Statistical mechanics of optimization problems

Statistical mechanics of combinatorial optimization problems with site disorder.

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite-temperature traveling salesman problem on several different domains and various problems in one dimension such as the so-called descent problem. We first motivate our method by analyzing these problems using...

Statistical mechanics methods and phase transitions in optimization problems

Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools and concepts designed by physicists to deal with optimization or decision problems in...

Constraint Optimization and Statistical Mechanics

In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the presentation I will describe in details only the problems related to the coloring of a random graph.

Statistical Mechanics of Learning and Optimization

Topology Optimization of Fluid Mechanics Problems

Optimal shape design problems in fluid mechanics have wide and valuable applications in aerodynamic and hydrodynamic problems such as the design of car hoods, airplane wings and inlet shapes for jet engines. One of the first studies is found in Pironneau (1974). It is devoted to determine a minimum drag profile submerged in a homogeneous, steady, viscous fluid by using optimal control theories ...