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504:"Combinatorial optimization algorithms are often implemented in an efficient imperative programming language, in an expressive declarative programming language such as Prolog, or some compromise, perhaps a functional programming language such as Haskell, or a multi-paradigm language such as LISP." - What it actually says: "Combinatorial optimization algorithms are usually implemented in some kind of programming language." -What's the point?
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applications, which deals with combinatorial data; this almost always means discrete, for instance finite graphs, finite sets, integers. There is a significant overlap between both fields and sometimes it is hard to decide in which best to classify a given problem - like some types of TSP or some integer programming problems.
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interpretable as network problems, but we can as well find hard integer programming problems, or hard problems on other combinatorial structures. Arguably there should be a series on combinatorial optimization, or one on combinatorial algorithms containing optimization as subseries/section. Perhaps the page on
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Besides mention of simulating annealing, the
Metropolis algorithm (to be found in Knowledge, not by "Metropolis" but by "Metropolis-Hastings") should very definitely be referenced or cross-referenced here. More generally, Hill-Climbing should be referenced. And in Hill-Climbing entry, I don't see
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Probabilistic hill-climbing is a counter-intuitive notion. Well, after a while (like when everybody see a unicorn -- so what), the notion seems less counter-intuitive, but in each step you have some chance (probability) of going towards a "worse" configuration -- and in that way you (most likely)
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Although network science treats some combinatorial optimization problems the subject of combinatorial optimization is not a part of network science, and not even tightly linked to network science. Of course in each complexity class we can find hard problems dealing with some types of graph, thus
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Operations research is a field of applied mathematics, that is concerned with applications to real-world, usually industrial or logistical problems; it often uses continuous data, thus real values. Combinatorial optimization is arguably foremost a field of pure mathematics, though with many
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Add: Agree. This is an important aspect of combinatorial optimization as it is how most real-world applications solve it. In the "Distributed
Combinatorial Section," a probabilistic hill-climbing algorithm is cited.
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I also agree with constantin, and I think that information about implementation would be better located towards the end of the article, as seems to be the style for most algorithm articles in
Knowledge.
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avoid getting stuck in local optimum as opposed to global optimum. This central notion should be part of combinatorial optimization entry.
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should be used as a replacement for the general combinatorial optimization page, this page, in the network science series.
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I've always wondered what is the difference between
Combinatorial Optimization and
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This page is probably wrongly classified as part of the series on network science
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I found the listing of programs and their classifications helpful and useful.
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Difference between
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Find pictures for the biographies of computer scientists (see
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Metropolis and Hill-Climbing Cross
References Needed
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