Multi objective optimization in chemical engineering, developments and applications (2013)

Multi-Objective Optimization in Chemical Engineering Multi-Objective Optimization in Chemical Engineering Developments and Applications Edited by GADE PANDU RANGAIAH Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore ´ BONILLA-PETRICIOLET ADRIAN Department of Chemical Engineering, Instituto Tecnol´ogico de Aguascalientes, Mexico A John Wiley & Sons, Ltd., Publication This edition first published 2013 C 2013 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication 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added warnings and precautions The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read No warranty may be created or extended by any promotional statements for this work Neither the publisher nor the author shall be liable for any damages arising herefrom Library of Congress Cataloging-in-Publication Data Multi-objective optimization in chemical engineering : developments and applications / [edited by] Gade Rangaiah, Adri´an Bonilla-Petriciolet pages cm ISBN 978-1-118-34166-7 (hardback) Chemical processes Mathematical optimization Chemical engineering I Rangaiah, Gade Pandu II Bonilla-Petriciolet, Adri´an TP155.7.M645 2013 660–dc23 2012048233 A catalogue record for this book is available from the British Library ISBN: 9781118341667 Set in 10/12pt Times by Aptara Inc., New Delhi, India Contents List of Contributors Preface Part I Overview Introduction Adri´an Bonilla-Petriciolet and Gade Pandu Rangaiah xiii xv 1.1 Optimization and Chemical Engineering 1.2 Basic Definitions and Concepts of Multi-Objective Optimization 1.3 Multi-Objective Optimization in Chemical Engineering 1.4 Scope and Organization of the Book References 15 Optimization of Pooling Problems for Two Objectives Using the ε-Constraint Method Haibo Zhang and Gade Pandu Rangaiah 17 2.1 2.2 Introduction Pooling Problem Description and Formulations 2.2.1 p-Formulation 2.2.2 r-Formulation 2.3 ε-Constraint Method and IDE Algorithm 2.4 Application to Pooling Problems 2.5 Results and Discussion 2.6 Conclusions Exercises References 17 19 19 21 25 27 28 32 33 33 Multi-Objective Optimization Applications in Chemical Engineering Shivom Sharma and Gade Pandu Rangaiah 35 3.1 3.2 3.3 35 37 Introduction MOO Applications in Process Design and Operation MOO Applications in Petroleum Refining, Petrochemicals and Polymerization 57 vi Contents 3.4 MOO Applications in the Food Industry, Biotechnology and Pharmaceuticals 3.5 MOO Applications in Power Generation and Carbon Dioxide Emissions 3.6 MOO Applications in Renewable Energy 3.7 MOO Applications in Hydrogen Production and Fuel Cells 3.8 Conclusions Acronyms References Part II Multi-Objective Optimization Developments Performance Comparison of Jumping Gene Adaptations of the Elitist Non-dominated Sorting Genetic Algorithm Shivom Sharma, Seyed Reza Nabavi and Gade Pandu Rangaiah 4.1 4.2 4.3 4.4 4.5 57 66 66 82 82 87 87 103 105 Introduction Jumping Gene Adaptations Termination Criterion Constraint Handling and Implementation of Programs Performance Comparison 4.5.1 Performance Comparison on Unconstrained Test Functions 4.5.2 Performance Comparison on Constrained Test Functions 4.6 Conclusions Exercises References 105 107 110 112 114 114 121 124 124 125 Improved Constraint Handling Technique for Multi-Objective Optimization with Application to Two Fermentation Processes Shivom Sharma and Gade Pandu Rangaiah 129 5.1 5.2 5.3 5.4 5.5 5.6 129 131 132 133 136 139 Introduction Constraint Handling Approaches in Chemical Engineering Adaptive Constraint Relaxation and Feasibility Approach for SOO Adaptive Relaxation of Constraints and Feasibility Approach for MOO Testing of MODE-ACRFA Multi-Objective Optimization of the Fermentation Process 5.6.1 Three-Stage Fermentation Process Integrated with Cell Recycling 5.6.2 Three-Stage Fermentation Process Integrated with Cell Recycling and Extraction 5.6.3 General Discussion 5.7 Conclusions Acronyms References 139 145 152 153 153 154 Contents Robust Multi-Objective Genetic Algorithm (RMOGA) with Online Approximation under Interval Uncertainty Weiwei Hu, Adeel Butt, Ali Almansoori, Shapour Azarm and Ali Elkamel 6.1 6.2 Introduction Background and Definition 6.2.1 Multi-Objective Genetic Algorithm (MOGA) 6.2.2 Multi-Objective Robustness with Interval Uncertainty: Basic Idea 6.3 Robust Multi-Objective Genetic Algorithm (RMOGA) 6.3.1 Nested RMOGA 6.3.2 Sequential RMOGA 6.3.3 Comparison between Nested and Sequential RMOGA 6.4 Online Approximation-Assisted RMOGA 6.4.1 Steps in Approximation-Assisted RMOGA 6.4.2 Sampling 6.4.3 Metamodeling and Verification 6.4.4 Sample Selection and Filtering 6.5 Case Studies 6.5.1 Numerical Example 6.5.2 Oil Refinery Case Study 6.6 Conclusions References Chance Constrained Programming to Handle Uncertainty in Nonlinear Process Models Kishalay Mitra 7.1 7.2 7.3 Introduction Uncertainty Handling Techniques Chance-Constrained Programming: