Optimal Design Using Clonal Selection Algorithm
Yi-Hui Su1, Wen-Jye Shyr2, and Te-Jen Su31 Dept. of Information Management, Tzu-Hui Institute of Technology
Pintung 926, Taiwan, R.O.C.
2 Dept. of Industrial Education and Technology, National Changhua University of Education
Changhua 500, Taiwan, R.O.C. [email protected]
3 Dept. of Electronic Engineering, National Kaohsiung University of Applied Sciences
Kaohsiung 807, Taiwan, R.O.C. [email protected]
Abstract. In this paper, the Clonal Selection Algorithm (CSA) is employed by
the natural immune system to define the basic features of an immune response to an antigenic stimulus. This paper synthesizes the advantages of clonal selection algorithm and proposed optimal design problem using clonal selection algorithm which is a basis of the immune system. CSA, the essence of immune algorithm, is effective to solve optimal problem. The clonal selection algorithm is highly paral-lel and presents a fine tractability in terms of computational cost. Like the genetic algorithm, clonal selection algorithm is a tool for optimum solution. Clonal se-lection algorithm and genetic algorithm are used to reach the optimization perfor-mances for two numerical function. Then those results are compared each other. These proposed algorithms are shown to be an evolutionary strategy capable of solving optimal design problem.
1
Introduction
Many heuristic optimization algorithms have been developed and adapted to several problems [1-3]. The problems of finding a maximum or a minimum of a function under some constraint conditions are called optimization problem. Almost every engineering evaluation problem can be formulated as an optimization problem. Optimization pri-marily aims to find the best possible combination of factors which can be defined as evaluation parameters to maximize or minimize an objective function subjected to a set of constraints.
The genetic algorithm paradigm is a stochastic optimization method for combinato-rial optimization problems. Because genetic algorithm is based on multipoint search and uses crossover operator, genetic algorithm can search large region of the solutions. But genetic algorithm has two main disadvantages. The one is lack of the local search ability and the other is the premature convergence. In order to overcome these drawbacks, sev-eral researchers have studied new optimization methods based on the immune system [4, 5].
The immune system has two types of response: primary and secondary. The primary response is reaction when the immune system encounters the antigen for the first time. At this point the immune system learns about the antigen, thus preparing the body for
R. Khosla et al. (Eds.): KES 2005, LNAI 3681, pp. 604–610, 2005. c
Optimal Design Using Clonal Selection Algorithm 605 any further invasion from that antigen. This learning mechanism creates the immune system’s memory. The secondary response occurs when the same antigen encountered again. This has response characterized by a more rapid and more abundant production of antibody resulting from the priming of the B-cells in the primary response [6]. By using this mechanism, immune algorithm shows a good performance as an optimization algorithm. Over the last few years, there has been an ever increasing interest in the area of artificial immune systems and their applications [7-10].
In this work, we use the clonal selection concept, together with the affinity matu-ration process, and demonstrate that these biological principles can lead to the devel-opment of powerful computational tools. The algorithm to be presented focuses on a systemic view of the immune system. It shows that some basic immune principles can help us not only to better understand the immune system itself, but also to solve engi-neering evaluation problems. This paper addresses comparison of optimal design using clonal selection algorithm and genetic algorithm.
2
The Human Immune System
The human immune system is a complex system of cells, molecules and organs that represent an identification mechanism capable of perceiving and combating dysfunction from our own cells and the action of exogenous infectious microorganisms. The human immune system protects our bodies from infectious agents such as viruses, bacteria, fungi and other parasites. Any molecule that can be recognized by the adaptive immune system is known as an antigen. The basic component of the immune system is the lymphocytes or the white blood cells.
Lymphocytes exist in two forms, B cells and T cells. These two types of cells are rather similar, but differ with relation to how they recognize antigens and by their func-tional roles, B-cells are capable of recognizing antigens free in solution, while T cells require antigens to be presented by other accessory cells. Each of this has distinct chem-ical structures and produces many Y shaped antibodies form its surfaces to kill the anti-gens. Antibodys are molecules attached primarily to the surface of B cells whose aim is to recognize and bind to antigens [11].
The immune system possesses several properties such as self/nonself discrimination immunological memory, positive /negative selection, immunological network, clonal selection and learning which performs complex tasks.
3
Artificial Immune System
3.1 Clonal Selection Theory
In order to explain how an immune response is mounted when a nonself antigenic pat-tern is recognized by a B cell, clonal selection theory [12] is been developed.
The main goal of the immune system is to protect the human body from the attack of foreign (harmful) organisms. The immune system is capable of distinguishing between the normal components of our organism and the foreign material that can cause us harm. These foreign organisms are called antigens. The molecules called antibodies
606 Yi-Hui Su, Wen-Jye Shyr, and Te-Jen Su
play the main role on the immune system response. The immune response is specific to a certain foreign organism (antigen). When an antigen is detected, those antibodies that best recognize an antigen will proliferate by cloning. This process is called clonal selection theory.
The main features of the clonal selection theory are explored as follows [13]: (1) generation of new random genetic changes subsequently expressed as diverse
anti-body patterns by a form of accelerated somatic mutation;
(2) phenotypic restriction and retention of one pattern to one differentiated cell (clone); (3) proliferation and differentiation on contact of cells with antigens.
3.2 Clonal Selection Algorithm
The clonal selection algorithm developed on the basis of clonal selection theory of the immune system. It was proved that can perform and adapt to solve design of optimiza-tion tasks. In all runs of the algorithm, the stopping criterion is a predefined maximum number of generations.
The clonal selection algorithm can be described as follows [14]:
(1) Generate a set (P) of candidate solutions, composed of the subset of memory cells (M) added to the remaining (Pr) population (P = Pr + M);
(2) Determine (Select) the n best individuals of the population (Pn), based on an affinity measure;
(3) Reproduce (Clone) these n best individuals of the population, giving rise to a tem-porary population of clones (C). The clone size is an increasing function of the affinity with the antigen;
(4) Submit the population of clones to a hypermutation scheme, where the hypermu-tation is proportional to the affinity of the antibody with the antigen. A maturated antibody population is generated (C∗);
(5) Re-select the improved individuals from C∗to compose the memory set M. Some members of P can be replaced by other improved members of C∗;
(6) Replace d antibodies by novel ones (diversity introduction). The lower affinity cells have higher probabilities of being replaced.
4
Simulation Results
To verify the excellence of clonal selection algorithm, we considered three numerical objective functions and use for comparing the performance of genetic algorithms. The experiment 1 was run for 50 iterations and the experiment 2 was run for 100 iterations. In addition, the parameters are created and tested to ensure that results are listed in Table 1.
4.1 Simple Evaluation Function
Equation (1) is a simple evaluation function for clonal selection algorithm and genetic algorithm as follows:
f(x,y) = x3+ y3 (1)
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Further work is clearly required. We have also done some work on this and it will be written in the future. Eventually, it is hopeful that this optimization approach of clonal selection algorithm can be helpful for the numerical optimization as a useful and effective alternative.
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