[論文レビュー] 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被引用数 137

ひとこと要約

この論文は単一目的連続タスクの多因子 Evolutionary optimization を定式化し、 derivative-free なタスク間シナジー指標を導入し、最適解の類似性と交差を変化させた9つのベンチマークタスクペアを構築し、基準となる MFEA と SOEA の結果を提供します。

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.

研究の動機と目的

• Motivate and formalize evolutionary multitasking (multifactorial optimization) for a single population solving multiple related tasks simultaneously.
• Define and compute a simple, derivative-free inter-task synergy metric to quantify task similarity.
• Construct and publish a benchmark suite of nine task pairs with varying degrees of optima intersection and similarity.
• Provide baseline results using Multifactorial Evolutionary Algorithm (MFEA) and a Single-Task Evolutionary Algorithm (SOEA) on the benchmark sets.
• Offer MATLAB implementations and a baseline evaluation framework to guide future research in evolutionary multitasking.

提案手法

• Adopt a unified genotype space Y and a decoding scheme to map Y to multiple task spaces Xj using a random-key representation.
• Define factorial cost, factorial rank, skill factor, scalar fitness, and multifactorial optimality to enable cross-task selection and evaluation within a single population.
• Utilize the Multifactorial Evolutionary Algorithm (MFEA) with vertical cultural transmission (selective imitation) to transfer knowledge across tasks during crossover and mutation.
• Quantify inter-task synergy with a derivative/integration-free Spearman rank correlation between factorial ranks of paired tasks across many decoded solutions.
• Construct nine benchmark problem pairs from seven classic single-task functions (Sphere, Rosenbrock, Ackley, Rastrigin, Griewank, Weierstrass, Schwefel) under various optima intersection and similarity regimes.
• Provide baseline performance using MFEA and SOEA with SBX crossover and polynomial mutation, and report average results over 20 runs.

実験結果

リサーチクエスチョン

• 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?

主な発見

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.