Fundamentals 7.3.1 Calculation of P (hk (x, ξ ) ≥ 0) ≥ p (k = 1, , u) 7.3.2 Calculation of max f˜ P f (x, ξ ) ≥ f˜ ≥ α 7.4 Industrial Case Study: Grinding 7.4.1 Grinding Process and Modeling 7.4.2 Optimization Formulation 7.4.3 Results and Discussion 7.5 Conclusions Nomenclature Appendices A.1 CCP for Normally Distributed Uncertain Parameters A.2 Calculation of Mean and Variance for General Function References vii 157 157 159 160 161 163 163 165 167 168 168 169 170 171 172 172 175 178 179 183 183 184 186 192 193 193 193 195 199 206 209 210 210 212 212 viii Contents Fuzzy Multi-Objective Optimization for Metabolic Reaction Networks by Mixed-Integer Hybrid Differential Evolution Feng-Sheng Wang and Wu-Hsiung Wu 8.1 8.2 Introduction Problem Formulation 8.2.1 Primal Multi-Objective Optimization Problem 8.2.2 Resilience Problem 8.3 Optimality 8.4 Mixed-Integer Hybrid Differential Evolution 8.4.1 Algorithm 8.4.2 Constraint Handling 8.5 Examples 8.6 Conclusions Exercises References Part III Chemical Engineering Applications Parameter Estimation in Phase Equilibria Calculations Using Multi-Objective Evolutionary Algorithms Sameer Punnapala, Francisco M Vargas and Ali Elkamel 9.1 9.2 10 217 217 219 219 221 223 228 228 231 233 240 241 242 247 249 Introduction Particle Swarm Optimization (PSO) 9.2.1 Multi-Objective Particle Swarm Optimization (MO-PSO) 9.3 Parameter Estimation in Phase Equilibria Calculations 9.4 Model Description 9.4.1 Vapor Liquid Equilibrium 9.4.2 Heat of Mixing 9.5 Multi-Objective Optimization Results and Discussion 9.6 Conclusions Nomenclature Exercises References 249 250 251 253 253 254 255 257 260 260 261 264 Phase Equilibrium Data Reconciliation Using Multi-Objective Differential Evolution with Tabu List Adri´an Bonilla-Petriciolet, Shivom Sharma and Gade Pandu Rangaiah 267 10.1 Introduction 10.2 Formulation of the Data Reconciliation Problem for Phase Equilibrium Modeling 10.2.1 Data Reconciliation Problem 10.2.2 Data Reconciliation for Phase Equilibrium Modeling 10.3 Multi-Objective Optimization using Differential Evolution with Tabu List 267 270 270 271 274 Contents 11 12 ix 10.4 Data Reconciliation of Vapor-Liquid Equilibrium by MOO 10.4.1 Description of the Case Study 10.4.2 Data Reconciliation Results 10.5 Conclusions Exercises References 277 277 278 287 290 290 CO2 Emissions Targeting for Petroleum Refinery Optimization Mohmmad A Al-Mayyahi, Andrew F.A Hoadley and Gade Pandu Rangaiah 293 11.1 Introduction 11.1.1 Overview of the CDU 11.1.2 Overview of the FCC 11.1.3 Pinch Analysis 11.1.4 Multi–Objective Optimization (MOO) 11.2 MOO-Pinch Analysis Framework to Target CO2 Emissions 11.3 Case Studies 11.3.1 Case Study 1: Direct Heat Integration 11.3.2 Case Study 2: Total Site Heat Integration 11.4 Conclusions Nomenclature Exercises Appendices A.1 Modeling of CDU and FCC A.2 Preliminary Results with Different Values for NSGA-II Parameters A.3 Pinch Analysis Techniques A.3.1 Composite Curves (CC) A.3.2 Grand Composite Curve (GCC) A.3.3 Total Site Profiles References 293 295 296 297 301 303 304 305 310 315 315 317 318 318 320 320 322 326 326 331 Ecodesign of Chemical Processes with Multi-Objective Genetic Algorithms Catherine Azzaro-Pantel, Adama Ouattara and Luc Pibouleau 335 12.1 Introduction 12.2 Numerical Tools 12.2.1 Evolutionary Approach: Multi-Objective Genetic Algorithms 12.2.2 Choice of the Best Solutions 12.3 Williams–Otto Process (WOP) Optimization for Multiple Economic and Environmental Objectives 12.3.1 Process Modelling 12.3.2 Optimization Variables 12.3.3 Objectives for Optimization 12.3.4 Problem Constraints 335 337 337 337 338 338 339 340 341 x 13 Contents 12.3.5 Implementation 12.3.6 Procedure Validation 12.3.7 Tri-Objective Optimization 12.3.8 Discussion 12.4 Revisiting the HDA Process 12.4.1 HDA Process Description and Modelling Principles 12.4.2 Optimization Variables 12.4.3 Objective Functions 12.4.4 Multi-Objective Optimization 12.5 Conclusions Acronyms References 341 341 343 346 346 346 349 350 354 361 363 364 Modeling and Multi-Objective Optimization of a Chromatographic System Abhijit Tarafder 369 13.1 13.2 13.3 13.4 13.5 14 Introduction Chromatography—Some Facts Modeling Chromatographic Systems Solving the Model Equations Steps for Model Characterization 13.5.1 Isotherms and the Parameters 13.5.2 Selection of Isotherms 13.5.3 Experimental Steps to Generate First Approximation 13.6 Description of the Optimization Routine—NSGA-II 13.7 Optimization of a Binary Separation in Chromatography 13.7.1 Selection of the Objective Functions 13.7.2 Selection of the Decision Variables 13.7.3 Selection of the Constraints 13.8 An Example Study 13.8.1 Schemes of the Optimization Studies 13.8.2 Results and Discussion 13.9 Conclusions References 369 371 373 376 377 378 379 382 387 387 387 388 389 390 390 393 396 397 Estimation of Crystal Size Distribution: Image Thresholding Based on Multi-Objective Optimization Karthik Raja Periasamy and S Lakshminarayanan 399 14.1 Introduction 14.2 Methodology 