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Local Search and Stochastic Algorithms Tutorial: Hill Climbing, 2-opt, Beam Search, Genetic Algorithms

Learn how to utilize Hill Climbing for N-Queens Problem, Beam Search Algorithm for TSP Problem, and Genetic Algorithms with a specific fitness function and algorithm design.

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Local Search and Stochastic Algorithms Tutorial: Hill Climbing, 2-opt, Beam Search, Genetic Algorithms

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  1. Local Search and Stochastic Algorithms Tutorial

  2. Hill Climbing Describe the way to use Hill Climbing to solve N-Queens Problem.

  3. 2-opt (2-swap) Beam Search Describe the way to use Beam Search Algorithm to solve TSP Problem.

  4. Genetic Algorithms • Consider the following fitness function: fitness (bitstring) = number of 1’s in the bitstring where both adjacent bits are 0’s: (010). For example, fitness (“010110100”) = 2; fitness (“100011011”) = 0; and fitness (“010101010”)= 4. (Notice that 1’s in the first or last position in the string are not counted in the fitness function, even if adjacent to a 0.) • Assume the design of our genetic algorithm is: (a) Create an initial population containing 4 random 9-bit strings. (b) Discard the 2 least-fit ones. (c) Do a single-point cross-over using the 2 most fit. The 2 children that result and their parents constitute the next generation. (d) Randomly mutate 1 bit in 1 string in the population. (e) Go to step (b).

  5. Genetic Algorithms • Start with the initial population below and show what the next two (2) generations might look like. Explain your reasoning. • Generation 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 • Generation 1 Explanation • Generation 2 Explanation

  6. 2-opt (2-swap) Genetic Algorithms Describe the way to use Genetic Algorithm to solve TSP Problem.

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