Multi-objective immune algorithm with Baldwinian learning

By replacing the selection component, a well researched evolutionary algorithm for scalar optimization problems (SOPs) can be directly used to solve multi-objective optimization problems (MOPs). Therefore, in most of existing multi-objective evolutionary algorithms (MOEAs), selection and diversity maintenance have attracted a lot of research effort. However, conventional reproduction operators designed for SOPs might not be suitable for MOPs due to the different optima structures between them. At present, few works have been done to improve the searching efficiency of MOEAs according to the characteristic of MOPs. Based on the regularity of continues MOPs, a Baldwinian learning strategy is designed for improving the nondominated neighbor immune algorithm and a multi-objective immune algorithm with Baldwinian learning (MIAB) is proposed in this study. The Baldwinian learning strategy extracts the evolving environment of current population by building a probability distribution model and generates a predictive improving direction by combining the environment information and the evolving history of the parent individual. Experimental results based on ten representative benchmark problems indicate that, MIAB outperforms the original immune algorithm, it performs better or similarly the other two outstanding approached NSGAII and MOEA/D in solution quality on most of the eight testing MOPs. The efficiency of the proposed Baldwinian learning strategy has also been experimentally investigated in this work. . Introduction Many optimization problems in real-life applications have more han one objective in conflict with each others. These optimizaion problems are known as multi-objective optimization problems MOPs) [1]. With the advantage of producing a set of Pareto optimal olutions in a single run, evolutionary algorithms (EAs) have been ecognized to be very successful in solving MOPs. Since Schaffer’s pioneer work on evolutionary multi-objective ptimization (EMO) [2], a number of multi-objective evolutionry algorithms (MOEAs) had been developed. According to Coello oello’s overview of works on EMO [3], MOEAs are categorized nto two generations by their characteristics. In the early 1990s, he first generation MOEAs which are characterized by the use of election mechanisms based on Pareto ranking and fitness sharing o maintain diversity were proposed. The Multi-objective Genetic lgorithm (MOGA) [4], the Niched Pareto Genetic Algorithm NPGA) [5] and the Non-dominated Sorting Genetic Algorithm NSGA) [6] are representative ones. Since the end of the 1990s, he second generation MOEAs using the elitism strategy had been resented. The major contributions include the Strength Pareto ∗ Corresponding author at: School of Computer Science and Technology, Xidian niversity, Xi’an, China. 568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. ttp://dx.doi.org/10.1016/j.asoc.2012.04.005 © 2012 Elsevier B.V. All rights reserved. Evolutionary Algorithm (SPEA) [7] and its improved version SPEA2 [8], the Pareto archived evolution strategy (PAES) [9], the Pareto envelope based selection algorithm (PESA) [10] and its revised version PESAII [11], and the improved version of NSGA (NSGAII) [12]. More recently, Zhang et al. [13] combined decomposition methods in mathematics and the optimization paradigm in evolutionary computation and proposed the distinguished MOEA/D. MOEA/D maintains a good diversity by optimizing a set of various scalar subproblems synchronously and outperforms other compared MOEAs based on Pareto selection in solving MOPs with complicated PS shapes. Gong and Jiao et al. [14] utilized the superiority of the immune inspired clonal selection evolution paradigm in maintaining population diversity and proposed a multi-objective immune algorithm with nondominated neighbor-based selection (NNIA) which is an efficient and effective immune inspired multi-objective algorithm for MOPs. As only nondominated solutions have the chance to be proliferated in NNIA, the algorithm may be trapped in local optimal Pareto front if current isolated nondominated antibodies selected for proportional cloning are very few. To remedy this, Yang et al. [15] introduced vicinity distances based selection and adaptive ranks clone scheme into NNIA and proposed its enhanced version NNIA2. NNIA2 has made a significant improvement in convergence and diversity maintaining, it is could be an efficient and effective algorithm for MOPs.