IJCSNS International Journal of Computer Science and Network Security, VOL.11 No.3, March 2011 80 An Improved Version of opt-aiNet Algorithm (I-opt-aiNet) for Function Optimization Hamdy N. Agiza † , Ahmed E. Hassan †† , Ahmed M. Salah ††† agizah@mans.edu.eg arwaahmed1@gmail.com a_salah@mans.edu.eg † Mathematics Department, Faculty of Science, Mansoura University, Egypt †† Electrical Engineering Department, Faculty of Engineering, Mansoura University, Egypt ††† Mathematics Department, Statistics and Computer Science Branch, Faculty of Science, Mansoura University, Egypt Abstract This paper presents an improved version of opt-aiNet, which is an algorithm for multimodal function optimization based on the natural immune system metaphor. The proposed algorithm has some major and minor changes on the way the clonal selection principle is applied within the original opt-aiNet algorithm which allows for fast localization of the optima. The output of the proposed algorithm is tested on the same data as the original opt-aiNet and the results show the validity of the new improved one. Key words: Artificial Immune Systems, Clonal Selection, opt-aiNet, Function Optimization 1. Introduction Artificial Immune Systems (AIS) are computational systems inspired by theoretical immunology, observed immune functions, principles and mechanisms in order to solve problems [1]. The fundamental features of the natural immune system, like distribution, adaptability, learning from experience, complexity, and coordination have decided that immune algorithms have been applied to a wide variety of tasks, including optimization. The task of natural immune system is to identify and destroy foreign invaders or antigens. The basic elements of natural immune system are immune cells (such as B cells, T cells, and other lymphocytes), B-cells produce antibodies, which bind to the invading antigens and help destroy them. Each B-cell produces only one kind of antigenic receptors. When an antigen enters the body, it activates only the lymphocytes whose receptors can bind to it. Activated by an antigen and with a second signal from accessory cells, such as the T-cells, the B- cells proliferates (divides) producing large number of clones. In the final stage these clones can mutate in order to produce antibodies with very high affinity to a specific antigen [2]. This process is explained by the clonal selection principle [3], according to which only those cells that recognize the antigens are selected to proliferate. The selected cells are subject to affinity maturation, which improves their affinity to the antigens. Manuscript received March 5, 2011 Manuscript revised March 20, 2011 This paper reviews work done in optimization using AIS and briefly introduce immune optimization algorithm (opt-aiNet). An improved version of opt-aiNet is presented with detailed description of the modifications made together with a theoretical comparison to original opt-aiNet algorithm followed by the results of experimental comparison of the proposed and the original one. The paper ends with conclusion of the proposed work. 2. Optimization using Artificial Immune Systems There is a natural parallel between the immune system and optimization. Whilst the immune system is not specifically an optimizer, the process of the production of antibodies in response to an antigen is evolutionary in nature; hence the comparison with optimization, the location of better solutions. The process of clonal selection (a theory widely held by many immunologists [4]) describes how the production of antibodies occurs in response to an antigen, and also explains how a memory of past infections is maintained. This process of clonal selection has proved to be a source of inspiration of many people in AIS and there have been a number of algorithms developed for optimization inspired by this process [5]. Opt-aiNet, proposed in [1], is an optimization version of aiNet which is a discrete immune network algorithm that was developed for data compression and clustering [6]. AiNet and has subsequently been developed further and applied to areas such as bioinformatics [7] and even modeling of simple immune responses [8]. Opt-aiNet evolves a population that consists of a network of antibodies (considered as candidate solutions to the function being optimized). These undergo a process of evaluation against the objective function, clonal expansion, mutation, selection and interaction between themselves. Opt-aiNet creates a memory set of antibodies that represent (over time) the best candidate solutions to the objective function. Opt-aiNet is capable of either unimodal or multimodal optimization and it has defined stopping criteria.