14.3 Image Simulation 14.3.1 Camera Model 14.3.2 Process Model 14.3.3 Assumptions 14.4 Image Preprocessing 399 401 402 402 402 403 404 New PI Controller Tuning Methods Using Multi-Objective Optimization 497 1.6 Controlled variable 1.2 0.8 0.4 –0.4 20 40 Time (s) 60 80 Figure 17.13 Closed-loop responses for the simulated fourth-order system (solid line) and FOPDT system (dotted line) for relative ITAE values of and for (a) a unit set point change and (b) a first-order disturbance corresponding objective function values are listed in Table 17.3 The dynamic responses were calculated for a total of 100 s using an integration step of 0.001 s Figure 17.13(a) and Table 17.3 clearly demonstrate that the controller configuration determined using the developed tuning method was effective in controlling the fourth-order system Both systems showed very similar responses, with all three performance criteria very similar in value These results show that the proposed tuning method can be applied to higher order systems as well as FOPDT systems The obvious limitation is that the process can be represented adequately by a FOPDT and its open-loop behavior does not oscillate 17.7.3 Application to a Process with a First-Order Disturbance The proposed tuning method was also evaluated for the case of a disturbance The controller parameters determined in section 17.7.2 were used to control the same fourth-order Table 17.3 Performance criteria for the simulated fourth-order and FOPDT systems for a unit set point change corresponding to Figure 13.12(a) Relative ITAE System Fourth-order system FOPDT system Fourth-order system FOPDT system ISDU ITAE Settling time 7.51 × 10−5 7.51 × 10−5 2.44 × 10−5 2.44 × 10−5 78.62 85.71 132.13 143.53 19.95 20.70 25.28 25.65 498 Multi-Objective Optimization in Chemical Engineering Table 17.4 Parameters of the first-order disturbance and the resulting objective functions Relative ITAE System fourth-order system FOPDT system fourth-order system FOPDT system ISDU ITAE Settling time 8.80 × 10−8 8.90 × 10−8 5.80 × 10−8 5.84 × 10−8 163.73 175.83 256.84 274.61 25.15 25.83 30.24 30.48 system subject to a unit set point change for a first-order disturbance The first-order disturbance transfer function had a gain of 1.5 and a time constant of three time units as shown in Table 17.4 The closed-loop responses of the fourth-order and FOPDT systems are shown in Figure 17.13(b) and the associated performance criteria are presented in Table 17.4 Figure 17.13(b) and Table 17.4 show that the developed tuning method performed well for the fourth-order process with a first-order disturbance A similar settling time was realized for this simulation as for both responses shown in section 17.7.2 The ITAE was larger for the response to a disturbance, but the ISDU was reduced All of the results from section 17.7.0 clearly show that the tuning method developed by approximating the Pareto domain leads to excellent controller performance, and is applicable to a wide variety of processes 17.8 Conclusions In this study, PI controller tuning methods were developed considering multiple objectives The methods were developed by optimizing the ITAE, ISDU, and settling time for a FOPDT system The Pareto domain identifying the region of optimal solutions was approximated using the PCGA due to its demonstrated high level of accuracy and efficiency It was found that a strong correlation exists in the Pareto domain between the two controller input parameters, the relative controller gain, and the relative integral time This implies that when configuring the controller, only one of the controller parameters needs to be specified, as the other is obtained via the strong correlation Using the controller optimization results, two methods were proposed for tuning the PI controller The first tuning method allows for optimum controller performance to be obtained by initially specifying either one of the controller input parameters The second tuning method involves first specifying the preferred relative objective function values from the Pareto domain, which correspond to specific values of the controller parameters The developed controller tuning methods were compared to several previously developed controller correlations It was found that all previously developed controller correlations showed equal or worse performance than that identified by the Pareto domain, but with the limitation of not allowing for enhanced understanding of the many optimal solutions and the tradeoff between each performance criterion Finally, the tuning methods were applied to a fourth-order process and a process with a disturbance, and were shown to perform well for these two applications New PI Controller Tuning Methods Using Multi-Objective Optimization 499 Acknowledgments The authors would like to thank the Natural Science and Engineering Research Council (NSERC) for the financial assistance Nomenclature Variable b Cov D f ISDU ITAE Kc Kp M m n N P T tset u x