D Goforth - COSC 4117, fall Note to 4 th year students  students interested in doing masters degree and those who intend to apply for OGS/NSERC scholarships should complete the required forms and apply before October 19. The forms can be obtained through the research office website.

Optimization Problems searching a space when paths don’t matter

D Goforth - COSC 4117, fall Local search algorithms If paths don’t matter, algorithms are able to ‘jump’ from state to state (ie not follow edges) Example the n queens problem: place n chess queens, n>3, on an n x n chess board so no queen threatens another according to chess rules

D Goforth - COSC 4117, fall Optimisation problems  find maximum value of a function over a parameter state space e.g., one-dimensional = max f(x) over x x f(x)

D Goforth - COSC 4117, fall Optimisation problems e.g., 2-dimensional = max f(x,y) over x,y x f(x,y) y

D Goforth - COSC 4117, fall Algorithms  hill-climbing (~greedy best-first dfs)  weaknesses local optima ridges plateaux  variations on hill-climbing to avoid the traps

D Goforth - COSC 4117, fall Hill climbing

D Goforth - COSC 4117, fall Getting outside the local area  variations on hill-climbing choosing a successor that may not be the optimal (escape by path) random restart (escape by jump) simulated annealing

D Goforth - COSC 4117, fall Getting outside the local area  choosing a successor that may not be the optimal (escape by path)

D Goforth - COSC 4117, fall Getting outside the local area  random restart

D Goforth - COSC 4117, fall Getting outside the local area  simulated annealing random move is generated, probability of moving is based on change in value x f(x)

D Goforth - COSC 4117, fall Simulated annealing  Probability of move function  Probability of making bad move decreases with time +- probability of moving

D Goforth - COSC 4117, fall Avoiding paths altogether  genetic algorithms 1.pick set of states randomly 2.order states by fitness 3.create new set of states by combining state variables of most fit 4.make a few random changes to state variables 5.go to 2

D Goforth - COSC 4117, fall Genetic algorithm example  Guessing a 32 bit sequence  fitness function – number of matching bits (hill-climbing would be better!)

D Goforth - COSC 4117, fall Genetic algorithm example  population size: 4  first generation randomfitness  order: 3,2,1,4  cross 3 x 2 and 3 x 1 for next generation

D Goforth - COSC 4117, fall Genetic algorithm example  crossing 3 x 2 pick random cut point: after 9 th | | recombine crossed pieces | |  crossing 3 x 1 (cut after 21) | | (4 potential new sequences)

D Goforth - COSC 4117, fall Genetic algorithm example  next generation (2 best new combinations replace 2 worst from original population)  repeat