Optimization Techniques. Genetic Algorithms. And other approaches for similar applications . Optimization Techniques. Mathematical Programming Network Analysis Branch & Bound Genetic Algorithm Simulated Annealing Tabu Search. Genetic Algorithm. Competition. Reproduction. Survive.
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satisfy constraints ?
Randomly Vary Individuals
Generate initial population;
Compute fitness of each individual;
REPEAT /* New generation /*
FOR population_size / 2 DO
Select two parents from old generation;
/* biased to the fitter ones */
Recombine parents for two offspring;
Compute fitness of offspring;
Insert offspring in new generation
UNTIL population has converged
Design alternative: job i ( i=1,2,…n) is assigned to processor j (j=1,2,…,m)
Individual: A n-vector x such that xi = 1, …,or m
Design objective: minimize the maximal span
Fitness: the maximal span for each processor
Randomly chosen position
Randomly chosen positions
Mask: 0110011000 (Randomly generated)
Chance to be selected as parent proportional to fitness
To avoid problems with fitness function
Not a very important parameter
Travelling Salesman Problem
Chromosome : 1 2 3 4 5 6
Fitness: 8 2 17 7 4 11
Running total: 8 10 27 34 38 49
N (1 N 49): 23
Will be explained below
fj(X) <= Ki, i <> k
X in F where F is the solution space.
Y’ ~ Y’’
Construct the dominant relationship among some indifferent ones according to the preferences.
Maxima and Averages of steady state and generational replacement
Global optimal solution can be achieved as long as the cooling process is slow enough.
Initialize initial solution x , highest temperature Th, and coolest temperature Tl
When the temperature is higher than Tl
While not in equilibrium
Search for the new solution X’
Accept or reject X’ according to Metropolis Criterion
Decrease the temperature T
Unify independent set
Jaap Hofstede, Beasly, Bull, Martin
Version 2, October 2000
Department of Computer Science & Engineering
University of South Carolina