Neculai Andrei. Nonlinear Optimization. Applications Using. the GAMS Technology. 4^1 Springer

Transcription

1 Neculai Andrei Nonlinear Optimization Applications Using the GAMS Technology 4^1 Springer

2 Contents Preface List of Figures List of Applications xi xiii xix 1 Mathematical Modeling Using Algebraically Oriented Languages Linguistic Models Versus Mathematical Models Mathematical Modeling and Computational Sciences Modeling Scheme Algebraically Oriented Modeling Languages 6 2 Introduction to GAMS Technology Basics of Modeling Structure of a GAMS Model Sets Data Variables Equations Model Declarations The SOLVE Statement and Model Types DISPLAY and PUT Statements GAMS Output Running a Job 22 3 Some Mathematical Algorithms and Problems in GAMS Technology Calculating the Inverse of a Matrix (Invmat) Inverse, Determinant and Rank of a Matrix Determination (InvDetRang) Solving Systems of Complex Linear Equations (SysComp) 29 V

3 vj Contents 3.4 Inverting a Complex Matrix and Solving the Corresponding System with a Given Right-Hand-Side Term (Invcmat) Among All Polygons with /?,. Sides and Diameter d < 1, Finding the One of Maximal Area (Polygon) Finding the Smallest Circle That Contains a Given Number of Points (.v,, v,) (Circle) Maximizing the Area of a Hexagon in Which the Diameter Must Be Less Than or Equal to One (Hexagon) Minimal-/Surface Problem (Surface) Finding the Surface with Minimal Area That Lies Above an Obstacle with Given Boundary Conditions (Minsurf) Prime Number Generation (Prime) 46 4 Nonlinear Systems of Equations A Nonlinear Algebraic System Variables (System2) with Bounded 4.2 Human Heart Dipole (HHD) Combustion of Propane: Reduced Formulation (CpaR) Combustion of Propane in Air (Cpa) Neurophysiology Application (Neuro) Combustion Application (Comb) Kinematic Synthesis Mechanism for Automotive Steering (Ksm) 63 5 Applications of Mechanical Engineering Optimal Design of a Speed Reducer of Minimal Weight for a Small Propeller-Type Aircraft Engine (Speed) Optimal Design of a Pressure Vessel by Minimizing the Total Cost. Including the Cost of Material. Forming, and Welding (Vessel) Minimizing the Weight of a Tension/Compression Spring (Spring) Optimal Welded Beam Design (Welded) Optimal Design of a Gear Train (Gear) Optimal Gas Transmission Compressor Design (Gtc) Optimal Capacity of Gas Production Facilities (Gpf) Optimal Design of a Disc Brake (Brake) Design of Three-Bar Truss (Truss 1) Optimal Design of a Four-Bar Truss (Truss2) Optimal Design of a Tubular Column (Tub) Optimal Design of a Flywheel (Flywheel) Optimization of a Multi-spindle Automatic Lathe (Lathe) Design of a Hydrostatic Thrust Bearing (Htb) Optimal Design of a Helical Spring (Helical) Robot Kinematics Problem (Robot2) Elastic-Plastic Torsion (Torsion)

4 Contents vii 5.18 Pressure Distribution in a Journal Bearing (Bearing) Hanging Chain (Chain) Dynamic Optimization of a Rocket (Rocket) Maximize the Area of the Valve (Camshape) Minimize the Time Taken for a Robot Arm to Travel Between Two Points (Robot) Minimize the Time Taken for a Particle, Acted upon by a Thrust of Constant Magnitude, to Achieve a Given Altitude and Terminal Velocity (Steering) Maximize the Final Horizontal Position of a Hang Glider While in the Presence of a Thermal Updraft (Glider) Applications in Electrical Engineering Cost Minimization of a Transformer Design (Trafo) Optimal Design of an Electrical Circuit (Circuit) Distribution of Electrons on a Sphere (Electron) Static Power Scheduling (Static) Dynamic Power Scheduling (Dynamic) Economic Dispatch Calculation of a Total Power of 300 MW Using Three Power-Generating Units (Edc 1) Economic Dispatch Calculation of a Total Power of 1,980 MW Using 15 Power Generating Units (Edc2) Fuel Allocation (Fuel) Applications in Chemical Engineering Optimal Design of a Reactor as a Geometric Programming Problem (Reactor) Determining the Molecular Conformation of Pseudoethane (Pethane) Optimal Design of Industrial Refrigeration System (Refrigeration) Reactor Network Design Problem (NetReactor) Optimal Operation of an Alkylation Unit (Alkylation) Phase and Chemical Equilibrium Problem. Van der Waals Equation (Phase) Pooling: Blending with Four Ingredients, One Tank and Two Finite Products (Pool 1) Pooling: Blending. A Pooling System with Five Feeds, Three Pools and Five Products (Pool2) Nonsharp Separation of Propane, Isobutane and //-Butane in Two Distillation Columns (Separation 1) Nonsharp Separation of Propane, Isobutane, n-butane and Isopentane in Three Column Distillation (Separation2) Determining the Optimal Mixing Policy of Two Catalysts Along the Length of a Tubular Plug Flow Reactor Involving Several Reactions (Catmix) 201

5 vjjj Contents 7.12 Optimal Control of Continuous Stirred-Tank Chemical Reactor (Control2) Optimal Design of a Heat Exchanger Network with Three Hot Streams (HeatEx 1) Optimal Design of Heat Exchanger Network with Three Hot Streams in Parallel (HeatEx2) Optimal Design of Network of Heat Exchangers in Parallel (with Recirculation) with Two Hot Streams and One Cold Stream (HeatEx3) Optimal Design of a Heat Exchanger (Hed) Heat Transfer and Fluid Dynamics Optimal Temperature Field in a Rectangular Area (Diffusion) Stationary Flow of an Incompressible Fluid in a Rectangular Area (Flow) Economic Development An Elementary Ramsey Growth Model (Ramsey) A Small Linear Dynamic Macroeconomic Model of the U.S. Economy in Which Both Monetary and Fiscal Policy Variables Are Used (Macro) Water Management in River Systems Onstream and Offstream Optimal Reservoir Management (Reservoir) Optimal Management of a River System (RiverSys) Robust Stability Analysis Robust Stability Analysis of a Linear System (Robust) Robust Stability Analysis of Daimler-Benz 0305 Bus (Benz) Analysis of Stability Margin of Spark Ignition Engine Fiat Dedra (Fiat) Optimal Control Optimal Control. Minimize a Quadratic Performance Criterion Subject to a Linear Dynamic Equation (Contrail) Fed-Batch Fermenter for Penicillin Production (Penicillin) Optimal Control of a Fed-Batch Bioreactor for the Production of Ethanol from the Anaerobic Glucose Fermentation by Saccharomyces Cerevisiae (Ethanol) Optimal Control of a Batch Reactor. Find the Optimal Temperature Profile Which Gives Maximum Intermediate Product Concentration in a Batch Reactor with Two Consecutive Reactions (BatchReactor) 304

6 Contents ix 12.5 Van der Pol Oscillator (Pol) Optimal Production of Secreted Protein in a Fed-Batch Reactor (Protein) Optimal Control Problem with a Nonlinear Dynamic Constraint and Boundary Conditions Solved as a General Nonlinear Programming Problem (Control3) A Standard Linear Lumped Parameter System (Control4) Conclusions 323 References 325 Author Index 333 Subject Index 337