[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

• 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.