Immune algorithm with orthogonal design based initialization, cloning, and selection for global optimization

In this study, an orthogonal immune algorithm (OIA) is proposed for global optimization by incorporating orthogonal initialization, a novel neighborhood orthogonal cloning operator, a static hypermutation operator, and a novel diversity-based selection operator. The orthogonal initialization scans the feasible solution space once to locate good points for further exploration in subsequent iterations. Meanwhile, each row of the orthogonal array defines a sub-domain. The neighborhood orthogonal cloning operator uses orthogonal arrays to scan uniformly the neighborhood around each antibody. Then the new algorithm explores each clone by using hypermutation. The improved maturated progenies are selectively added to an external population by the diversity-based selection, which retains one and only one external antibody in each sub-domain. The OIA is unique in three aspects: First, a new selection method based on orthogonal arrays is provided in order to preserve diversity in the population. Second, the orthogonal design with a modified quantization technique is introduced to generate initial population. Third, the orthogonal design is introduced into the cloning operator. The performance comparisons of OIA with two known immune algorithms and three evolutionary algorithms in optimizing eight benchmark functions and six composition functions indicate that OIA is an effective algorithm for solving global optimization problems.