Optimization algorithms in physics

The past few years have witnessed a substantial growth in the number of applications for optimization algorithms in solving problems in the field of physics. Examples include determining the structure of molecules, estimating the parameters of interacting galaxies, the ground states of electronic quantum systems, the behavior of disordered magnetic materials, and phase transitions in combinatorial optimization problems. This book serves as an introduction to the field, while also presenting a complete overview of modern algorithms. The authors begin with the relevant foundations from computer science, graph theory and statistical physics, before moving on to thoroughly explain algorithms - backed by illustrative examples. They include pertinent mathematical transformations, which in turn are used to make the physical problems tractable with methods from combinatorial optimization. Throughout, a number of interesting results are shown for all physical examples. The final chapter provides numerous practical hints on software development, testing programs, and evaluating the results of computer experiments.

Ch. 1. Introduction to Optimization, p. 1-7 -- ch. 2. Complexity Theory, p. 9-35 -- ch. 3. Graphs, p. 37-52 -- ch. 4. Simple Graph Algorithms, p. 53-72 -- ch. 5. Introduction to Statistical Physics, p. 73-90 -- ch. 6. Maximum-Flow Methods, p. 91-127 -- ch. 7. Minimum-Cost Flows, p. 129-157 -- ch. 8. Genetic Algorithms, p. 159-184 -- ch. 9. Approximation Methods for Spin Glasses, p. 185-226 -- ch. 10. Matchings, p. 227-254 -- ch. 11. Monte Carlo Methods, p. 255-272 -- ch. 12. Branch-and-Bound Methods, p. 273-292 -- ch. 13. Practical Issues, p. 293-357.