[论文解读] Stochastic Population Update Can Provably Be Helpful in Multi-Objective Evolutionary Algorithms

Chao Bian, Yawen Zhou+2 more|arXiv (Cornell University)|Jun 5, 2023

Advanced Multi-Objective Optimization Algorithms被引用 10

一句话总结

本文表明在 SMS-EMOA 和 NSGA-II 中引入随机化种群更新，相较于确定性更新，在两个双目标问题上可呈指数级加速找到帕累托前沿。

ABSTRACT

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.

研究动机与目标

• 挑战普遍观点，即确定性、贪婪的种群更新在多目标进化算法中总是优越的。
• 从理论上分析随机化种群更新如何影响基准 MOEAs 的运行时间。
• 在选定的双目标问题上展示指数级的运行时间改进。

提出的方法

• 为 SMS-EMOA（算法 5）和 NSGA-II（算法 6）引入随机化种群更新机制，以取代它们的确定性更新。
• 对两个双目标问题进行理论运行时间分析：OneJumpZeroJump 和双目标 RealRoyalRoad。
• 给出在确定性更新与随机更新下的期望代数的上、下界，突出在某些参数范围内的指数级降低。
• 提供经验性实验以验证理论发现。

实验结果

研究问题

• RQ1 引入种群更新步骤中的随机性是否会在标准双目标基准上改善 SMS-EMOA 和 NSGA-II 的理论运行时间？
• RQ2 在哪些问题实例和参数设置下，随机化种群更新相对于确定性更新能产生指数级加速？
• RQ3 随机更新如何影响在 OneJumpZeroJump 和 RealRoyalRoad 的帕累托最优近邻区域的探索能力？

主要发现

• 在某些 k 和 μ 设置下，随机化种群更新可使 SMS-EMOA 求解 OneJumpZeroJump 的期望代数呈指数级降低。
• 在某些条件下，随机化种群更新可使 NSGA-II 求解 OneJumpZeroJump 的期望代数呈指数级降低。
• 对于双目标 RealRoyalRoad 问题，随着 μ 增大，随机更新在运行时间界限上带来显著、有时是指数级的改进。
• 理论结果得到实证研究的补充，验证所提随机更新的有效性。