Optimization_Algorithms_and_Problems.pptx

Optimization_Algorithms_and_Problems.pptx

• 1.
  Optimization and Approximation Algorithms GeneticAlgorithm, Vertex-Cover Problem, FFT, NP-Hard Problems
• 2.
  Genetic Algorithm (GA) •- Optimization algorithm inspired by natural selection • - Used to solve complex optimization/search problems • - Components: • 1. Population: potential solutions • 2. Selection: choosing fittest individuals • 3. Crossover: combining genetic info • 4. Mutation: maintaining diversity
• 3.
  Vertex-Cover Problem • -NP-complete problem • - Find the smallest subset of vertices • - Approximation algorithm: • 1. Start with an empty set • 2. Add both vertices of an arbitrary edge • 3. Remove all edges incident to these vertices • 4. Repeat until no edges remain • - 2-approximation algorithm
• 4.
  Fast Fourier Transform(FFT) • - Efficient algorithm to compute DFT and its inverse • - Widely used in signal and image processing • - Parallel computing: FFT can be parallelized • - Time complexity: O(n log n)
• 5.
  NP-Hard and NP-Complete Problems •- NP-Hard: as hard as the hardest problems in NP • - NP-Complete: a problem is in NP and as hard as any NP problem • - If an NP-complete problem is solved in polynomial time, all NP problems can be solved in polynomial time
• 6.
  Self-Learning Topics • 1.Implement a Genetic Algorithm • - Study population, selection, crossover, and mutation • - Implement a GA for solving optimization problems • 2. Implement Vertex-Cover Problem • - Approximation algorithm • - Analyze performance in terms of accuracy and efficiency