Stochastic adaptive search for global optimization. (Q1414003)

Global optimization methods using randomised search strategies are considered. Such methods are popular among engineers and applied scientists since they are applicable to the problems characterised as ``black box'' optimization. Well known representatives of stochastic global optimization methods are simulated annealing and evolutionary optimization methods. The focus of the book is on theoretical aspects of several versions of random search methods. The book consits of seven chapters. The first chapter is an introduction, the seventh chapter is devoted to engineering applications, and the other five chapters consider theoretical properties of varios random search methods. In Chapter 2 two algorithms are considered: pure random search and pure adaptive search. The first algorithm choses the trial points randomly according to uniform distribution over the feasible region. The second algorithm distributes the points uniformly over the prospective subregion. The last algorithm is mainly theoretical. Its more applicable version called Hesitant Adaptive Search is considered in Chapter 3. The most important result of the considered algorithms is the assessment of their performance measured as the number of iterations until the convergence. In Chapter 4 the cooling schedule for a simulated annealing based random search algorithm is analysed, and performance of the annealing adaptive search is evaluated. Chapters 5 and 6 consider further steps toward more realistic algorithms. Different versions of random search algorithms aiming at approximating the attractive theoretical method, Pure Adaptive Search, are considered: backtracking adaptive search, hit-and run and its related versions. Here, under the name backtracking, are considered the algorithms allowing the backtrack, i.e. accepting points with worse objective function values. The Hit-and-Run methods take steps of random length in randomly generated directions. The analysis of the performance of these methods is based on Markov chain models. The examples of application of the global random search methods (Chapter 7) include fuel allocation, three-bar and ten-bar truss optimal design, and optimization of composite structures.