[论文解读] Evolutionary Multitasking for Single-objective Continuous Optimization: Benchmark Problems, Performance Metric, and Baseline Results

Bingshui Da, Yew-Soon Ong+7 more|arXiv (Cornell University)|Jun 12, 2017

Advanced Multi-Objective Optimization Algorithms被引用 137

一句话总结

本文将多因素进化优化正式化为单目标连续任务，提出一个无导数的任务间协同度度量，构建具有不同相似性和最优解交集的九对基准任务，并给出基线的 MFEA 和 SOEA 结果。

ABSTRACT

In this report, we suggest nine test problems for multi-task single-objective optimization (MTSOO), each of which consists of two single-objective optimization tasks that need to be solved simultaneously. The relationship between tasks varies between different test problems, which would be helpful to have a comprehensive evaluation of the MFO algorithms. It is expected that the proposed test problems will germinate progress the field of the MTSOO research.

研究动机与目标

• 动机并将进化多任务（多因素优化）形式化为在同一群体中同时解决多个相关任务。
• 定义并计算一个简单的、无导数的任务间协同度度量，用以量化任务相似性。
• 构建并发布九对具有不同最优解交集程度和相似性的基准任务对。
• 在基准集上提供使用多因素进化算法（MFEA）和单任务进化算法（SOEA）的基线结果。
• 提供 MATLAB 实现和基线评估框架，以指导未来的进化多任务研究。

提出的方法

• 采用统一的基因型空间 Y，并使用随机密钥表示将 Y 解码映射到多个任务空间 Xj。
• 定义因子成本、因子等级、技能因子、标量适应度，以及多因素最优性，以在单群体内实现跨任务选择与评估。
• 在交叉与变异过程中，使用具有垂直文化传递（选择性模仿）的多因素进化算法（MFEA），在任务之间转移知识。
• 使用对多解解码结果的成对任务的因子等级的 Spearman 等级相关性，且不需要导数/积分，来量化任务间协同。
• 从七个经典单任务函数（Sphere、Rosenbrock、Ackley、Rastrigin、Griewank、Weierstrass、Schwefel）构建九对基准问题，在不同的最优解交集与相似性条件下。
• 提供使用 SBX 交叉和多项式变异的 MFEA 与 SOEA 的基线性能，并报告 20 次重复的平均结果。

实验结果

研究问题

• RQ1 What is the impact of inter-task synergy on multitask optimization performance for single-objective problems?
• RQ2 How do complete, partial, and no intersections of global optima influence transfer and convergence in evolutionary multitasking?
• RQ3 How does task similarity, quantified by Spearman rank correlation of factorial ranks, correlate with performance gains of the MFEA?
• RQ4 What baseline performancedo MFEA and SOEA achieve on the nine constructed benchmark pairs across varying similarity regimes?

主要发现

Category	T1 (MFEA)	T2 (MFEA)	Score (MFEA)	T1 (SOEA)	T2 (SOEA)	Score (SOEA)
CI+HS	0.3732	194.6774	-37.6773	0.9084	410.3692	37.6773
CI+MS	4.3918	227.6537	-25.2130	5.3211	440.5710	25.2130
CI+LS	20.1937	3700.2443	-25.7157	21.1666	4118.7017	25.7157
PI+HS	613.7820	10.1331	-6.8453	445.1040	83.9985	6.8453
PI+MS	3.4988	702.5026	-33.1556	5.0665	23956.6394	33.1556
PI+LS	20.0101	19.3731	36.1798	5.0485	13.1894	-36.1798
NI+HS	1008.1740	287.7497	-33.7021	24250.9184	447.9407	33.7021
NI+MS	0.4183	27.1470	-35.2738	0.9080	36.9601	35.2738
NI+LS	650.8576	3616.0492	4.2962	437.9926	4139.8903	-4.2962

• A derivative-free Spearman rank correlation is proposed to quantify inter-task synergy between task pairs.
• Nine composite benchmark problem pairs are constructed from seven classic continuous functions, spanning complete/partial/no optima intersections and high/medium/low similarity.
• Baseline results show diverse transfer effects: some task pairs yield clear benefits from multitasking (e.g., CI+HS, CI+MS, NI+MS), while others exhibit limited or negative gains depending on similarity and intersection.
• Table IV reports mean performances across 20 runs showing MFEA and SOEA results across all nine problem pairs, illustrating the relative strengths of multitasking versus single-task optimization under different synergy regimes.
• The authors provide MATLAB implementations of the MFEA and the benchmark suite to support replication and future research.