A two-phase differential evolution for minimax optimization

Abstract

The optimum of a minimax optimization problem is the minimum of maximal outputs in all possible scenarios. A minimax optimization problem includes two decision spaces: the scenario space and the solution space. When optimizing this kind of problem, an algorithm should consider three issues: (1) in the scenario space, how to decide which promising individuals to be optimized; (2) in the solution space, how to avoid discarding promising individuals; (3) how to properly allocate the optimization resources to these two spaces. Bearing these in mind, a two-phase differential evolution algorithm is proposed. To address the first issue, it optimizes a better individual with a higher probability instead of updating the best one directly. The second issue is addressed as follows. On the one hand, individuals with better objective function values are modified less frequently; On the other hand, an archive-based comparison strategy is developed to avoid selecting an offspring that owns a good objective function value but has not been optimized adequately in the scenario space. To properly monitor these two phases, the optimization resources are allocated dynamically. Experiments on benchmark test functions and an open problem in epidemic spreading control over complex networks demonstrate that the proposed method is competitive.