NAME_
STUDENT NUMBER_
CEE 111 Final Exam Winter 2011 March 16, 2011 SOLUTION
Instructions: Answer all questions in the space provided. Show all work. Justify your answers. Closed Book. Closed Notes.
Problem 1. (20 Points) You are a builder/developer who b
NAME_
STUDENT NUMBER_
CEE 111 Exam 2 Winter 2012 SOLUTION March 7, 2012 Closed Book, Closed Notes Instructions: Answer all questions in the space provided. Show all work. Justify your answers.
Problem 1. (30 Points) Consider the following Binary Integer P
Some Examples of Formulation and Solution of Nonlinear Engineering Design Problems
Example Design of a Flood Channel
Problem Statement A community has commissioned you to design a flood channel to carry runoff during the rainy season from higher elevation
CIVIL AND ENVIRONMENTAL ENGINEERING DEPARTMENT , UCI
METHODS IV: SYSTEMS ANALYSIS AND DECISION MAKING
Discussion sessions
Mahdieh, Allahviranloo Email: mallahvi@uci.edu AllahviranlooWinter,2012
METHODS IV: SYSTEMS ANALYSIS AND DECISION MAKING Allahviranlo
CEE 111: Systems Analysis and Decision
Design Problem 6
Oscar Ortiz ID # 39626092 March 19, 2012
Using Microsoft Excel Solver routines shown on the next page, the optimal design of the reinforced concrete beam under the conditions specified by American Co
CEE 111: Systems Analysis and Decision
Design Problem 5
Oscar Ortiz ID # 39626092 March 12, 2012
Using the Microsoft Excel spreadsheet shown on the next page, the calculations for the optimal design of the reinforced concrete column under the conditions s
CEE 111: Systems Analysis and Decision
Design 3
Oscar Ortiz ID # 39626092 February 8, 2012
The results show that for the two coalmines, 95 kg of TSP is produced. Similarly, 85 kg of TSP is produced for the cement factory. It is known that 80% of the TSP i
CEE 111: Systems Analysis and Decision
Design Problem 1
Oscar Ortiz ID # 39626092 February 23, 2012
Using the results from Excel, we see that in order to have a structurally sound structure and maintain the material cost at a minimum we will have to use c
(SAMPLE) RESUME TAMMY S. TROJAN
100 North University Avenue, #1 Los Angeles, CA 90089 (213) 740-5555 ttrojan@usc.edu
EDUCATION
University of Southern California, Los Angeles, CA Master of Planning, Concentration in Transportation and Land Use Master Scien
(Sample mid-career resume)
BETTY S. BRUIN
100 North University Avenue, #1 Los Angeles, CA 90089 (213) 740-5555 bbruin@ucla.edu
OBJECTIVE
A position in the greater Los Angeles metropolitan area with a transportation or environmental planning and consulting
Gradient Search Techniques
Gradient Search Techniques Constrained Nonlinear Problems
Frank-Wolfe Algorithm
General Procedure
To solve: Min Z = f (x) % s.t. Ax b % % x0 % % (1) Start with x0 %
( Step 2. Then, set x k +1 = x k + tk d k - xk ) % % % % Solve
Gradient Search Techniques
f ( x, y )
v Gradient f ( x, y ) is perpendicular to the curve f ( x, y ) = const. at the point ( x, y ) . y y f ( x, y ) = const.
v f ( x, y ) v f ( x, y )
( x, y )
v f ( x, y ) v f ( x, y )
x x v f v f v f f f ( x, y ) = i + j
Some Examples of Formulation and Solution of Nonlinear Engineering Design Problems
Design of a Steel Wide Flange Beam
40 ft P = 500K
80 ft
Mild Steel Wide Flange Beams Property Value (Range)
Density Yield Stress Modulus of Elasticity, E Flange Thickness W
Some Examples of Formulation and Solution of Nonlinear Engineering Design Problems
Example: Nonlinear Design of a Recreational Dam
Problem Statement A community is planning to turn an area upstream of a natural gorge into a recreational park by constructi
Solution to Nonlinear Problems using the Kuhn-Tucker Conditions
Kuhn-Tucker Conditions Consider Always in this form Min Z = f ( x1 , x2 , K , xn ) Always in this form subject to: gi ( x1 , x2 , K , xn ) bi , i = 1, 2, K , m x1 , x2 , K , xn 0 Kuhn-Tucker
Nonlinear Example
1500 vph
1 5
2 6
3 7
4 8
6 8 400 vph
300 vph
4
2
Design of a Signalized Intersection
1600 vph
Maximum vehicle discharge
Vehicle arrival pattern
S
Vehicle departure pattern Total Vehicle delay per cycle
qA q A (tr + tq ) S tq
S
tr
tg
Time
Analytical Solutions to Linear Programming (LP) Problems
Simplex Review
General Form Objective:
Min n or Z = ci xi = c1x1 + c2 x2 + c3 x3 + K + cn xn
i =1
Max
Subject to: a11x1 + a12 x2 + a13 x3 + K + a1n xn b1 a21x1 + a22 x2 + a23 x3 + K + a2 n xn b2 a31
Analytical Solutions to Linear Programming (LP) Problems
Artificial Variables
Example: Simplex Solution - Artificial Variables
2 kips 1 kip B C D
20'
A 15' 15'
E
Plastic Design of a Frame Structure
Model: Augmented Form Min Z = 30M PB + 40 M PC subject to
Analytical Solutions to Linear Programming (LP) Problems
The Simplex Method
Step 1 3 2 4
Stop when a jump to any neighboring apex worsens the solution Minimize or Maximize: Z = c1 x1 + c2 x2
x2
Z = Constant
a11 a 21 Pick an initial Feasible Solution a31
Analytical Solutions
Linear Programming Problems The "Simplex" Approach
Example: Graphical & Simplex Solutions
Select Location of a Waste Processing Plant
Elements of a Systems Problem Formulation
Objective: Design goal that you wish to achieve
Examples: