The basic ingredients of an optimization problem are the set of instances or input objects, the set of feasible solutions or output objects associated with any instance, and the measure defined for any feasible solution. Most of the NPO problems that I know of have discreet input space.
Are you looking for problems entirely in the continuous domain (e.g. multi-modal fitness functions often have an exponentially increasing number of local optima with respect to dimension, and fractal/fractured fitness landscapes which can approach combinatorial complexity at the level of the discrete representation of floating point numbers), or are you looking for mixed continuous and discrete problems (e.g. vehicle routing problems with movable customers and/or depots)?
What is the basis of your non-polynomial function? If it's dimensionality, it's well known that the search space increase exponentially as a function of dimensionality. I think this paper does a nice job of expressing some of the difficulties:
https://www.researchgate.net/publication/220314180_A_new_evolutionary_search_strategy_for_global_optimization_of_high-dimensional_problems?ev=srch_pub
If it's search space range, I think the problem would have to be fractal.
https://www.researchgate.net/publication/220233685_Towards_unbiased_benchmarking_of_evolutionary_and_hybrid_algorithms_for_real-valued_optimisation?ev=srch_pub
Article A new evolutionary search strategy for global optimization o...
Article Towards unbiased benchmarking of evolutionary and hybrid alg...
I have worked on feature weighting (FW) as a continuous search space problem. Feature weighting involves assigning weights to the features of the data sets before performing machine learning tasks (like classification). As it is reported by many authors, FW improves the performance of classification algorithms. When the weights are limited to 0/1, the task will be Feature selection (FS) instead of feature weighting. (Feature selection is a discrete search space problem). For more information you can study this article:
http://www.sciencedirect.com/science/article/pii/S0925231212004766
you may want to have a look at the sum of ratios problem, which is minimizing the sum of a number of fractional functions under convex constraints.
http://link.springer.com/article/10.1023/A:1008316327038
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Graphs