Stochastic Population Update Can Provably Be Helpful in Multi-Objective Evolutionary Algorithms
This work addresses a key bottleneck in MOEAs for optimization practitioners, offering a novel theoretical insight that could lead to more efficient algorithms, though it is incremental as it modifies existing methods.
The paper tackles the problem of deterministic population updates in multi-objective evolutionary algorithms (MOEAs) by proving that stochastic updates can reduce expected running time, showing exponential decreases for SMS-EMOA and NSGA-II on specific bi-objective problems.
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, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the best solutions from the current population and newly-generated solutions (irrespective of the selection criteria used such as Pareto dominance, crowdedness and indicators). In this paper, we analytically present that stochastic population update can be beneficial for the search of MOEAs. Specifically, we prove that the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II, for solving two bi-objective problems, OneJumpZeroJump and bi-objective RealRoyalRoad, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed population update method. This work is an attempt to show the benefit of introducing randomness into the population update of MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.