y Definition Controller input space intercept Element in Covariance Matrix Determinant Objective function in optimization problem Integral of the squares of the differences in the manipulated variable Integral of the time-weighted absolute error Controller gain Process gain Number of divisions in PCGA grid Number of objective criteria Number of input variables Number of points in Pareto domain Point in the Pareto domain Trace Settling time Manipulated variable Input function in optimization problem Controlled variable Greek Symbols t ε η θ τ τI Time step Error Controller input space slope Dead time Time constant Integral time s Varies Dimensionless s s s Subscripts Subscript f t j Definition Final Time Point in the Pareto domain Unit Dimensionless Dimensionless Dimensionless Varies Varies Varies Units of u/y Units of y/u Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless Dimensionless s Varies Varies Varies 500 Multi-Objective Optimization in Chemical Engineering Exercises 17.1 Starting with Equation (17.14), show that the FOPDT that best represents this fourthorder process is indeed given by Equation (17.15) 17.2 The transfer function of a chemical process can be accurately represented with the following equation in the Laplace domain: 0.82e− 0.6s y(s) = u(s) (5s + 1)(4s + 1)(2s + 1) (17.16) Approximate this transfer function with a FOPDT and calculate the parameters Kc and τ I of a PI controller using Method for a relative ITAE of 2.5 17.3 For the previous problem, using Method 1, determine the value of τ I of a PI controller if the controller gain Kc is 0.43 What are the approximate values of the three performance criteria (ITAE, ISDU and settling time) associated with these controller parameters? 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altruism, 106, 110, 124 American Society for Testing and Materials (ASTM), 431 antibiotic production, 66, 70 anti-Langmuir isotherm, 380–382, 386 approximation, 157–163, 165, 167–171, 173, 175, 177–179 approximation - offline, 168, 169 approximation - online, 158, 159, 168–171, 174, 175, 178, 179 Aspen Plus, 4, 14, 15, 73, 74, 427, 429, 430–436, 456 attachment of solute molecules, 371, 379, 381, 382, 389 augmented Lagrange function, 232 auxiliary variable, 185, 192, 197 average absolute constraint violation (AACV), 143, 145, 150–152 azeotropes, 260, 282, 285, 287 baking, 66–68 ball mill, 193, 194, 196, 209 bare module cost, 458 BARON, 52, 238–240 batch plant, 37, 41, 62, 132 benchmark problems, 7, 28, 115, 116, 136, 137 benzene-hexafluorobenzene system, 277–282, 284, 286 BET, 380–382, 386 bilinear programming formulation, 19 binary-coded GA, 160 binary-coded NSGA-II, 12, 105–107, 303 binary separation, 381, 387 biodiesel, 66, 79, 81 bioethanol, 13, 14, 66, 79, 81, 139–152, 423–445 biofuel, 46, 66, 78, 139, 423, 424 biogenetic-NSGA-II-aJG, 106 bio-synthesis factory, 66, 69 biotechnology, 8, 9, 36, 37, 57, 66, 67 blob analysis, 414, 417, 418 boiling point, 295, 304 branch and bound (BB), 40, 46, 47, 55, 219 bubble cap trays, 427 bypass, 19, 23, 28, 29 candidate point, 161–163 capital cost, 60, 66, 299, 303, 340, 351, 449, 451, 456, 457, 459 carbon-intensive, 294 Multi-Objective Optimization in Chemical Engineering: Developments and Applications, First Edition Edited by Gade Pandu Rangaiah and Adri´an Bonilla-Petriciolet © 2013 John Wiley & Sons, Ltd Published 2013 by John Wiley & Sons, Ltd 504 Index catalytic cracking, 12, 294, 296 CCPNSGA II, 195, 198, 199 cell mass, 40, 81, 139, 140, 142, 145, 146, 149 cell recycling, 139–145, 152 cell separator, 139, 146 cell viability, 11, 218, 220–222, 233, 237, 240 CEPCI, 457, 458 chance constrained programming, 11, 40, 184–187 chi2 test, 112 chromatography, 13, 369–373, 387, 388, 396 chronic toxicity, 452, 453, 462, 464 circulation load, 195, 204 CO2 absorber, 82, 84 CO2 emissions, 9, 12, 36, 37, 49, 59, 62, 72–76, 79 cognitive parameter, 251 compensating effect, 378, 379 composite curves, 298–301, 322–325, 328 composition of the mobile phase, 372, 389, 391 compromise programming, 85 computational effort/time, 38, 132, 152, 165, 167, 400, 409 concave Pareto front, CONOPT, 42, 52 consequential emission, 295, 300 CONSTR problem, 111, 114, 116, 121–123 constrained test functions, 106, 113, 114, 116, 121–124, 136, 137 constraint handling, 107, 112, 129–132, 137, 141, 153 ε-constraint method, 9, 18, 19, 25–33, 40, 42, 45–57, 62–65, 68, 70, 72, 74, 75, 77, 80, 81, 84, 85, 224–226, 336, 434 constraint programming, 40 constraints, 3, 5, 7, 9–11, 13, 130, 137 constraint violation, 130–132, 137, 143, 152, 153 controller tuning methods, 14, 480, 491, 494, 498 convergence, 18, 26, 106, 113, 118, 124, 137, 149, 198, 230, 232, 234, 251, 274, 387, 435, 436 conversion, 35, 37, 49–52, 56–63, 66, 67, 78–82 convex Pareto front, cooling water, 299, 315, 318, 428, 443, 445 CPLEX, 53, 56, 78, 80 cradle-to-gate, 348 crossover, 108, 110 crossover probability, 114, 172, 276, 304, 321, 342, 464 crowding distance, 134–136 crystallization, 