We present a modification of the simulated annealing algorithm designed for solving discrete stochastic optimization problems. Like the original simulated annealing algorithm, our method has the hill climbing feature, so it can find global optimal solutions to discrete stochastic optimization problems with many local solutions. However, our method differs from the original simulated annealing algorithm in that it uses a constant (rather than decreasing) temperature. We consider two approaches for estimating the optimal solution. The first approach uses the number of visits the algorithm makes to the different states (divided by a normalizer) to estimate the optimal solution. The second approach uses the state that has the best average estimated objective function value as estimate of the optimal solution. We show that both variants of our method are guaranteed to converge almost surely to the set of global optimal solutions, and discuss how our work applies in the discrete deterministic optimization setting. We also show how both variants can be applied for solving discrete optimization problems when the objective function values are estimated using either transient or steady-state simulation. Finally, we include some encouraging numerical results documenting the behavior of the two variants of our algorithm when applied for solving two versions of a particular discrete stochastic optimization problem, and compare their performance with that of other variants of the simulated annealing algorithm designed for solving discrete stochastic optimization problems.

This paper puts forward a new automatic clustering algorithm based on Multi-Objective Particle Swarm Optimization and Simulated Annealing, “MOPSOSA”. The proposed algorithm is capable of automatic clustering which is appropriate for partitioning datasets to a suitable number of clusters. MOPSOSA combines the features of the multi-objective based particle swarm optimization (PSO) and the Multi-Objective Simulated Annealing (MOSA). Three cluster validity indices were optimized simultaneously to establish the suitable number of clusters and the appropriate clustering for a dataset. The first cluster validity index is centred on Euclidean distance, the second on the point symmetry distance, and the last cluster validity index is based on short distance. A number of algorithms have been compared with the MOPSOSA algorithm in resolving clustering problems by determining the actual number of clusters and optimal clustering. Computational experiments were carried out to study fourteen artificial and five real life datasets.