| 7.3 Parameter Estimation Algorithms | |
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Grid Cellware 1.0 provides the parameter estimation tool based on Swarm algorithms. Swarm strategies have received considerable attention over recent years as optimization methods for complex problems. Kennedy and Eberhart (1995) proposed the original concept of particle swarm optimization (PSO). Unlike evolutionary methods, the swarm strategy is based on simulation of social behavior where each individual in a swarm adjusts its flying according to its own flying experience and companions' flying experience. The key to the success of such a strategy in solving an optimization problem lies with the mechanism of effective information sharing among individuals. Shi and Eberhart (1999) reported an interesting observation out of their numerical experiments, that a PSO method has a fast convergence capability and its performance is fairly insensitive to the size of the swarm. These two features of PSO make it extremely attractive as a method to solve engineering design optimization problems where the evaluation of every solution is computationally expensive. Furthermore, a smaller swarm size saves at least on the evaluation of randomly generated initial solutions. In attempts to further enhance the performance of PSO algorithms, Kennedy (2000) reported the use of information sharing among individuals within clusters. All the above PSO models rely on the methods of velocity and acceleration updates, knowledge of an individual's past and the information about the best performer in the swarm to orchestrate individual movements quite closely as observed in a real swarm. Ray and Saini (2001) proposed a version of a swarm algorithm that is based on the concepts of learning from the good. The focus of the algorithm is to understand and model the effective means of information sharing among individuals in a swarm and not to mimic individual or collective movements observed in a real swarm. The individuals of a swarm are divided into a set of leaders and a set of followers depending upon their performance. The followers communicate with the leaders and move to their neighborhoods in search for better solutions. This is the key concept behind the algorithm that is adopted in Grid Cellware version 1.0. For the current version, the objective function is based on the L2 norms of the errors between observed data and simulated data. |