Altruistic population algorithm: A metaheuristic search algorithm for solving multimodal multi-objective optimization problems

Although many intelligent optimization algorithms have been applied to the multimodal multi-objective optimization problems (MMOPs) which are complex and difficult, challenges of MMOP such as loss of PS in decision space and low efficiency have not been well solved. To better solve these problems, an altruistic population algorithm (APA) which is based on the altruism behavior in some animal populations, is proposed in this paper. The proposed APA has five major operations: parent selection, procreation variation, altruistic nurturing, crowd competition and archive updating. A few important features of the proposed APA are: (1) The nurturing cost according to a pair of parents’ condition is introduced. It can accelerate the convergence speed while maintaining the diversity of the Pareto optimal solutions (PS). (2) The application of altruism allows the transfer of nurturing cost between descendant siblings to improve the efficiency and decrease the unnecessary variations. (3) A selection strategy called neighboring selection based on the distance in the objective space is proposed. It is an effective way to delete the redundant individuals in the objective space. The experimental results reveal that APA preforms better than other existing algorithms for solving various MMOPs.