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I once had this question https://math.stackexchange.com/questions/1083338/structural-design-meta-optimization-is-there-mathematical-theory-optimiza about the methods for finding optimal structures, designs and policies (as another kind of structures - set of rules), i.e. optimization of the structure of the models not just the parameters for some pre-selected structure. So far I am sure that the genes of evolutionary computation (EC) can effectively encode structure and evolutionary computing can perform effective search for more optimal structures. EC algorithms are quite sophisticated - there is evolutionary programming (for search of strings in some grammar) and there is cultural algorithms (which incorporates already known certain knowledge for speedup of the search). But are there some other kind of search procedures (besides evolutionary computing) for searching more efficient structures. EC is stochastic search methods and is there deterministic search methods for the search of optimal structure? I expect only key-words, pointers and trends.

Or - more clearly - is EC the most general search framework? Are there search alogrithms or approaches than can not be reduced to the string of application of crossover, mutation and other operators of EC?

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  • $\begingroup$ This sounds too broad and ill-defined to me. "structures, designs and policies" could cover a lot of territory. It's not clear what you mean by "structures" so I'm not sure how we would answer it or evaluate proposed answers. This site works best for specific, answerable questions. $\endgroup$
    – D.W. ♦
    Commented May 9, 2018 at 22:19
  • $\begingroup$ Whoever has done some thinking, will understand me. There can be robot with prespecified structure - e.g. with 3 rods and 2 joints. Simple optimization is the determination of the length of rods. And then there can be more general problem - determine the optimal number and joining of rods and joints. This is the thing I call the structural optimization. Similar problems arouse everywhere - whe can select one queue design and optimize its numerical parameters. That is simple. And then we can choose to find the optimal policy among many possible policies. Everyhing - robot design, policies... $\endgroup$
    – TomR
    Commented May 10, 2018 at 5:26
  • $\begingroup$ ... can be expressed as graphs of strings in some language. So - one should do some kind of search for optimal graph of optimal string. Not just numerical parameters of the model. $\endgroup$
    – TomR
    Commented May 10, 2018 at 5:27
  • $\begingroup$ ... can be expressed as graphs or as strings in some language. So - one should do some kind of search for optimal graph of optimal string. Not just numerical parameters of the model. $\endgroup$
    – TomR
    Commented May 10, 2018 at 5:33

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At a broad level, there are two types of optimization: continuous optimization, and discrete optimization. They tend to use different techniques.

Continuous optimization deals with problems where the parameters are continuous; methods include gradient descent, Newton's method, and other iterative methods, linear programming, and more.

Discrete optimization, or combinatorial optimization, deals with problems where the parameters come from a finite site; methods include integer linear programming, SAT, simulated annealing, particle swarm optimization, and more.

Genetic algorithms are another technique. However, my experience is that they are rarely the best one; other methods often beat genetic programming and evolutionary optimization methods. Your experience may vary.

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