[论文解读] Evolutionary Multitasking for Multiobjective Continuous Optimization: Benchmark Problems, Performance Metrics and Baseline Results

Yuan Yuan, Yew-Soon Ong+8 more|arXiv (Cornell University)|Jun 8, 2017

Advanced Multi-Objective Optimization Algorithms参考文献 9被引用 134

一句话总结

本文提出九个基准 MO-MFO 问题（两任务多任务学习用于多目标优化），在不同的交集和适应度景观相似度下，定义评估指标（IGD、MSS），并给出基线 MO-MFEA 相对于 NSGA-II 的跨多对任务的结果。

ABSTRACT

In this report, we suggest nine test problems for multi-task multi-objective optimization (MTMOO), each of which consists of two multiobjective 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 MO-MFO algorithms. It is expected that the proposed test problems will germinate progress the field of the MTMOO research.

研究动机与目标

• Motivate and formalize evolutionary multitasking for multiobjective optimization (MO-MFO).
• Define nine benchmark problem pairs with controlled task relationships (intersection and similarity).
• Propose evaluation metrics (IGD, MSS) and standardized experimental protocol.
• Provide baseline results comparing MO-MFEA to NSGA-II across all benchmark problems.

提出的方法

• Define MO-MFO benchmark problems based on q(x) landscape and task pair relations (complete/partial/no intersection × high/medium/low similarity).
• Use a single population to solve two MO tasks concurrently (MO-MFEA) and compare with solving tasks separately (NSGA-II).
• Evaluate with inverted generational distance (IGD) and derive mean standard score (MSS) for overall ranking.
• Run 30 independent trials with fixed evaluation budgets; standard crossover/mutation settings (p_c=0.9, p_m=1/D, eta_c=eta_m=20).
• Report baseline results and convergence/density of solutions on Pareto fronts.

实验结果

研究问题

• RQ1 How do task relationships (intersection and landscape similarity) affect knowledge transfer in MO-MFO?
• RQ2 Can MO-MFEA outperform single-task MOEAs (NSGA-II) on paired MO tasks across the proposed benchmarks?
• RQ3 What are the convergence and diversity characteristics of MO-MFEA vs NSGA-II on these MO-MFO benchmarks?

主要发现

问题	sim(T1,T2)	任务	IGD_NSGA-II	IGD_MO-MFEA	SD_MO-MFEA
CIHS	0.97	T1	2.0234E-3	3.9912E-4	(9.7671E-5)
CIHS	0.97	T2	4.3621E-3	2.6491E-3	(5.6744E-4)
CIMS	0.52	T1	1.0045E-1	4.5705E-2	(7.5847E-2)
CIMS	0.52	T2	2.2897E-2	8.7723E-3	(1.9082E-2)
CILS	0.07	T1	2.5503E-1	2.7105E-4	(1.0821E-1)
CILS	0.07	T2	1.9905E-4	1.8986E-4	(6.513E-6)
PIHS	0.99	T1	1.1145E-3	1.1029E-3	(3.8107E-4)
PIHS	0.99	T2	5.654E-2	3.0406E-2	(1.6188E-2)
PIMS	0.55	T1	4.4903E-3	2.6206E-3	(1.6131E-3)
PIMS	0.55	T2	1.5577E1	1.0892E1	(3.7002E0)
PILS	0.002	T1	2.7647E-4	3.2401E-4	(1.2629E-4)
PILS	0.002	T2	6.3458E-1	1.099E-2	(8.8258E-4)
NIHS	0.94	T1	3.1286E1	1.5523E0	(6.0683E1)
NIHS	0.94	T2	7.8558E-4	5.0224E-4	(1.6655E-4)
NIMS	0.51	T1	4.7021E-1	2.792E-1	(3.3048E-1)
NIMS	0.51	T2	9.1944E-2	2.8576E-2	(8.8784E-2)
NILS	0.001	T1	8.3588E-4	8.3483E-4	(5.4979E-5)
NILS	0.001	T2	6.4226E-1	6.4316E-1	(2.5715E-4)

• MO-MFEA generally outperforms NSGA-II on most task pairs, with significant IGD improvements across several problems.
• MO-MFEA tends to converge faster than NSGA-II on many problems when solving two MO tasks concurrently.
• Performance gains vary by problem; some cases (e.g., PILS-T1, NILS) show smaller or mixed advantages.
• Table shows IGD values where MO-MFEA often achieves lower IGD than NSGA-II across tasks.
• MSS comparisons indicate MO-MFEA usually yields better overall performance, except for selected cases like NILS where NSGA-II performance is closer.
• Convergence visualizations indicate MO-MFEA provides PF approximations that are typically more diverse and closer to the true PF