An evolutionary annealing-simplex algorithm for global optimisation of water resource systems

The evolutionary annealing-simplex algorithm is a probabilistic heuristic global optimisation technique that joins ideas from different methodological approaches, enhancing them with some original elements. The main concept is based on a controlled random search scheme, where a generalised downhill simplex methodology is coupled with a simulated annealing procedure. The algorithm combines the robustness of simulated annealing in rugged problems, with the efficiency of hill-climbing methods in simple search spaces. The following-up procedure is based on a simplex-searching scheme. The simplex is reformulated at each generation going either downhill or uphill, according to a probabilistic criterion. In the first case, it moves towards the direction of a candidate local minimum via a generalised Nelder-Mead strategy. In the second case, it expands itself along the uphill direction, in order to escape from the current local minimum. In all possible movements, a combination of deterministic as well as stochastic transition rules is applied. The evolutionary annealingsimplex algorithm was first examined in a variety of typical benchmark functions and then it was applied in two global optimisation problems taken from water resources engineering, the calibration of a hydrological model and the optimisation of a multiple reservoir systems' operation. The algorithm has been proved very reliable in locating the global optimum, requiring reasonable computational effort.