Stochastic Population Update Can Provably Be Helpful in Multi-Objective Evolutionary Algorithms

Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update is a key component in multi-objective EAs (MOEAs), and it is performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the first population-size ranked solutions (based on some selection criteria, e.g., non-dominated sorting, crowdedness and indicators) from the collections of the current population and newly-generated solutions. In this paper, we question this practice. We analytically present that introducing randomness into the population update procedure in MOEAs can be beneficial for the search. More specifically, we prove that the expected running time of a well-established MOEA (SMS-EMOA) for solving a commonly studied bi-objective problem, OneJumpZeroJump, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed stochastic population update method. This work is an attempt to challenge a common practice for the population update in MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

Robust Subset Selection by Greedy and Evolutionary Pareto Optimization

Subset selection, which aims to select a subset from a ground set to maximize some objective function, arises in various applications such as influence maximization and sensor placement. In real-world scenarios, however, one often needs to find a subset which is robust against (i.e., is good over) a number of possible objective functions due to uncertainty, resulting in the problem of robust subset selection. This paper considers robust subset selection with monotone objective functions, relaxing the submodular property required by previous studies. We first show that the greedy algorithm can obtain an approximation ratio of $1-e^{-\beta\gamma}$, where $\beta$ and $\gamma$ are the correlation and submodularity ratios of the objective functions, respectively; and then propose EPORSS, an evolutionary Pareto optimization algorithm that can utilize more time to find better subsets. We prove that EPORSS can also be theoretically grounded, achieving a similar approximation guarantee to the greedy algorithm. In addition, we derive the lower bound of $\beta$ for the application of robust influence maximization, and further conduct experiments to validate the performance of the greedy algorithm and EPORSS.