| Determining ground states of frustrated and disordered spin systems in general is an exponentially hard optimization problem, which turns out to be prototypic for many other hard optimization problems occurring in many fields, ranging from statistical and bio-physics to engineering. Generic minimization procedures such as simulated annealing often turn out to be insufficient to reach useful system sizes in these problems and, instead, specifically tailored optimization heuristics taking advantage of structural features of the free-energy landscapes at hand are called for. I will discuss here, how a well-adapted combination of techniques borrowed from combinatorial optimization, genetic algorithms and the systematic extension of phase space with extra dimensions allows to successfully tackle ground-state problems for discrete and continuous spin systems, and I will present some of the physical insight gained by these studies. |
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