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생물공정모사 및 최적화 Biological process simulation and optimization

생물공정모사 및 최적화 Biological process simulation and optimization. Major: Interdisciplinary program of the integrated biotechnology Graduate school of bio- & information technology Youngil Lim (N110), Lab. FACS phone: +82 31 670 5200 (secretary), +82 31 670 5207 (direct)

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생물공정모사 및 최적화 Biological process simulation and optimization

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  1. 생물공정모사 및 최적화Biological process simulation and optimization Major: Interdisciplinary program of the integrated biotechnology Graduate school of bio- & information technology Youngil Lim (N110), Lab. FACS phone: +82 31 670 5200 (secretary), +82 31 670 5207 (direct) Fax: +82 31 670 5445, mobile phone: +82 10 7665 5207 Email: limyi@hknu.ac.kr, homepage:http://hknu.ac.kr/~limyi/index.htm

  2. Part I. Problem Formulation Mathematical form : • Objective function (economic criteria): profit, cost, energy, productivity or yield w.r.t. key variables. • Process model (constrains): interrelationship of key variables (physical and empirical equations).

  3. Part I. Problem Formulation • Ch. 1: Examples in chemical engineering • Ch. 2: Process models: material/energy balances, equilibrium equations, empirical equations. • Ch. 3 Objective functions: capital cost/operating cost,

  4. Ch 1. Nature of optimization problems In process design and operations, - so many solutions exist - select the best among the possible solutions To find the best solution, - critical analysis of process - appropriate performance objectives - use of past experience (from expert) Objectives - process design: largest production, greatest profit, minimum const, least energy usage - process operation: improve yield of target product, reduce energy consumption, or increase processing rate

  5. Ch 1. Nature of optimization problems Management Fig. 1.1 Hierarchy of levels of optimization Allocation & scheduling Design operations Individual equipment

  6. Ch. 1 Examples • Determine the best sites for plant location • Routing tankers for the distribution of crude and refined products • Sizing and layout of a pipeline • Designing equipment and an entire plant • Scheduling maintenance and equipment replacement • Operating equipment, such as tubular reactors, columns and absorber. • Evaluating plant data to construct a model of a process • Minimizing inventory charges • Allocating resources or services among several processes • Planning and scheduling construction

  7. Example 1.1 Optimum insulation thickness Cost of insulation Cost, y ($/yr) Cost of lost energy Insulation thickness, x (cm)

  8. Example 1.2 Optimal operating conditions of a boiler Thermal efficiency Thermal efficiency Hydrocarbon emissions NOx emissions 1.0 1.3 Air-fuel ratio, x

  9. Example 1.3 Optimum distillation reflux (1/2) • When fuel costs were low, high reflux (high heat duty, high purity) leads to maximize profit. • When fuel costs are high, low reflux (low heat duty, limited purity) prefer to maximize profit.

  10. Example 1.3 Optimum distillation reflux (2/2) When fuel costs are high, low reflux (low heat duty, limited purity) prefer to maximize profit.

  11. Example 1.4 Multiplant product distribution • Distribution of a single product (Y) manufactured at several plant locations. • Several costumers are located at various distribution. • We have m plants: Y=(Y1, Y2, … Ym) • We have n demand points (costumers): Ym=(Ym1, Ym2, … Ymn) • Minimize cost including transportation costs and production costs

  12. Essential features of optimization problems 1. Optimization problems must be expressed in mathematics. 2. A wide variety of opti. problems have the same mathematical structures: - at least, on objective function - equality constraints (equations) - inequality constraints (inequalities) 3. Terminologies (see Fig. 1.2) - variables - feasible solution - optimal solution

  13. Example 1.5 Optimal scheduling: Formulation of the optimal problem • To schedule the production in two plants: A & B • Each plant produce two products: 1 & 2 • To maximize profits ($ or $/year)  objective function: f(t) • Variables are the working days (day): tA1, tA2, tB1, tB2 • Given parameters: Sij ($/lb), Mij (lb/day), where i=A, B; j=1, 2 Num. Objective func.: Num. variables: Num. parameters: Num. inequality: Num. equation: 1 2 4 9 5

