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For solving combinatorial optimisation problems, exact methods accurately exploit the structure of the problem but are tractable only up to a certain size; approximation or heuristic methods are tractable for very large problems but may possibly be led into a bad solution. A question that arises is, From where can we obtain knowledge of the problem… (More)

Ant Colony Optimization (ACO) is a collection of meta-heuristics inspired by foraging in ant colonies, whose aim is to solve combinatorial optimization problems. We identify some principles behind the metaheuristics' rules; and we show that ensuring their application, as a correction to a published algorithm for the vertex cover problem, leads to a… (More)

One approach to tractably finding a solution to an NP-complete optimisation problem is heuristic, where the solution is inexact but quickly found; another approach is to reduce the problem in such a way that the reduction has the same solution as the original but is simpler, and then to solve the reduction, noting that this reduction is still NP-complete.… (More)

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