2,114 research outputs found
Phase Transitions and Symmetry Breaking in Genetic Algorithms with Crossover
In this paper, we consider the role of the crossover operator in genetic algorithms. Specifically, we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem. As an example of such a problem, we consider the subset sum problem. In so doing, we demonstrate a previously unobserved phenomenon, whereby the genetic algorithm with crossover exhibits a critical mutation rate, at which its performance sharply diverges from that of the genetic algorithm without crossover. At this critical mutation rate, the genetic algorithm with crossover exhibits a rapid increase in population diversity. We calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations. Finally, we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm
Roman towns as meaning-laden places: reconceptualising the growth and decline of towns in Roman Britain, Volume 1
Standard furniture
I seek simplicity through my intention to establish a particular beauty, a certain calm achieved both visually and through the intangible feel of my furniture - itself simply a reservoir for the collection and ordering of possessions. The result will reflect the balance between the order inherent in the modest furniture forms that follow function and the emphasized personal quality of certain components of the whole. Through exercising restraint in form, the central element is emphasized, thereby omitting the unimportant to magnify the important. I chase an elusive beauty and an ethereal quality in my furniture. I intend to explore this idea through the marriage of conventional forms - founded on appropriate proportions, material selection, and well considered subtle details - with specific elements whose consideration allows for a softened, human feel to the object. This approach may facilitate a process of making where a form can be standardized, produced, and given its individual voice through the introduction of the specifically considered components with the goal of achieving various, yet consistently unique furniture
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