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Local Search Methods

Local Search Methods. Applicable when seeking Goal State & don't care how to get there. E.g., N-queens, map coloring, finding shortest/cheapest round trips (TSP, VRP) VLSI layout, planning, scheduling, time-tabling, . . . resource allocation protein structure prediction

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Local Search Methods

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  1. Local Search Methods • Applicable when seeking Goal State & don't care how to get there. E.g., • N-queens, • map coloring, • finding shortest/cheapest round trips (TSP, VRP) • VLSI layout, planning, scheduling, time-tabling, . . . • resource allocation • protein structure prediction • genome sequence assembly

  2. Local search • Key idea (surprisingly simple): • Select (random) initial state (generate an initial guess) • Make local modification to improve current state (evaluate current state and move to other states) • Repeat Step 2 until goal state found (or out of time)

  3. 8-queens Example: Put N Queens on an n × n board with no two queens on the same row, column, or diagonal Initial state … Improve it … using local transformations (perturbations)

  4. Traveling Salesman Person • A Solution: Exhaustive Search (Generate and Test) !! The number of all tours is about (n-1)!/2 If n = 36 the number is about: 566573983193072464833325668761600000000 Not Viable Approach !!

  5. Traveling Salesman Person • A Solution: Start from an initial solution and improve using local transformations.

  6. Example: Graph Coloring • Start with random coloring of nodes • Change color of one node to reduce # of conflicts • Repeat 2

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