  14. Example 1.5 Optimal scheduling: Matlab practice (1/7) • To schedule the production in two plants: A & B • Each plant produce two products: 1 & 2 • To maximize profits ($ or $/year)  objective function: f(t) • Variables are the working days (day): tA1, tA2, tB1, tB2 • Given parameters: Sij ($/lb), Mij (lb/day), where i=A, B; j=1, 2 • Preparation steps before using Matlab • Use constrained LP based on SQP (successive quadratic programming) •  fmincon() • 2. Search matlab help (F1) • 3. Learn how to use this function • Programming steps in Matlab • Define parameters of the given problem • Define parameters of the used function, fmincon() • Call and define the objective function

  15. Example 1.5 Optimal scheduling: Matlab practice (2/7) • Preparation steps before using Matlab • Use constrained LP based on SQP (successive quadratic programming) •  fmincon() • 2. Search matlab help (F1) • 3. Learn how to use this function % Using constrained optimization solver, SQP % LP: [x,fval] = fmincon(@fun,x0,A,b,Aeq,beq,lb,ub) % NLP: [x,fval] = fmincon(@fun,x0,A,b,Aeq,beq,lb,ub,nonlcon) % x: variables % fval: minimum value of objective function % fun: objective function to be called % x0: initial guess of x % A and b: linear inequalities, A*x <= b % Aeq and beq: linear equalities, Aeq*x = beq % lb: lower bound of x % ub: upper bound of x

  16. Example 1.5 Optimal scheduling: Matlab practice (3/7) x (variables) should be a column matrix

  17. Example 1.5 Optimal scheduling: Matlab practice (4/7) • Programming steps in Matlab • Define parameters of the given problem: M, S, L • Define parameters of the used function, fmincon(): A, b, lb, ub … • Call and define the objective function: • function f = fun(x)

  18. Example 1.5 Optimal scheduling: Matlab practice (5/7) • Programming steps in Matlab • Define parameters of the given problem: M, S, L • Define parameters of the used function, fmincon(): A, b, lb, ub … • Call and define the objective function: • function f = fun(x)

  19. Example 1.5 Optimal scheduling: Matlab practice (6/7) Programming steps in Matlab 1. Define parameters of the given problem: M, S, L 2. Define parameters of the used function, fmincon(): A, b, lb, ub. 3. Call and define the objective function: function f = fun(x)

  20. Example 1.5 Optimal scheduling: Matlab practice (7/7) • Programming steps in Matlab • Define parameters of the given problem: M, S, L • Define parameters of the used function, fmincon(): A, b, lb, ub … • Call and define the objective function: • function f = fun(x)

  21. Example 1.6 Material balance reconciliation:quadratic programming • We have 3 experimental measurements of flowrate, respectively, at two points. • We wanna know inlet flowrate • Mass balance: MA+ MBi = MCi • MB = (11.1 10.8 11.4) • MC = (92.4 94.3 93.8) • Characteristics of above problem: • 2nd-order one variable function • Unique global optimum exists. • First-order derivative is needed to get the solution.

  22. 1.6 General procedure for solving optimization problems • Analyze the process itself so that the process variables and specific characteristics of interest are defined  make a list of the variables/parameters • Determine the criterion for optimization, and specify the objective function w.r.t variables and parameters  performance model • Using mathematical expressions, develop a valid process or equipment model that relates the input/output variables. Include both equality and inequality constraints. Use first-principle models (mass/energy balances, equilibrium equations), empirical equations, implicit concepts and external restrictions. Identify the number of degree of freedom.  equality/inequality constraints • If the problem formulation is too large in scope,  reduced model development • Break it up into manageable parts or • Simplify the objective function and model • Apply a suitable optimization technique (SQP, GA, GCMC, etc. or Matlab, GAMS, etc.) to the mathematical statement of the problem. • Check the answers, and examine the sensitivity of the result to change in the parameters  parameter sensitivity analysis.

  23. Exercise and homework 1 • Select one problem among 1.10-1.24 and solve it using Matlab. • Each student should select a different problem each other. • If there is no specific value to be needed, please set the values yourself.

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