1. A system for operating a cloud computing system comprising: a memory storage device; and a processor device, coupled to the memory storage device, and configured to: receive a user application request having one or more user specified objectives and allocation constraints, said user request specifying requirements for placing logical entities on physical entities in a computing infrastructure; generate one or more bias weights based on said user specified objectives and allocation constraints by employing an allocation domain that is created using a set of primitive variables, a set of functional definitions for the set of primitive variables, a policy specification for the set of functional definitions, and at least one post-allocation change to the set of primitive variables; compute a probability distribution using said bias weights, said bias weights increasing likelihood of generating an optimized placement solution; generate, using said biased computed biased probability distribution, several sample placement solutions; obtain an optimized placement solution from said several sample solutions that satisfies all said user specified objectives and said user specified allocation constraints; and dynamically reconfigure the computing infrastructure by allocating the logical entities in the request to the physical entities based on said optimized placement solution.