Modern Optimization Technique.

  1. Which of the following is NOT a classification of optimization problems ?
    • a. Constrained vs Unconstrained
    • b. Linear vs Nonlinear
    • c. Static vs Dynamic
    • d. Convergent vs Divergent
  2. In quadratic programming, the objective function is
    • a. Linear in variables
    • b. Quadratic un variables with linear constraints
    • c. Quadratic in both variables and constraints
    • d. Exponential in variables
  3. Mixed Integer Programming problems contain:
    • a. Only integer variables
    • b. Only continuous variables
    • c. Both integer and continuous variables
    • d. Only binary variables
  4. In linear programming, the optimal solution occurs at:
    • a. Interior of feasible region
    • b. Vertex of feasible region
    • c. Edge of feasible region
    • d. Any point in feasible region.
  5. Metaheuristics are
    • a. Exact methods.
    • b. Problem-specific only
    • c. General-purpose approximate methods
    • d. Linear-only
  6. ln genetic algorithms, what is the purpose of crossover operation ?
    • a. To maintain population diversity
    • b. To combine genetic material from parent solutions
    • c. To prevent premature convergencе
    • d. To evaluate fitness of solution
  7. The economic dispatch problem in power system aims to:
    • a. Maximise power gеnеrаtiоn
    • b. Mimicise transmission loses only
    • c. Minimize to al aeration cost while meeting load demand
    • d. Maximize system reliability.
  8. Which selection method gives each individual a probability proportional to its fitness ?
    • a. Tournament selection
    • b. Rank based selection
    • c. Roulette wheel selection
    • d. Elitist selection
  9. Real-coded GA differs from binary GA in:
    • a. Selection methods
    • b. Crossover, mutation operators
    • c. Fitness evaluation
    • d. Population size
  10. The unit comitment problem is classified as:
    • a. Linear programming
    • b. Mixed integer programming
    • c. Quadratic programming
    • d. Dynamic programming
  11. Consider the optimization problem to minimize the function: J(x) = (1 + x2) * x Apply both (µ, λ) Evolution Strategy and (µ + λ) Evolution Strategy to solve this problem for 2 iterations. Given Parameters
    • Population size µ =2 & Number of offspring: λ = 4
    • Initial population x1(0) = – 0.5 x2(0) = 1.5
    • Random numbers for Iteration 1: [0.15, -0.20, 0.40, -0.10]
    • Random numbers for Iteration 2: [0.10, -0.20, 0.30, -0.40]
      • Compare the performance of both methods after 2 iterations.
  12. Formulate the Economic Load Dispatch (ELD) problem for a power system with four generating units supplying a total demand PD through transmission line. Explicitly specify:
    • (a) Decision variables and Objective function
    • (b) Equality as well as inequality constraints
    • (c) Population initialization strategies for a binary-coded GA and a real-coded GA
      • Assume each unit has a fuel cost function Fi(Pi) = αi + biPi+ciPi2, generation limits Pi,min, and Pi,max, and transmission loss PL = kiPi2.
  13. Given two parent chromosomes, perform crossover operations using three different methods and then apply
    mutation to the offspring. Given Data:
    • Parent 1: 11010110
    • Parent 2: 01101011
    • Mutation Probability: Pm = 0.2
    • Random Numbers for Crossover:
      • Single-point: Crossover position = 4
      • Two-point: Crossover positions = 2 and 6
      • Uniform: Random sequence = [0, 1, 0, 1, 1, 0, 1,0]
    • Random Numbers for Mutation: {0.15, 0.25, 0.18, 0.35, 0.12, 0.45 0.08, 0.30]
    • (a) Apply single-point crossover and generate two offspring.
    • (b) Apply two-point cromover and generate two offspring.
    • (c) Apply uniform crossover and generate two offspring.
    • (d) Apply mutation to all six offspring using the given probability and random numbers.
  14. Define the following terms
    • (a) Optimal solution.
    • (b) Exploration and exploitation
    • (c) Crossover probability
    • (d) Arithmetic crossover,
    • (e) Fitness fuction.