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Lagrange Multipliers: Two Constraints01:28

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Updated: Jul 9, 2026

Robotic Sensing and Stimuli Provision for Guided Plant Growth
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Multi-UAV cooperative path planning based on multi-strategy enhanced multi-objective phototropic growth algorithm.

Anruo Wei1, Kang Kang2, Hailiang Liu3

  • 1School of Artificial Intelligence, Chongqing Industry and Trade Polytechnic, Chongqing, 408000, China. weianruo@cqgmy.edu.cn.

Scientific Reports
|July 7, 2026
PubMed
Summary

This study introduces an Enhanced Multi-Objective Phototropic Growth Algorithm (EMOPGA) for efficient multi-Unmanned Aerial Vehicle (UAV) transport in hilly terrain. EMOPGA significantly improves path planning optimization, enhancing logistics and emergency response capabilities.

Keywords:
Collaborative planningMulti-UAVMulti-strategy EMOPGAPath planning

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Area of Science:

  • * Optimization Algorithms
  • * Robotics and Automation
  • * Logistics and Transportation

Background:

  • * Traditional ground transportation faces significant challenges in hilly terrain due to topographical constraints.
  • * Existing optimization algorithms like Phototropic Growth Algorithm (PGA) suffer from local optima and suboptimal initial populations.
  • * Cooperative transport using multiple Unmanned Aerial Vehicles (UAVs) offers a potential solution but requires advanced path planning.

Purpose of the Study:

  • * To develop an enhanced optimization algorithm, EMOPGA, for efficient multi-UAV cooperative transport in complex terrains.
  • * To overcome the limitations of the standard PGA by incorporating novel initialization, mutation, and selection strategies.
  • * To evaluate the performance of EMOPGA against existing algorithms in various simulation scenarios.

Main Methods:

  • * Integration of chaotic mapping for improved initial population quality.
  • * Inclusion of Lévy flight mutation operators to enhance exploration capabilities.
  • * Implementation of an environmental selection mechanism based on Pareto dominance and elite retention.

Main Results:

  • * EMOPGA demonstrated a 112.11% improvement in Average Hypervolume (HV) and a 43.11% reduction in Spacing (SP) compared to MOPGA.
  • * In complex scenarios, EMOPGA achieved an average HV of 9.31 × 1013 and an average SP of 0.0322.
  • * EMOPGA outperformed 11 representative algorithms, showing significant improvements in HV and SP metrics.

Conclusions:

  • * EMOPGA provides an efficient and robust optimization paradigm for multi-UAV path planning in complex terrains.
  • * The algorithm combines high convergence, strong uniformity, and superior performance.
  • * EMOPGA shows significant potential for practical applications in logistics and emergency response operations.