A hybrid of simplex method and simulated annealing

One of basic concepts of the well-known simplex optimization method is that from the current simplex set of points (solutions) a new point – reflection is constructed. The reflection point is used for a conditional updating of the simplex set. This simple and efficient idea is applied in the simulated annealing to suggest a new version of this stochastic optimization method. As a forerunner of the presented simulated annealing is the controlled random search invented by Price in the middle of seventies. He proposed the very important idea that a population of points is considered and from this population the simplex set is randomly selected. Reflection points update the population so that they conditionally substitute points with highest values of objective function. The simplex simulated annealing enhances further stronger stochastic and evolution character of this method. The construction of reflection points is randomized and their returning to the population is solved by the Metropolis criterion. A parallel version of simplex simulated annealing uses a decomposition of the whole population into disjoint subpopulations for which independent simulated annealings are done. The subpopulations randomly interact so that between two subpopulations their best points are exchanged and worst ones are eliminated.