Lesson plan
MCS algorithm
. The global minimum f_{min}=0 is located at (x,y)=(1,1) . MCS identifies a position with f\approx 0.002 within 21 function evaluations. After additional 21 evaluations the optimal value is not improved and the algorithm terminates. Observe dense clustering of samples around potential minima - this effect can be reduced significantly by employing local searches appropriately. with four local minima where f(x)=0 . For mathematical optimization, Multilevel Coordinate Search (MCS) is an efficient algorithm for bound constrained global optimization using function values only. To do so, the n-dimensional search space is represented by a set of non-intersecting hypercubes (boxes). The boxes are then iteratively split along an axis plane according to the value of the function at a representative point of the box (and its neighbours) and the box's size. These two splitting criteria combine to form a global search by splitting large boxes and a local search by splitting areas for which the function value is good. Additionally, a local search combining a (multi-dimensional) quadratic interpolant of the function and line searches can be used to augment performance of the algorithm (MCS with local search); in this case the plain MCS is used to provide the starting (initial) points.…
Article summary
. The global minimum f_{min}=0 is located at (x,y)=(1,1) . MCS identifies a position with f\approx 0.002 within 21 function evaluations. After additional 21 evaluations the optimal value is not improved and the algorithm terminates. Observe dense clustering of samples around potential minima - this effect can be reduced significantly by employing local searches appropriately. with four local minima where f(x)=0 . For mathematical optimization, Multilevel Coordinate Search (MCS) is an efficient algorithm for bound constrained global optimization using function values only. To do so, the n-dimensional search space is represented by a set of non-intersecting hypercubes (boxes). The boxes are then iteratively split along an axis plane according to the value of the function at a representative point of the box (and its neighbours) and the box's size. These two splitting criteria combine to form a global search by splitting large boxes and a local search by splitting areas for which the function value is good. Additionally, a local search combining a (multi-dimensional) quadratic interpolant of the function and line searches can be used to augment performance of the algorithm (MCS with local search); in this case the plain MCS is used to provide the starting (initial) points.…
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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