Solving Constrained Global Optimization via Artificial Immune System

Artificial immune systems (AISs) are computational intelligence (CI) oriented methods using information based on biological immune systems. In this study, an AIS, which combines the metaphor of clonal selection with idiotypic network theories, is developed. Although they are contradictory approaches, clonal selection and idiotypic network may prove useful in designing a stochastic global optimization tool. The AIS method consists of idiotypic network selection, somatic hypermuation, receptor editing and bone marrow operators. The idiotypic network selection operator determines the number of good solutions. The somatic hypermutation and receptor editing operators comprise the searching mechanisms for the exploration of the solution space. Diversity on the population of solutions is ensured by the bone marrow operator. The performance of the proposed AIS method is tested on a set of global constrained optimization problems (GCO), comprising of four benchmark nonlinear programming problems and four generalized polynomial programming (GPP) problems, where GPP problems are nonconvex optimization problems. The best solution found by the AIS algorithm is compared with the known global optimum. Numerical results show that the proposed method converged to the global optimal solution to each tested CGO problem. Moreover, this study compares the numerical results obtained by the AIS approach with those taken from published CI approaches, such as alternative AIS methods and genetic algorithms.