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Multiobjective Optimization Subset Selection Proven NP-Hard in Three Objectives

By PulseAugur Editorial · [1 sources] ·

Researchers have identified that selecting representative points from a multiobjective optimization Pareto front is NP-hard for three objectives. However, they also demonstrated that the integral R2 indicator, a measure of Pareto front quality, is a monotone submodular set function. This property allows for a greedy approximation algorithm that can achieve at least a (1-1/e) fraction of the maximum possible R2 gap. The study also provides an implementation of this greedy approach, which has a worst-case running time of O(n^6). AI

IMPACT This research provides theoretical underpinnings for subset selection in complex optimization problems, potentially impacting AI systems that rely on efficient decision-making in multi-objective scenarios.

RANK_REASON Academic paper detailing theoretical results and algorithmic approaches in multiobjective optimization. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv cs.NE (Neural & Evolutionary) →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Multiobjective Optimization Subset Selection Proven NP-Hard in Three Objectives

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Academic paper detailing theoretical results and algorithmic approaches in multiobjective optimization. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv cs.NE (Neural & Evolutionary) TIER_1 English(EN) · Michael T. M. Emmerich ·

    Three-Objective Integral R2 Subset Selection: NP-Hardness and Submodular Approximation

    Selecting a fixed number of representative points from a finite Pareto-front approximation is a fundamental post-processing task in multiobjective optimization. This paper studies this problem for the integral R2 indicator in three objectives, where the indicator is defined as th…

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