Influence maximization (IM) problem in social network analysis aims to select a set of the most influential users that can maximize the influence spread in a network. The existing majority of efforts merely focus on the purpose of maximizing the spread of influence. Whereas the budget cost is a major factor needed to be taken into consideration in practical scenarios. In this paper, we consider both the influence maximization and the cost minimization simultaneously in the process of influence spreading, and formulate the two targets as a multi-objective combinational optimization problem. A discrete multi-objective differential evolution optimization (DMODE) with mutation, crossover and selection operators specifically for the topological network structure is proposed. The algorithm combines multiple mutation operators to enhance exploration and exploitation, and an exploiting strategy based on degree ranking is developed to improve the convergence performance. Numerous experiments on four real-world social networks are conducted, and the obtained results demonstrate the outperformance of the proposed algorithm over the state-of-the-art methods.
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