13, 37, 39, 42, 399–403, 412, 419 crystallization process control, 399, 400, 416–418 crystal size distribution (CSD), 399–402, 414–418 cumene process, 14, 451, 455–462, 464–471 current density, 76, 82, 83 cutting plane, 219 cycle time, 37, 39, 45, 49, 393 damage index (DI), 452, 453, 459, 462, 464–471 damage radius (DR), 453, 454, 459–464 data reconciliation, 12, 267–291 DECHEMA, 277 decision making/makers, 12, 31, 39, 56, 71, 75, 206, 218, 295, 336, 357, 361, 432 decision variables, 3, 5–8, 13 decomposition approaches, 219 deficit, 298, 328 degree of polymerization, 57 demand, 19–21, 30, 33 dependent variables, 23–25 depreciable capital, 459 derivative properties, 250 detector, 373 deterministic equivalent, 11, 186–188, 190, 209–211 deterministic methods, 4, 7, 9, 11, 379 Index DICOPT, 58, 62, 238–240 diesel, 176, 293–296, 305, 319 differential algebraic equations, 194 differential evolution, 7–12, 18, 130, 131, 133, 135, 141, 217, 219, 228, 229, 267, 269, 274 differential evolution with tabu list, 267, 269, 274 digital image, 404 dilution rate, 140–151 disconnected Pareto front, distillation, 8, 12, 14, 37, 39, 43, 44, 49, 50, 54, 57, 62, 64, 175, 176, 309, 318, 338, 347, 425, 457, 460 dominated solutions, 435 Dow CEI, 451 Dow F&EI, 450, 451 drug design, 66, 68 duplicate non-dominated solutions, 119, 121 ecodesign, 12, 336, 354, 361–363 Eco indicator (EI), 99, 37, 42, 46, 47, 52, 53, 80 economic assessment/objective, 340, 341, 343, 345, 346, 350, 354, 449– 451, 455, 456, 464, 467, 471 electrical efficiency, 61, 86 electric power, 295, 297, 436, 443 emissions, 36, 37, 43, 53, 57, 59, 62, 66, 72–82, 85, 293–329, 348, 349, 352–354, 361, 423, 450, 464 enantiomers, 13, 370 energy, 3–5, 8–12, 14 energy consumption, 39, 42, 46, 50–53, 56, 62, 64, 293, 295, 298 energy efficiency, 49, 76, 82, 85, 294, 296, 297 energy integration, 12, 295, 347, 433, 457 energy saving strategies, 293 enhancement, 401, 404 enthalpy, 298, 299, 303, 316, 317, 328, 349 environmental objective, 56, 80, 81, 304, 315, 335, 336, 338, 341, 344, 345, 354, 362, 363, 450, 467, 471 505 environmental burden, 80, 347, 348, 352, 353, 363, 451 environmental impact, 4, 37, 41, 44–47, 52–55, 61, 62, 64, 66, 71, 76–82, 341, 344, 347, 348, 355, 360, 362, 363, 449, 450 equality constraint, 19, 21, 26, 27, 107, 129–132, 136–143, 149, 152, 153 equation(s) of state (EOS), 249, 253, 255, 260, 271, 318, 429 equilibrium based approach, 427, 429 equilibrium constant, 371, 380, 381, 386, 392 equilibrium dispersive model, 374 error-in-variable, 268, 270 estimation of the transport properties, 384 ethanol, see bioethanol ethanol loss, 425, 428, 431–433, 439, 445 ethanol productivity, 78, 79, 81, 140, 141, 143, 144, 146–152, 429 ethanol purity, 428, 430–439, 441–446 Euclidean distance, 112, 113, 136, 137, 171, 275 evolutionary algorithms, 112, 130, 199, 218, 219, 229, 230, 249, 250, 260, 264 evolutionary strategies, 335 excess enthalpy, 249, 253–255, 258–262 exergetic efficiency, 49, 63, 66, 73, 76, 77, 79 expectation term, 184, 185 feasibility approach, 10, 130–133, 136, 137, 142, 153, 276, 462 feature extraction, 400, 401, 413, 414, 418 feed solution, 378, 382, 389, 392 feedstock, 55, 79–81, 139, 145, 295, 296, 423, 424 fermentation process, 67, 68, 130, 131, 139–141, 143–153 filtering techniques, 404 fitness value, 161, 251, 387 fludized catalytic cracking (FCC), 57, 58, 63, 111, 175, 176, 294–297, 304–306, 309–315 flux balance analysis, 48, 68, 222 fmincon, 28, 84 506 Index FMOOP, 226 food industry, 8, 9, 36, 37, 57, 66 FOPDT, 480, 481, 491, 495–500 FORTRAN, 113, 435 framework, 46, 71, 163, 186, 188, 219, 295, 303, 304, 315, 354, 363, 491 fuel blending, 57 fuel cell, 8, 36, 37, 76, 82, 83 fuel cell system, 82–86 fuel cost, 66, 72, 75, 79 fuzzy approach/optimization, 11, 44, 66–68, 76, 218, 226 fuzzy mathematical programming, 184 GAMS, 4, 42, 47, 52, 53, 56, 58, 62, 78, 80, 235, 238–240 gasification, 47, 65, 66, 73, 74, 76, 78, 82, 294 gasoline, 29, 58, 176, 293, 296, 424 gasoline-ethanol mixture, 431 gas separation, 57, 59 gate-to-gate, 347 Gaussian correlation function, 170 Gaussian curves, 405 generalized M-Pareto-optimal solution, 227 general rate model, 373 generating method, 218 generational distance (GD), 110, 112–114, 116–124, 137–139 genetic algorithm, 7, 10, 13, 132, 133, 157, 160, 172, 250, 269, 337, 341, 342, 355, 357, 363, 379, 387, 445, 483 genetic perturbation, 218 GFMOOP, 218, 219, 222, 223, 226–228, 240 Gibbs free energy, 69, 271 Gibbs-Helmholtz equation, 255 global optimal solutions, 435 global optimization methods/techniques, 4, 18, 172, 187, 269 global warming potential (GWP), 37, 50, 73, 77, 80, 353, 363, 450 glucose concentration, 79, 140, 141, 143 glucose conversion, 78, 79, 140, 141, 143, 144, 147, 148 goal attainment, 38, 41, 51, 78, 79, 141, 223, 226–228 grand composite curve, 62, 298, 299, 316, 326 gray level, 400, 403–406, 409, 418, 419 green degree (GD), 37, 53, 64, 450 greenhouse gases, 57, 74, 293 grid search approach, 484 grinding