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 conditi onal updating of the simplex set. This simple and efficient idea is ap plied in the simulated annealing to suggest a new version of this stoc hastic optimization method. As a forerunner of the presented simulated annealing is the controlled random search invented by Price in the mi ddle of seventies. He proposed the very important idea that a populati on of points is considered and from this population the simplex set is randomly selected. Reflection points update the population so that th ey conditionally substitute points with highest values of objective fu nction. The simplex simulated annealing enhances further stronger stoc hastic and evolution character of this method. The construction of ref lection points is randomized and their returning to the population is solved by the Metropolis criterion. A parallel version of simplex simu lated annealing uses a decomposition of the whole population into disj oint subpopulations for which independent simulated annealings are don e. The subpopulations randomly interact so that between two subpopulat ions their best points are exchanged and worst ones are eliminated. (C ) 1997 Elsevier Science B.V.