[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

• 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.