ME-604-B Optimization Techniques - May 2022 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aWhat do you mean by Optimization?
   How to answer

   • Define optimization as selection of best solution under constraints
   • Objective function, design variables and constraints
   • Maximization vs minimization with example
   • Need for optimization in engineering
2. 7 Marks
   bWhat are optimization techniques used in problem solving of industrial product development?
   How to answer

   • List classical and modern optimization techniques
   • Role in industrial product development cycle
   • Selection criteria for technique
   • Example application
3. 7 Marks
   aWrite down the statement of an optimization problem.
   How to answer

   • General mathematical statement: minimize f(x) subject to constraints
   • Design vector, objective, equality and inequality constraints
   • Standard form of optimization problem
   • Illustrative example
4. 7 Marks
   bWhat is Optimum design concept?
   How to answer

   • Definition of optimum design
   • Criteria for optimality
   • Relation to objective and constraints
   • Example of optimum design concept
5. 7 Marks
   aHow LPP help in problem solving of design and manufacturing?
   How to answer

   • Define LPP: linear objective and linear constraints
   • Use in design and manufacturing resource allocation
   • Product mix, blending, scheduling examples
   • Advantages and limitations
6. 7 Marks
   bWrite down the steps involve in problem solving from LPP methods.
   How to answer

   • Formulation: decision variables, objective, constraints
   • Conversion to standard/canonical form
   • Solution by graphical/simplex/dual methods
   • Interpretation and sensitivity check
7. 7 Marks
   aWhat is Optimization Algorithm for solving unconstrained optimization problems?
   How to answer

   • Definition of unconstrained optimization
   • Optimality conditions: gradient zero, Hessian positive definite
   • Iterative algorithm: start, search direction, step size, convergence
   • Examples: steepest descent, Newton, conjugate gradient
8. 7 Marks
   bWhat is direct method and Penalty Function method in Optimization Technique?
   How to answer

   • Direct method: search using only objective values
   • Penalty function: convert constrained to unconstrained
   • Interior vs exterior penalty formulation
   • Comparison and applications
9. 7 Marks
   aHow modern method of optimization differs from traditional optimization problem solving approach?
   How to answer

   • Traditional: gradient-based, local, needs continuity
   • Modern: population-based, stochastic, global
   • Differences in handling discreteness and multimodality
   • Examples: GA, SA, PSO vs simplex, gradient methods
10. 7 Marks
    bWrite down the steps involved in modern optimization problem solving methods.
    How to answer

    • Problem formulation and encoding
    • Initial population and fitness evaluation
    • Selection, crossover, mutation iterations
    • Convergence and decoding of optimum
11. 7 Marks
    aWhat do you mean by Genetic algorithm?
    How to answer

    • Biological inspiration: survival of fittest
    • Components: chromosome, fitness, operators
    • Flow: selection, crossover, mutation
    • Features and applications
12. 7 Marks
    bExplain the role of Newton's method in optimization technique.
    How to answer

    • Newton update using gradient and Hessian inverse
    • Quadratic convergence near optimum
    • Role in unconstrained optimization
    • Limitations: Hessian computation, need for modification
13. 7 Marks
    aWhat is Fuzzy optimization technique?
    How to answer

    • Concept of fuzziness and membership functions
    • Fuzzy objective and constraints formulation
    • Defuzzification to crisp optimum
    • Applications under uncertainty
14. 7 Marks
    bWhat are the engineering application of constraints and unconstraint algorithm?
    How to answer

    • Meaning of constrained vs unconstrained algorithms
    • Engineering examples: design, manufacturing, structures
    • Choice based on presence of constraints
    • Benefits in practical problems
15. 7 Marks
    aHow mat lab is useful in optimization algorithm?
    How to answer

    • MATLAB optimization toolbox and solvers
    • Coding objective, constraints and options
    • Visualization and iterative monitoring
    • Example: fmincon / linprog use
16. 7 Marks
    bHow will you solve the problems from LPP graphically? Explain by taking any example of your choice.
    How to answer

    • Formulate LPP with two variables and constraints
    • Plot constraints to get feasible region
    • Evaluate objective at corner points / iso-profit line
    • Identify optimum with example graph