[Paper Review] 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 Algorithms137 citations

TL;DR

This paper formalizes multifactorial evolutionary optimization for single-objective continuous tasks, introduces a derivative-free inter-task synergy metric, constructs nine benchmark task pairs with varying similarity and intersection of optima, and provides baseline MFEA and SOEA results.

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.

Motivation & Objective

• 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.

Proposed method

• 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.]
• research_questions_1_2_3_4_5_6_7_8_9_10_11_12_13_14_15_16_17_18_19_20_21_22_23_24_25_26_27_28_29_30_31_32_33_34_35_36_37_38_39_40_41_42_43_44_45_46_47_48_49_50_51_52_53_54_55_56_57_58_59_60_61_62_63_64_65_66_67_68_69_70_71_72_73_74_75_76_77_78_79_80_81_82_83_84_85_86_87_88_89_90_91_92_93_94_95_96_97_98_99_100_?
• research_questions_1_2_3_4_5_6_7_8_9_10_11_12_13_14_15_16_17_18_19_20_21_22_23_24_25_26_27_28_29_30_31_32_33_34_35_36_37_38_39_40_41_42_43_44_45_46_47_48_49_50_51_52_53_54_55_56_57_58_59_60_61_62_63_64_65_66_67_68_69_70_71_72_73_74_75_76_77_78_79_80_81_82_83_84_85_86_87_88_89_90_91_92_93_94_95_96_97_98_99_100_?

Experimental results

Research questions

• 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?

Key findings

• 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.