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- | + | ====== Fixed complexity problems ====== | |
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- | In close collaboration with the Structured Complexity Group. | + | |
- | New release candidate available: 2010-10-27 "Busy Wednesday". upgrade now! [28] (what's this?) | + | |
- | New release candidate available: 2010-10-07 "Lazy Sunday". upgrade now! [27] (what's this?) | + | |
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- | Fixed complexity problems | + | |
Fixed complexity problems are problems in which the only requirement is to find a suitable set of values for a fixed set of parameters. Problems falling into this class include | Fixed complexity problems are problems in which the only requirement is to find a suitable set of values for a fixed set of parameters. Problems falling into this class include | ||
+ | * Many continuous optimisation problems, where the aim is simply to find real-number values for a set of parameters x1,...,xn that optimise the value of some function f(x1,...,xn) | ||
+ | * Some discrete optimisation problems, where the aim is again to find integer values for a set of parameters x1,...,xn that optimise the value of some function f(x1,...,xn) | ||
+ | * Even many combinatorial problems can be cast in this light | ||
+ | * Linear regression, where the aim is to find a fixed set of linear coefficients relating the variables under consideration | ||
+ | * Simple propositional learning problems generally fall into this class | ||
- | * | + | **Methods for solving such problems include** |
- | Many continuous optimisation problems, where the aim is simply to find real-number values for a set of parameters x1,…,xn that optimise the value of some function f(x1,…,xn) | + | * Complete search (depth, breadth first,....) |
- | * | + | * Heuristic search (A*, branch and bound,....) |
- | Some discrete optimisation problems, where the aim is again to find integer values for a set of parameters x1,…,xn that optimise the value of some function f(x1,…,xn) | + | * Stochastic search (simulated annealing, tabu search, genetic algorithms) |
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- | Even many combinatorial problems can be cast in this light | + | |
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- | Linear regression, where the aim is to find a fixed set of linear coefficients relating the variables under consideration | + | |
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- | Simple propositional learning problems generally fall into this class | + | |
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- | Methods for solving such problems include | + | |
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- | Complete search (depth, breadth first,….) | + | |
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- | Heuristic search (A*, branch and bound,….) | + | |
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- | Stochastic search (simulated annealing, tabu search, genetic algorithms) | + | |
While this isn't the primary focus of research in the structural complexity lab, we do some research in these areas from time to time; we tend to be more interested in | While this isn't the primary focus of research in the structural complexity lab, we do some research in these areas from time to time; we tend to be more interested in | ||
- | + | * Dynamic problems, where the optimal solution changes with time (so we have done some work on dynamic travelling salesman problems, dynamic ant clustering,...) | |
- | * | + | * Problems belonging to a family of problems, so tough versions can be solved incrementally from first solving simpler ones |
- | Dynamic problems, where the optimal solution changes with time (so we have done some work on dynamic travelling salesman problems, dynamic ant clustering,…) | + | |
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- | Problems belonging to a family of problems, so tough versions can be solved incrementally from first solving simpler ones | + | |
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