Using simulated annealing to design good codes

A NNEAL, as defined in Webster’s New Collegiate Dictionary, means: 1) to heat (as glass) in order to fix laid-on colors, and 2) to heat and then cool (as steel or glass) usually for softening and making less brittle. The cooling stage of annealing is usually done slowly to reduce the number of defects in the crystal structure (as steel) and to minimize the potential energy stored in the molecular configuration (as glass). A fundamental question in statistical mechanics concerns whether the system solidifies in the limit of low temperature, and if it does, whether it forms a crystalline solid or a glass. Motivated by a subtlety in numerical integration, the Metropolis algorithm [l] has often been used to simulate numerically the annealing process to gain an understanding of the ground-state configuration. A typical combinatorial optimization problem seeks the minimum of a given objective (or cost) function of many variables. The variables are subject to intertwining constraints, and they interact with each other in complicated ways not unlike the molecules in a physical system. By appropriately defining an effective temperature for the multivariable system and imitating the physical annealing process, researchers have sought to solve a diverse collection of problems, with varying degrees of success. Kirkpatrick [2] first investigated the use of simulated annealing in connection with the physical design of com-