What makes an optimization problem hard?
Complexity
Kolmogorov Random Graphs and the Incompressibility Method
SIAM Journal on Computing
Information perspective of optimization
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
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This tutorial focuses mainly on Kolmogorov's notion of information that is, the information content of a binary string is the length of the shortest program that can produce this string and halt but more importantly, it concentrates on the applicability of this notion to Optimisation problems and Black-Box algorithms. For example, we will discuss how informal observations of the kind, "ONEMAX contains good information", "NIAH does not contain any" connects with the formal definition.The tutorial covers the following major issues: decomposition of a fitness-function, the entropy of a fitness-function as a bound on the expected performance, Kolmogorov complexity (KC) and its relation to Shannon information theory, KC and problem hardness, the relation between KC and other (applicable) predictive measures to problem difficulty (e.g., auto-correlation, ruggedness) and KC vs. the no-free-lunch theorems.