Generalized hill climbing (GHC) algorithms provide a well-defined framework
for describing the performance of local search algorithms for discrete opt
imization problems. Necessary and sufficient convergence conditions for GHC
algorithms are presented. These convergence conditions are derived using a
new iteration classification scheme for GHC algorithms. The implications o
f the necessary and the sufficient convergence conditions for GHC algorithm
s with respect to existing convergence theory for simulated annealing are a
lso discussed.