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Maximizing Nash Social Welfare Based on Greedy Algorithm and Estimation of Distribution Algorithm.

Weizhi Liao1, Youzhen Jin1, Zijia Wang2

  • 1School of Information Science and Engineering, Jiaxing University, Jiaxing 314001, China.

Biomimetics (Basel, Switzerland)
|November 26, 2024
PubMed
Summary
This summary is machine-generated.

Maximizing Nash social welfare (NSW), an APX-hard problem, is addressed by two new methods. An Estimation of Distribution Algorithm (EDA) with neighborhood search shows superior results compared to a general greedy algorithm (GA).

Keywords:
Nash social welfareestimation of distribution algorithmgreedy algorithmneighborhood search

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Area of Science:

  • Computer Science
  • Economics
  • Operations Research

Background:

  • The Nash social welfare (NSW) problem is crucial in economics and computer science.
  • Maximizing NSW is computationally challenging, classified as an APX-hard problem.

Purpose of the Study:

  • To propose and evaluate novel algorithms for enhancing Nash social welfare maximization.
  • To address NSW problems for agents with both identical and differing valuations.

Main Methods:

  • Development of a general greedy algorithm (GA) applicable to various agent valuation types.
  • Introduction of an innovative evolutionary approach integrating Estimation of Distribution Algorithms (EDAs) with neighborhood search.
  • Empirical implementation and comparison of the proposed GA and EDA methods on diverse instances.

Main Results:

  • The GA aligns with existing methods for identical agent valuations.
  • The EDA-based approach demonstrates superior performance in approximating maximal Nash social welfare.
  • Experimental results confirm the effectiveness of the EDA over the GA for NSW maximization.

Conclusions:

  • The proposed EDA with neighborhood search offers a more effective strategy for maximizing Nash social welfare.
  • This study advances computational approaches to welfare maximization problems in multi-agent systems.