**6. Suitability and sensitivity of adaptive simulated annealing**

In the application discussed here, Simulated Annealing is utilized for finding the global minimum of a cost function that characterizes large and complex systems such as transport of pollutants in groundwater.Simulated Annealing, as an algorithm, is very efficient in solving non-convex optimization problems by ensuring that it does not always move downhill on a complex non-convex search space and hence avoids getting trapped in local minimum. Simulated annealing also differs significantly from conventional iterative optimization algorithms in that gross features of the final state of the system are seen at higher temperatures whereas the finer details of the state appear at lower temperatures [10]. The fact that simualted annealing ensures a global optimal solution enhances its suitability for solving

#### 16 Will-be-set-by-IN-TECH 172 Simulated Annealing – Single and Multiple Objective Problems Application of Simulated Annealing in Water Resources Management: Optimal Solution of Groundwater Contamination Source Characterization Problem and Monitoring

ill-posed inverse problems in general and the problem of unknown groundwater pollutant source characterization in particular.

Network Design Problems 17

Groundwater Contamination Source Characterization Problem and Monitoring Network Design Problems

Application of Simulated Annealing in Water Resources Management: Optimal Solution of

173

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Its ease of use and remarkable efficiency in handling complex objective functions and constraints has made simulated annealing an attractive choice for solving a wide range of complex optimization problems. However, the slow convergence and hence long time of execution of standard Boltzmann-type simulated annealing has been a constraint. Adaptive Simulated Annealing removes that constraint by making the annealing schedules decrease exponentially in annealing-time, thereby making the convergence much faster. A major difference between ASA and traditional Boltzamnn Annealing algorithms is that the ergodic sampling takes place in terms of n parameters and the cost function. In ASA the exponential annealing schedules permit resources to be spent adaptively on re-annealing and on pacing the convergence in all dimensions, ensuring ample global searching in the first phases of search and ample quick convergence in the final phases[15].

Another major advantages of using Adaptive Simulated Annealing is also the fact that the parameters of algorithm are adjusted adaptively and hence the solutions do not vary widely if parameter values are changed within reasonable limits. This is in contrast with Genetic Algorithm where even minor changes to parameters such as mutation probability, cross over probability or population size causes a significant difference in the solutions.
