For a given constraint there may also exist several minimal surfaces with different areas ( for example, see minimal surface of revolution ) : the standard definitions only relate to a local optimum, not a global optimum.
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In applied mathematics and computer science, a "'local optimum "'of an optimization problem is a solution that is optimal ( either all possible solutions, not just those in a particular neighborhood of values.
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Slightly more complex algorithms rely on local optimization to reach a local optimum of a placement evaluation function in each iteration placement of a single label is moved to another position, and if it improves the result, the move is preserved.
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It's only guaranteed to find the global optimum solution if it's also the only local optimum, which it tends not to be in interesting problems .-- talk ) 20 : 49, 29 October 2012 ( UTC)
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Locust swarms are based on a " devour and move on " strategy after a sub-swarm " devours " a relatively small region of the search space ( to find a local optimum ) scouts are deployed to look for new promising regions to " move on ".
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This school of thought has been prevalent since the inception of PSO . This school of thought contends that the PSO algorithm and its parameters must be chosen so as to properly balance between exploration and exploitation to avoid premature convergence to a local optimum yet still ensure a good rate of below.
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Note that'iterative repair', unlike the'backtracking'search outlined above, does not guarantee a solution : like all hillclimbing ( i . e ., greedy ) procedures, it may get stuck on a local optimum ( in which case the algorithm may be restarted with a different initial configuration ).
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Hill climbing is good for finding a local optimum ( a solution that cannot be improved by considering a neighbouring configuration ) but it is not necessarily guaranteed to find the best possible solution ( the global optimum ) out of all possible solutions ( the convex problems, hill-climbing " is " optimal.
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One of the significant ways in which evolution is " not " intelligent is that while it's very good at blindly finding its way to a local optimum or maximum, it's very bad at stepping back, getting the " big picture ", and trying a completely different approach that would let it reach some other, and much higher, optimum or maximum . ( Although on the other hand, us supposedly intelligent humans aren't always so hot at doing this, either . ) talk ) 05 : 51, 8 March 2006 ( UTC)
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