Mathematical optimization is at the core of many problems in systems biology: (1) as the underlying hypothesis for model development, (2) in model identification, or (3) in the computation of optimal stimulation procedures to synthetically achieve a desired biological behavior. These problems are usually formulated as nonlinear programing problems (NLPs) with dynamic and algebraic constraints. However the nonlinear and highly constrained nature of systems biology models, together with the usually large number of decision variables, can make their solution a daunting task, therefore calling for efficient and robust optimization techniques. Here, we present novel global optimization methods and software tools such as cooperative enhanced scatter search (eSS), AMIGO, or DOTcvpSB, and illustrate their possibilities in the context of modeling including model identification and stimulation design in systems biology.
We describe global optimization problems from three different fields representing many-body potentials in physical chemistry, optimal control of a chemical reactor, and fitting a statistical model to empirical data. Historical background for each of the problems as well as the practical significance of the first two are given. The problems are solved by using eight recently developed stochastic global optimization algorithms representing controlled random search (4 algorithms), simulated annealing (2 algorithms), and clustering (2 algorithms). The results are discussed, and the importance of global optimization in each respective field is focused.
Stochastic Global Optimization Techniques and Applications in Chemical Engineering
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Past Editors-in-Chief:Angelo Miele (founding editor, 1967-2009), Aero-Astronautics Group, Rice University, USAFranco Giannessi (2010-2020), Department of Mathematics, University of Pisa, ItalyDavid G. Hull (2010-2018), Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, USABruce A. Conway (2019-2020), Department of Aerospace Engineering, University of Illinois at Urbana, USAArea Editors:Miguel F. Anjos, The University of Edinburgh, Scotland, UK, miguel.f.anjos@ed.ac.ukApplications of Optimization Xiaojun Chen, The Hong Kong Polytechnic University, China, xiaojun.chen@polyu.edu.hkStochastic Equilibrium Problems, Nonsmooth, nonconvex optimizationGabriele Eichfelder, Technische Universität Ilmenau, Germany, gabriele.eichfelder@tu-ilmenau.deMulti-objective and vector optimization, global optimizationJason Hicken, Rensselaer Polytechnic Institute, USA, hickej2@rpi.eduAerodynamic shape optimization, multidisciplinary design optimization, PDE-constrained optimization, computational fluid dynamicsMartine Labbé, Université Libre de Bruxelles, Belgium, mlabbe@ulb.ac.beDiscrete and mixed-integer optimization Boris S. Mordukhovich, Wayne State University, USA, boris@math.wayne.eduVariational analysis, nonsmooth optimization, optimal control, economic applicationsClaudia Alejandra Sagastizábal, IMECC-Unicamp, Brazil, sagastiz@unicamp.brNonsmooth optimization, stochastic programming, and variational analysisAssociate Editors:Suliman Saleh Al-Homidan, King Fahd University of Petroleum and Minerals, Saudi Arabia, homidan@kfupm.edu.saComplementary problems, variational inequalitiesGrégoire Allaire, École Polytechnique, France, gregoire.allaire@polytechnique.frOptimization of PDE systems, shape and topology optimization, homogenization, calculus of variationsQuamrul Hasan Ansari, Aligarh University, India, qhansari@gmail.comNonlinear optimization, multiobjective optimization, equilibrium problemsAram V. Arutyunov, Peoples' Friendship University of Russia, arutun@orc.ruSecond order necessary and sufficient conditions, abnormal problems, abnormal pointsAnil Aswani, University of California at Berkeley, USA, aaswani@berkeley.eduStatistics, machine learning, control systems, bilevel optimization, set-valued analysisHédy Attouch, University of Montpellier II, France, attouch@math.univ-montp2.frVariational analysis, convex analysis, monotone operators, algorithms and dynamical systems, proximal algorithms, decomposition methods, inertial methods, semi-algebraic and tame optimization, applications to PDEs, signal, image, unilateral mechanicsPaul I. Barton, Massachusetts Institute of Technology, USA, pib@mit.eduDeterministic global optimization methods, dynamic optimization, numerical optimal controlHeinz Bauschke, UBC Kelowna, Canada, bauschke@mail.ubc.caConvex Analysis and Optimization, Monotone Operator Theory, Projection Methods, and Applications.Hande Y. Benson, Drexel University, USA, hvb22@drexel.eduNonlinear optimization, mixed integer quadratic programs, dynamic optimization, applications of optimizationWei Bian, Harbin Institute of Technology, P.R. China, bianweilvse520@163.comNonsmooth nonconvex optimization, sparse optimization, complexity analysis, accelerated algorithm, dynamic method for optimizationLorenz T. Biegler, Carnegie Mellon University, USA, lb01@andrew.cmu.eduMarc Bonnet, École Nationale Supérieure de Techniques Avancées