operation, 44, 186, 193, 194 Hammersley sequence sampling, 198 harmonic search, 250 hazard identification and ranking system, 452 hazard potential, 450, 454, 459, 460, 461, 466 HAZOP, 450, 454 HDA process, 336, 346–355, 361 heat capacity, 250, 262, 349 heat exchanger networks, 37, 39, 47, 52, 298, 315 heat integration, 54, 61, 75, 78, 294–298, 300, 303–305, 310, 315 heat of mixing, 253–261 heat recovery, 37, 49, 56, 75, 295–301, 314, 328 heat transfer area, 299 heavy cycle oil, 297 Henry’s constant, 381, 383, 384, 386, 391, 392 HETP, 384–386 heuristic, 427 high pressure steam, 297, 299, 456 homogeneous azeotrope, 282, 285 Hydrogen (H2 ) production, 36, 37, 59, 76, 82–86 hybrid methods (for constraint handling), 130 hydrocarbon inventory, 57, 60, 450 hydrocyclones, 193, 194, 196 hygroscopic, 431 hyper volume, 106, 110 hypothetical case, 162 Hysys, 4, 15, 50, 303, 304, 318, 451, 456, 463–465 Index ideal adsobed solution theory, 378, 382 image analysis, 400, 401, 418 image histogram, 400, 404–406 IMPACT 2002+, 37, 42, 53, 76 indirect optimization method, 217 individual chance constrained, 186 inequality constraint, 129–133, 136, 137, 142, 149, 153 inertia, 251 inherent environmental toxicity hazard (IETH), 53, 450 inherent safety index (ISI), 451–455, 459 injection molding, 39, 57, 64 integrated differential evolution, 9, 18, 26 integrated inherent safety index (I2SI), 14, 451, 452, 459, 464, 471, 472 inter-class variance, 405, 409, 410, 419 intermediate generations, 106, 113, 118, 122 inter-stage extraction, 78, 81, 139, 145, 152 interval uncertainty, 161–163, 173 inverse generational distance (IGD), 113–124 inverse method, 378, 386 ISDU, 481, 482, 489, 490, 498–500 isotherms, 375, 377–382, 386 ITAE, 481, 482, 490, 495, 498 joint chance constrained programming, 186 Joule Thomson coefficient, 249 jumping gene adaptations, 10, 18, 39, 52, 105, 107, 124, 132 jumping gene probability, 107, 108, 110, 114, 121 jumping gene variants, 105–107, 110 kinetic model, 139, 217, 222, 240 kinetic parameters, 38, 40, 43, 70, 139–141, 146, 147 kriging, 158, 168, 170–172, 175, 178 lactic acid production, 66, 67 Langmuir isotherm, 379–382, 386, 390, 392 507 Latin hypercube sampling, 169, 172 learning period, 28 lexicographic goal programming, 41 life cycle assessment, 347, 361, 363 linear isotherm, 381 linear physical programming, 48 linear programming, 3, 18, 19, 45, 53, 187, 217 LINGO, 56, 63 liquid liquid extraction, 44, 253, 254, 261 L2 norm, 409–412 local methods, logarithmic transformation, 217 log mean temperature difference, 465 lower level problem, 164, 168 lower level sub-problem, 164, 173 low pressure steam, 299, 352, 436 lumped kinetic model, 373 main fractionator, 297, 305, 316, 318 make-span, 67, 71 mass balance, 20, 129–132, 146, 153, 339, 377 mass transfer, 373–375, 427, 429 material loss, 451, 456, 464–471, 475 mathematical model, 146, 294, 339, 377 Matlab, 4, 28, 33, 54, 55, 69–71, 83, 84, 172, 176, 258, 341, 401, 469 maximum number of generations (MNG), 107, 108, 110, 112, 114, 133, 136, 164, 274, 276, 304, 321, 322, 463, 464 Maxwell–Stefan theory, 429 membrane bioreactor, 37, 50 membrane separation process, 14 metabolic adjustment, 218, 233 metabolic reaction networks, 11, 12, 66, 67, 217–220, 240 meta-heuristics, 157, 269, 274 metamodel, 158, 159, 168, 170–172, 174, 178 MIHDE, 219, 225, 228–235, 238–240 minimum area rectangle, 414, 417 minimum error, 251, 400, 405, 406, 410–413 minimum temperature difference, 317 min-max problem, 225, 226, 228, 407 508 Index mixed-integer linear programming, 218 mixed-integer nonlinear programming, 219, 221 mixed optimization, 407, 409 mobile phase, 371–380, 382, 384, 388–392 mobile phase flow rate, 392 model characterization, 377, 383 Monte Carlo, 175, 363 morphological image processing, 400, 410 M-Pareto-optimal solution, 226–228 MS Excel, 15, 25, 26, 33, 71, 139, 142, 146, 276, 303, 341 multi-criteria optimization, multi-level utilities, 299 multi-modal Pareto-optimal front, 114, 118 multi-objective differential evolution (MO DE), 60, 61, 75, 81, 130–139, 142–145, 149–153 multi-objective evolutionary algorithm (MO EA), 59, 61, 73, 79, 80 multi-objective genetic algorithm (MO GA), 10, 11, 38–41, 45, 46, 49, 51, 57, 59, 62, 64, 67, 70, 77, 79, 84, 157–160, 163, 172, 335, 337, 363 ε-multi-objective optimization problem, 225 multi-objective particle swarm optimization (MO PSO), 76, 84, 130, 251, 257 multi-objective simulated annealing (MO SA), 44, 52, 58, 59, 63, 106, 337 multiple choice decision-making (MCDM), 336, 337, 357, 363 multiplier updating method, 232 multivariate probability distribution, 186 mutant individual, 134, 229, 230 mutation, 108, 110, 134, 135, 198, 199, 229, 230, 274, 387, 462 mutation probability, 114, 172, 276, 304, 342, 462 naphtha pyrolysis, 57, 59 National Fire Protection Association (NFPA), 453, 460, 461, 473, 474 natural gas, 41, 47, 57, 59–61, 63, 66, 73–75, 77, 78, 80, 82, 349, 350 net present value/worth (NPV), 41, 42, 47, 49, 56, 63, 71, 72, 