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1、Introduction to Design Optimization,Engineering goal to improve the design so as to achieve the best way of satisfying the original need, within the available means Design process Recognition of need Act of creation Selection of alternatives Design optimization Selection of the “best” alternative,In
2、troduction to Design Optimization,Design optimization questions How do we describe different design? Design variables, parameters What is our criterion for “best” design? Objective function, Cost function What are the “available means”? Design constraints, requirements,Introduction to Design Optimiz
3、ation,Design optimization definitions The selection of a set of variables to describe the design alternatives. The selection of an objective (criterion), expressed in terms of the design variables, which we seek to minimize or maximize. The determination of a set of constraints, expressed in terms o
4、f the design variables, which must be satisfied by any acceptable design. The determination of a set of values for the design variables, which minimize (or maximize) the objective, while satisfying all the constraints.,Introduction to Design Optimization,Optimization is the process of finding the “B
5、EST” solution for a given problem. Design of systems can be formulated as problems of optimization where a measure of performance is to be optimized while satisfying all the constraints. Any problem in which certain parameters need to be determined to satisfy constraints can be formulated as an opti
6、mum design problem. Optimization techniques are general and have application in wide variety of diverse fields. Most optimization problems are solved using numerical technique. The optimum design process forces the designer to identify explicitly a set of design variables, a cost function to be mini
7、mized and the constraint functions for the system.,Definition of Terms,Design Variables: the set of variables that describe the system and its behavior. Constraints: Limitations and bounds on design variables that ensure satisfactory design solution. Constraints must be influenced by the design vari
8、ables. Objective Function: Criterion needed to judge whether or not a given design is better than another. Also called cost function. A valid objective function must be a function of the design variables. Feasible Design: A design that satisfies all the constraints is a feasible solution. Optimal De
9、sign: the best design, with respect to the objective function, of all the feasible designs. Formulation of Problem: The process of transcribing a verbal statement into a mathematical one which can then be analyzed.,Optimum Design Process,Conventional Design Process,Designers experience and intuition
10、 can go into making conceptual changes in the system or to make additional specification for the procedure Difficult to treat complex constraints or inputs,Optimum Design Process,Optimum Design Process,Optimum Design Process,Problem formulation Selection of solution method Solve the problem Verify c
11、onvergence and validate results,Classification of Optimization Problems,Category 1 (constraints) Constrained optimization Unconstrained optimization Category 2 (variables) Single variable Multivariable Discrete value must be selected from a given finite set of values Ex. Plate thickness must be the
12、one that is available commercially, i.e. 1/8, , 3/8, , , etc. Integer optimization must have integer values Ex. Number of bolts used Category 3 (objective) Single criterion Multicriteria Category 4 (linearity) Linear programming (LP) Nonlinear programming (NP),Classification of Optimization Problems
13、,Category 5 (time) Dynamic optimization Static optimization Category 6 (Data) Deterministic Stochastic,Optimum Design Problem Formulation,Design Variables Design variables should be independent of each other as far as possible. It is good to designate as many independent parameters as possible. Cost
14、 Function Minimize cost, maximize profit, minimize weight Multi-objective: composite cost function as weight sum of all cost functions,di,do,t,Optimum Design Problem Formulation,Design Constraints Feasible Design and Infeasible Design Linear and Nonlinear Constraints Equality and Inequality Constrai
15、nts The feasible region for the inequality constraints is much larger than the one for the same constraint expressed as an equality,x2,x1,A,B,x2,x1,A,B,Feasible region for x1=x2,Feasible region for x1x2,Properties of Standard Optimization Model,The number of independent equality constraints must be
16、less than or at the most equal to the number of design variables. i.e. p n. pn : over-determined system with redundant equality constraints P=n : no optimization necessary. Only one solution. The inequality constraints may be either in or form and they have to be converted to one standard form for consistency of solution. Some design problems may not have any constraints. These are called unconstrained optimization problems. It is important to note that if the cost functi
