The Convergence Speed of Single- And Multi-Objective Immune Algorithm Based Optimization Problems

Despite the considerable amount of research related to immune algorithms and its applications in numerical optimization, digital filters design, and data mining, there is still little work related to issues as important as sensitivity analysis, [1]-[4]. Other aspects, such as convergence speed and parameters adaptation, have been practically disregarded in the current specialized literature [7]-[8]. The convergence speed of the immune algorithm heavily depends on its main control parameters: population size, replication rate, mutation rate, clonal rate and hyper-mutation rate. In this paper we investigate the effect of control parameters variation on the convergence speed for single- and multi-objective optimization problems. Three examples are a devoted for this purpose; namely the design of 2-D recursive digital filter, minimization of simple function, and banana function. The effect of each parameter on the convergence speed of the IA is studied considering the other parameters with fix values and taking the average of 100 times independent runs. Then, the concluded rules are applied on some examples introduced in [2] and [3]. Computational results show how to select the immune algorithm parameters to speedup the algorithm convergence and to obtain the optimal solution.