74, 80, 81, 336, 340, 341, 346, 449 NFPA ranking for flammability (NF), 460, 473, 474 NFPA ranking for health (NH), 461, 473, 474 NFPA ranking for reactivity (NR), 460, 473 NIMBUS, 47, 71 no free lunch (NFL) theory, 336 noise, 401, 403, 404, 410 non-dominated set, 159–161 non-dominated solutions, 5–7 non-dominated sorting, 135, 136 non-dominated sorting genetic algorithm, see NSGA-II non-random two-liquid model (NRTL), 12, 253–261, 265, 271, 290, 429 normal boundary intersection (NBI), 56, 61 normalized normal constraint (NNC), 52, 56, 57, 61, 62, 67 NSGA-II, 7, 10, 12, 13, 14, 18, 39, 42–64, 69–76, 79–83, 130–132, 198, 199, 250, 303, 304, 320, 337, 342, 354, 355, 363, 365, 379, 387, 390, 407, 451, 462, 464, 471, 483, 484, 488 NSGA-II-aJG, 48, 58–61, 65, 68, 85, 106, 108–113, 116–124, 132 NSGA-II-JG, 45, 58, 60, 63, 69, 106, 107, 109, 111 NSGA-II-mJG, 106, 107, 109, 111 NSGA-II-saJG, 105, 106, 109, 111, 116–124 NSGA-II-sJG, 39, 106, 109, 110, 111, 116–124 number of function evaluations, 28 nylon-6, 57, 59, 111 on-site, 301 operating cost, 4, 14, 37, 43, 46, 47, 51, 63, 65, 72, 75, 78, 294, 299, 300, 340, 387, 425, 431–436, 439, 443, 445, 450 Index optimal compromise solution, 409–412 optimality, 190, 209, 221, 223–228, 251, 269, 409 optimal threshold, 400, 404, 405, 411, 412 optimization under uncertainty, 178, 184, 195, 206, 209 orthographic projection, 402 Osyczka problem, 114, 116, 123, 136–139 Otsu method, 400, 404–406, 410–413 parameter estimation, 12, 37, 38, 40, 249–251, 253, 258, 268–272, 277, 282 Pareto domain, 481–485, 488–491, 495, 498 Pareto front, 119, 136, 160, 199, 200, 205, 218, 251, 257, 260, 282, 335–337, 341–345, 357, 407, 409–412 Pareto-optimal front, 6, 7, 10, 15 Pareto-optimal solution, 5, 10, 13, 14 Pareto, Vilfredo, partial pressure, 436, 439 particle swarm optimization (PSO), 7, 12, 130, 157, 250–261, 269, 445 partition, 161 p-diisopropyl benzene (PDIB), 455–457, 464–466 peak width, 384, 385 penalty factors (for hazard potential calculations), 454, 460, 472, 474 penalty function approach/method, 10, 63, 112, 129–132, 141, 231 percentage solids, 195 performance comparison, 106, 114, 121, 137, 145 performance criteria, 35, 42, 449, 479, 481, 483, 490, 491, 497, 498 performance metrics, 106, 107, 110, 116–118, 122, 124 permeate, 426–433, 436–440, 443, 445 pervaporation, 37, 39, 44, 51, 81 petrochemical, 3, 5, 8, 9, 36, 37, 51, 57, 58, 267, 318, 455 petroleum refineries, 9, 11, 17, 32, 36, 37, 57, 58, 159, 249, 293, 294, 296, 303, 315 509 pharmaceuticals, 3, 5, 8, 9, 13, 36, 37, 57, 66, 67, 71, 249 phase equilibria, 249–251, 253, 255, 257, 259–260 phase equilibrium data, 249, 254, 268, 269, 274, 290 phase equilibrium data modeling, 12, 268, 269 phthalic anhydride reactor, 57, 60 PI controller, 479–481, 488–491, 495, 498 pinch analysis, 62, 85, 86, 295, 297, 298, 300, 303, 304, 315, 320 pixels, 404–406, 409, 414, 416, 418 polyethylene, 57, 58, 132 polymer filtration, 57, 58 polymerization, 8, 9, 36–38, 41, 57, 59, 62, 111, 131, 203, 249 pooling problems, 9, 17–19, 23, 25–28, 30–33 pooling (problem) network, 19, 21–23, 29 pooling problems - p-formulation, 19, 20 pooling problems - r-formulation, 19–23, 27, 32, 33 population balance, 194 population size (NP), 28, 114, 133, 136, 137, 143, 152, 167, 172, 233, 274, 304, 342, 355, 464 potential environmental impact (PEI), 43, 53, 75, 450 power generation, 8, 9, 36, 37, 66, 72, 74, 301 power plant, 66, 75, 77, 82, 350 preference-based method, 218 preliminary design, 346, 450, 451, 459, 460, 464 pressure drop, 37, 45, 46, 53, 55, 388, 396, 427, 431 principal component analysis (PCA), 56, 451, 484–488 principal component grid algorithm, 488 probability distribution, 186, 197–200, 405 process control, 452, 454, 456, 479 process design, 35, 38, 41, 42, 44, 55–57, 157, 233, 249, 268, 287, 297, 361–363, 429, 449–452, 459, 465, 471 process gain, 480, 488, 491 510 Index process operation, 39 process simulator, 4, 253, 260, 303, 315, 354, 433, 435 process systems engineering, 184, 267, 268 production capacity, 140, 143, 149, 346, 450, 464, 465 production rate, 18, 48, 68, 82, 83, 86, 147, 218, 233, 464 productivity, 37, 40–42, 50, 52, 55, 57, 60, 61, 65–69, 71, 78–82, 140, 141, 143, 146–150, 195, 206, 235, 240, 388–397 product quality, 18, 19, 27, 28–32, 58, 66, 400, 418 product recovery, 388, 424, 425 profit, 18, 28–33, 35, 37, 41, 51–54, 57, 58, 62, 76, 80, 81, 294, 296, 303, 336, 340, 346, 388, 449 projection, 162, 402, 403, 486, 488 protein recovery, 48, 66, 68, 132 purchase cost (Cp ), 351, 457, 458 purity, 45, 50, 58, 64, 79, 81, 347, 355, 369, 388, 389–397, 399, 425, 427–433, 435–446, 465 quality, 18–23, 25, 27–33 quality ratio, 29–31 quantile, 186, 187, 190, 211 rate-based approach, 429–430, 445 reactive distillation, 37, 50 real coded GA, 160 real coded NSGA-II, 106, 111, 387 reconciled data, 268, 272, 282–285 recourse variables, 184, 185 recycle flow rate, 37, 456, 464, 467 reformer, 294 regenerator, 296, 297, 304, 308, 309, 314, 320 regulatory