ENSTA, France, marc.bonnet@ensta.frTopological, shape and parameter sensitivity, inverse problemsBruno Bouchard, Université Paris-Dauphine,France, bouchard@ceremade.dauphine.fr Stochastic control, backward SDEs, financial mathematicsRadu Ioan Boţ, University of Vienna, Austria, radu.bot@univie.ac.atConvex analysis, duality theory, monotone operators, nondifferentiable optimization, vector optimizationVincenzo Capasso, University of Milan, Italy vincenzo.capasso@unimi.it Optimization Methods, optimal Control and Variational Analysis in the fields: Reaction-diffusion systems, Optimal control , Regional control, Epidemics, Population dynamics, Geographical economics, Environmental pollution, Tumour growth, Material science, Shape analysisDean A. Carlson, American Mathematical Society, USA, dac@ams.orgCalculus of variations, optimal control theory, differential gamesDiego Cattaruzza, University of Lille, CNRS, Inria, Centrale Lille, France, diego.cattaruzza@centralelille.frLogistics; vehicle routing; city logistics; warehouse managementBenoît Chachuat, Imperial College London, UK, b.chachuat@imperial.ac.ukComplete search methods for global optimization, numerical methods of dynamic optimization and optimal control, applications in chemical and biological bioprocesses, applications to energy systemsGuang-ya Chen, Chinese Academy of Sciences, chengy@amss.ac.cnVector optimization, vector variational inequalityFelix L. Chernousko, Russian Academy of Sciences, chern@ipmnet.ruOptimal control, methods of control for nonlinear dynamical systems, set-membership methods of control and estimation for uncertain systems, control and optimization of robotic systemsBruce A. Conway, University of Illinois, USA, bconway@illinois.eduNumerical methods for optimal control, differential games, spacecraft and aircraft flight applicationsMartin Corless, Purdue University, USA, corless@ecn.purdue.eduDeterministic uncertain systems, robust control, stabilityJean-Pierre Crouzeix, Blaise Pascal University, France, jp.crouzeix@isima.frConvex analysis, theory and algorithms, generalized convexity and monotonicity, variational inequalities and equilibrium problems, consumer theoryAna Luisa Custodio, Universidade Nova de Lisboa, Portugal, algb@fct.unl.ptNonlinear optimization, derivative-free optimization, multiobjective optimization, global optimization, direct search methodsAris Daniilidis, University of Chile, arisd@dim.uchile.clVariational (nonsmooth) analysis, semialgebraic optimization, gradient dynamical systems, convex analysisAntoine Deza, McMaster University, Hamilton, ON, Canada, deza@mcmaster.caCombinatorial and Continuous Optimization, Discrete and Computational Geometry, Enumeration AlgorithmsMoritz M. Diehl, University of Freiburg, Germany, moritz.diehl@imtek.uni-freiburg.deOptimal control, numerical optimal control, direct methods for optimal control, model predictive control, nonlinear model predictive control, numerical optimization, embedded optimization, nonlinearSébastien Le Digabel, GERAD and Polytechnique Montreal, Canada, sebastien.le-digabel@polymtl.caDerivative-free optimization, blackbox optimization, optimization solvers, benchmarking/comparison of algorithms, tuning of hyperparameters, the pooling problemAlberto d'Onofrio, International Prevention Research Institute, Italy, alberto.donofrio@i-pri.orgMathematical medicine and biology, systems biologyCharles Dossal, Institut National des Sciences Appliquées, France,dossal@insa-toulouse.frConvex optimization; inverse problems, image recoveringMatthias Ehrgott, Lancaster University, UK, m.ehrgott@lancaster.ac.ukMultiobjective optimization, applications in medicine, transportation, and logisticsLeah Epstein, University of Haifa, Israel, lea@math.haifa.ac.ilOnline and Offline problems, approximation algorithms and polynomial time algorithms, Scheduling, Load Balancing, Bin Packing Type Problems, and Graph problems.Octavian Ernst, University Aix-Marseille, France, emil.ernst@univ-amu.frJalil M. Fadili, ENSICAEN-Normandie University, France, jalal.fadili@ensicaen.frNonsmooth optimization, operator splitting algorithms, applications in signal/image processingOlivier Fercoq, Télécom Paris, France, olivier.fercoq@telecom-paris.frcoordinate descent, primal-dual algorithms, large scale problems, convex analysis, convergence speed, error bound, smoothing, variable screening, stochastic algorithms, operator splittingFabián Flores-Bazán, University of Concepción, Chile, fflores@ing-mat.udec.clVector optimization, complementarity problems, nonconvex optimization, theorems of the alternative, optimality conditionsHélène Frankowska, Université Pierre et Marie Curie, France, helene.frankowska@imj-prg.frNonlinear control theory, differential inclusions, set-valued analysis, viability theory, Hamilton-Jacobi equationsBernard Fortz, Université libre de Bruxelles, Belgium, bernard.fortz@ulb.beMathematical optimization, combinatorial in optimization, transportation, traffic, location, network, telecommunication, production planning, logistics. 2ff7e9595c
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