficiently calculated by applying the generalized Benders decomposition. Numerical results are illustrated in order to compare the proposed approach against brute-force and greedy-like optimization algorithms.

关键词： optimization Cellular networks Silicon Analytical models Bandwidth Stochastic processes Geometry Cellular networks stochastic geometry system-level analysis mixed-integer non-linear optimization

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Solving the index tracking problem based on a convex reformulation for cointegration

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FINANCE RESEARCH LETTERS 2020年 37卷

作者： Sant'Anna, Leonardo Riegel de Oliveira, Alan Delgado Filomena, Tiago Pascoal Caldeira, Joao Frois Univ Fed Rio Grande do Sul Sch Business 855 Washington Luis St BR-90010460 Porto Alegre RS Brazil Fed Univ Santa Dept Econ Catarina Campus Univ Reitor Joao David Ferreira L BR-88040900 Florianopolis SC Brazil

This paper derives a mixed-integer non-linear optimization (MINLP) problem from the cointegration methodology and checks its convexity. We apply this approach to solve the index tracking (IT) problem using datasets from two distinct stock markets. The MINLP reformulation encompasses stock selection procedure and is optimized through branch-and-cut algorithm. The quality of the generated portfolios demonstrated lower turnover, which implies lower transaction costs over time and better performance in most instances regarding their tracking error in-sample and out-of-sample when compared with the traditional cointegration based IT portfolios.

关键词： mixed-integer non-linear optimization Cointegration Index tracking

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Experimental Validation of Volume-Based Comparison for Double-McCormick Relaxations 14th

Experimental Validation of Volume-Based Comparison for Doubl...

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14th International Conference on the Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming (CPAIOR)

作者： Speakman, Emily Yu, Han Lee, Jon Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

ISBN: (纸本)9783319597768;9783319597751

Volume is a natural geometric measure for comparing polyhedral relaxations of non-convex sets. Speakman and Lee gave volume formulae for comparing relaxations of trilinear monomials, quantifying the strength of various natural relaxations. Their work was motivated by the spatial branch-and-bound algorithm for factorable mathematical-programming formulations. They mathematically analyzed an important choice that needs to be made whenever three or more terms are multiplied in a formulation. We experimentally substantiate the relevance of their main results to the practice of global optimization, by applying it to different relaxations of difficult box cubic problems (boxcup). In doing so, we find that, using their volume formulae, we can accurately predict the quality of a relaxation for boxcups based on the (box) parameters defining the feasible region. Specifically, we are able to conclude from our experiments that all of the relevant relaxations are round enough so that average objective gaps for a pair of boxcup relaxations can be predicted by appropriately combining the volumes of relaxations of the individual trilinear monomials.

关键词： Mccormick inequalities mixed-integer non-linear optimization Global optimization Trilinear monomials Spatial branchand-bound

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An iterated local search algorithm for water distribution network design optimization

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NETWORKS 2016年第3期67卷 187-198页

作者： De Corte, Annelies Sorensen, Kenneth Univ Antwerp ANT OR Operat Res Grp Antwerp Belgium

The optimal design of water distribution networks is a complex non-linear combinatorial optimization problem. It consists in finding the least-cost pipe configuration that satisfies hydraulic laws and customer requirements, using a limited set of available pipe types. In a previous paper (De Corte and Sorensen, Eur J Oper Res 228 (2013), 1-10), we have argued that state-of-the-art optimization algorithms proposed in this domain are unduly complicated and poorly tested. The main contribution of this article is a straightforward, fast, transparent, and effective iterated local search (ILS) algorithm that has at least equivalent performance when compared to the best approaches in the literature, but has a much simpler algorithmic structure. A full-factorial experiment is conducted to obtain the heuristic's best parameter settings. Contrary to existing algorithms, the ILS algorithm is additionally shown to perform well on a broad set of much more challenging HydroGen (De Corte and Sorensen, Water Resour Manage 28 (2014), 333-350) test instances. (c) 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(3), 187-198 2016

关键词： water distribution network design iterated local search mixed-integer non-linear optimization pipe sizing

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Solving difficult mixed integer and disjunctive non-linear problems on single and parallel processors

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APPLIED SOFT COMPUTING 2014年 24卷 385-405页

作者： Ostermark, Ralf Abo Akad Univ Sch Business & Econ Turku Finland

Difficult non-linear, mixed integer non-linear and general disjunctive programming (NLP/MINLP/GDP) problems are considered in the present study. We show using random relaxation procedures that sampling over a subset of the integer variables and parallel processing have potential to simplify large scale MINLP/GDP problems and hence to solve them faster and more reliably than conventional approaches on single processors. Gray coding can be utilized to assign problems to the local processors. Some efficient non-linear solvers have been connected to the Genetic Hybrid Algorithm (GHA) through a switchboard minlp_machine(), monitoring a vector of caller functions. The switch board is tested on single processor computers and massively parallel supercomputers in a sample of optimization problems. A new line search algorithm based on multi-sectioning, i.e. repeated bi-sectioning of parallel threads is applied to a set of irregular NLP-problems. Simulations indicate that step search based on multi-sectioning and recentering is robust. Time recording indicates that the step search procedure is fast also in large optimization problems. Parallel processing with Gray coding and random sampling over a subset of the integer variables improves the performance of the sequential quadratic programming algorithm with multi-sectioning in large-scale problems. An early mesh interrupt guarantees load balancing in regular problems. General disjunctive programming (GDP) problems can be simplified through parallel processing. Certain problems are solved in larger scale than reported previously. Function pointer logic and intelligent switching procedures provide a fruitful basis for solving high-order GDP problems, where the computational challenge in direct MINLP-formulations would be insurmountable. (C) 2014 Elsevier B.V. All rights reserved.

关键词： mixed-integer non-linear optimization General disjunctive programming Parallel processing

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Solving mixed-integer optimal control problems by branch&bound: a case study from automobile test-driving with gear shift

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OPTIMAL CONTROL APPLICATIONS & METHODS 2005年第1期26卷 1-18页

作者： Gerdts, M Univ Bayreuth Dept Math D-95440 Bayreuth Germany

The article discusses the application of the branch&bound method to a mixed integer non-linear optimization problem (MINLP) arising from a discretization of an optimal control problem with partly discrete control set. The optimal control problem has its origin in automobile test-driving, where the car model involves a discrete-valued control function for the gear shift. Since the number of variables in (MINLP) grows with the number of grid points used for discretization of the optimal control problem, the example from automobile test-driving may serve as a benchmark problem of scalable complexity. Reference solutions are computed numerically for two different problem sizes. A simple heuristic approach suitable for optimal control problems is suggested that reduces the computational amount considerably, though it cannot guarantee optimality anymore. Copyright (C) 2005 John Wiley Sons, Ltd.

关键词： optimal control direct methods mixed-integer non-linear optimization branch&bound double-lane change manoeuvre

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