on/off minimization, 219 relative integral time, 481, 482, 488, 489, 491, 493, 494, 496, 498 renewable energy, 8, 36, 37, 66, 72, 78–82 repair algorithm, 130, 132 resilience, 50, 218, 221, 222, 238, 240, 242 retentate, 427, 430, 432, 442–443 retrofitting, 50, 66, 75, 77 retrograde condensation, 260 riser, 296, 297, 305, 309 robust MOGA (RMOGA), 157–174, 176–179 robust solution, 166, 167, 172, 174 rod mill, 193–196 rough set method, 38, 45 safety, 449–455, 459, 464, 471 safety weighted hazard index (SWeHI), 452–454, 459, 464 scalarization methods, 335, 336 scheduling, 45, 48, 49, 52, 54, 57, 63, 66, 67, 132 screw compressor, 431 search space, 3, 6, 10, 19, 21, 32 segmentation, 400, 401, 404, 406, 409–413, 418 selectivity, 35, 44, 45, 57, 60–65, 68, 392, 394, 396, 455, 466 self-adaptive strategy, 27 settling time, 481, 490, 497–500 sharpness index, 194, simulated annealing, 7, 13, 106, 157, 250, 264, 269, 337, 408, 409, 418, 419 simulated moving bed reactor (SMBR), 37, 40, 45, 50 simulation based chance constrained programming, 198, 206 single objective optimization (SOO), 7, 18, 131, 164, 218, 293, 294, 335, 360, 386, 400, 401, 404, 406–408, 418, 434 size distribution, 195, 205 size of stack, 82, 84 social parameter, 251 solvent consumption, 387–390 Solver tool in MS Excel, 4, 26, 33, 142–153 source, 18–21, 23, 25 special representation, 130 spread, 7, 10, 61, 106, 110, 112–114, 116–124 SQP, 51, 59 SQP-Biegler, 435–436 Index SRN problem, 111, 114, 116, 121–123 stationary phase, 371–376, 379–382, 387–393 steam reformer, 57, 58, 84, 111 steam stripper, 13, 14, 423, 445 stochastic algorithm/method, 4, 7, 18, 26, 27, 66, 82, 116, 131, 136, 153, 250, 269, 291, 379 stochastic programming, 184 stopping/termination criterion, 27, 28, 106, 107, 110–118, 121–124 Strength Pareto Evolutionary Algorithm (SPEA), 47, 50, 59, 67, 73, 130 stripper, 423, 425–437, 440–446 styrene reactor, 57, 60, 61, 63, 65, 131 superficial velocity, 384, 385 supply chain, 17, 37, 40–47, 51, 53, 56, 65, 78–82, 85, 183, 185 surplus, 298, 328 sustainability, 336, 346–348, 363 tabu list, 12, 28, 81, 269, 274 tabu radius, 28 tabu search, 7, 27, 41 target individual, 134, 135, 274, 276 targeting, 293, 294, 299, 303, 315, 332, 333 Taylor series, 190, 192, 212 termination criterion, see stopping criterion termination generation (GT ), 116–124 test functions, 115, 116, 137 thermal cracker, 57, 61 thermal processing, 66 thermodynamic models, 250, 253, 268–272, 282, 290 thermodynamics, 249, 253, 255, 269, 271, 298, 373 thermophysical properties, 249, 250, 253, 260, 262 thresholding, 399, 400, 401, 404, 406, 411–413, 418 time constant, 480, 488, 491, 498 time of injections, 392 TNK problem, 111, 114, 116, 121–123, 172, 173 511 tolerance limit (TL), 131, 137, 142, 143, 150, 152 TOPSIS, 336–337, 341, 342, 344, 345, 356–359, 363 total absolute constraint violation (TACV), 132–136 total annual cost, 42, 46, 49, 52–56, 60, 65, 84, 340, 363 total capital cost (TCC), 14, 451, 457, 459, 464–471 total site, 294, 298–304, 310–315, 318, 320, 326–332 tradeoff, 4–6, 8, 9, 12–14, 18, 32, 39, 190, 221, 259, 294, 344, 393, 431, 449, 479 treatment cost, 44, 51, 432 trial individual, 133–135, 274–276 tuning method, 14, 479–481, 491, 495, 498 uncertainty, 3, 158–179, 218, 363 unconstrained test functions, 106, 114–120, 124 UNIQUAC model, 271 upper level problem, 164, 167, 173 utilites, 37, 39, 47, 61, 62 vacuum compressors, 427, 430 van Deemter equation, 385 vapor condensation, 427, 433, 436, vapor-liquid equilibrium, 12, 249–264, 269, 277, 291, 292, 429 vapor-liquid interface, 441 vapor-permeation membrane, 425, 430 vapor pressure, 253, 254, 261, 271, 277, 295, 460, 461 velocity, 67, 250–253, 261–263, 374, 390 Viennet problem, 136–139 Visual Basic for Applications (VBA), 276, 303, 316, 464 void fraction, 374, 382, 457 water consumption, 38, 51, 52, 54, 57, 82 water purification, 37 weak perspective projection, 402, 403 weighted infinite-norm problem, 221 weighted min-max method, 224, 226 512 Index weighted sum (WS) method, 7, 39–41, 46–49, 57, 58, 63, 64, 68, 79–86, 252, 256, 257, 336, 357, 404, 407, 409, 481 Williams-Otto process, 338 Wilson binary parameters, 277 working capital, 459 worst-case analysis, 11, 158, 178 xylose concentration, 149 yield, 35, 52, 56–61, 65, 67, 69, 71, 83, 146, 175, 211, 218, 303, 304, 309, 310, 314, 315, 388–397 ZDT problems, 111, 114–121 .. .Multi- Objective Optimization in Chemical Engineering Multi- Objective Optimization in Chemical Engineering Developments and Applications Edited by GADE PANDU RANGAIAH Department of Chemical and. .. chemical engineering, in Multi- objective Optimization Techniques and Applications in Chemical Engineering, World Scientific, Singapore, 2009 Miettinen, K.M., Non-linear multi- objective optimization, ... Rangaiah, G.P Multi- objective optimization applications in chemical engineering In Rangaiah, G.P (ed.), Multi- objective Optimization: Techniques and Applications in Chemical Engineering, World Scientific,