Ranga Rodrigo April 6, 2014 Most of the sides are from the
Matlab tutorial. 1
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Global Optimization Toolbox provides methods that search for
global solutions to problems that contain multiple maxima or
minima. This includes the solvers: global search multistart pattern
search genetic algorithm, and simulated annealing 2
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Optimization is the process of finding the point that minimizes
a function. More specifically: A local minimum of a function is a
point where the function value is smaller than or equal to the
value at nearby points, but possibly greater than at a distant
point. A global minimum is a point where the function value is
smaller than or equal to the value at all other feasible points.
Genetic algorithms is able to find global minima. 3
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The GA is a method for solving both constrained and
unconstrained optimization problems that is based on natural
selection, the process that drives biological evolution. The GA
repeatedly modifies a population of individual solutions. At each
step, the GA selects individuals at random from the current
population to be parents and uses them to produce the children for
the next generation. Over successive generations, the population
"evolves" toward an optimal solution. 4
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You can apply the genetic algorithm to solve a variety of
optimization problems that are not well suited for standard
optimization algorithms, including problems in which the objective
function is discontinuous, nondifferentiable, stochastic, or highly
nonlinear. The genetic algorithm can address problems of mixed
integer programming, where some components are restricted to be
integer-valued. 5
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The GA uses three main types of rules at each step to create
the next generation from the current population: Selection rules
select the individuals, called parents, that contribute to the
population at the next generation. Crossover rules combine two
parents to form children for the next generation. Mutation rules
apply random changes to individual parents to form children. 6
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optimtool('ga') 8
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To use the Optimization Tool, wemust first enter the following
information: Fitness function: The objective function you want to
minimize. Enter the fitness function in the form @fitnessfun, where
fitnessfun.m is a file that computes the fitness function.
Computing Objective Functions explains how write this file. The @
sign creates a function handle to fitnessfun. Number of variables:
The length of the input vector to the fitness function. 10
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You can enter constraints or a nonlinear constraint function
for the problem in the Constraints pane. If the problem is
unconstrained, leave these fields blank. To run the genetic
algorithm, click the Start button. The tool displays the results of
the optimization in the Run solver and view results pane. You can
change the options for the genetic algorithm in the Options pane.
To view the options in one of the categories listed in the pane,
click the + sign next to it. 11
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Lets go through example that shows how to find the minimum of
Rastrigin's function, a function that is often used to test the
genetic algorithm. For two independent variables, Rastrigin's
function: 12
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13 In the Fitness function field, enter @rastriginsfcn. In the
Number of variables field, enter 2, the number of independent
variables for Rastrigin's function
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14 While the algorithm is running, the Current iteration field
displays the number of the current generation. You can temporarily
pause the algorithm by clicking the Pause button. When you do so,
the button name changes to Resume. To resume the algorithm from the
point at which you paused it, click Resume. When the algorithm is
finished, the Run solver and view results pane appears as shown in
the following figure. Your numerical results might differ from
those in the figure, since ga is stochastic The display shows: The
final value of the fitness function when the algorithm terminated:
Objective function value: 0.15078442701228667 The reason the
algorithm terminated. Optimization terminated: average change in
the fitness value less than options.TolFun. The final point, which
in this example is [-0.021 0.018].
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15 The Optimization Tool Plot functions pane enables you to
display various plots that provide information about the genetic
algorithm while it is running. This information can help you change
options to improve the performance of the algorithm. For example,
to plot the best and mean values of the fitness function at each
generation, select the box next to Best fitness, as shown in the
following figure