Deep Neural Network-guided PSO for Tracking a Global Optimal Position in Complex Dynamic Environment

Stephen Raharja; Toshiharu Sugawara

arxiv: 2604.14064 · v1 · submitted 2026-04-15 · 💻 cs.NE

Deep Neural Network-guided PSO for Tracking a Global Optimal Position in Complex Dynamic Environment

Stephen Raharja , Toshiharu Sugawara This is my paper

Pith reviewed 2026-05-10 11:32 UTC · model grok-4.3

classification 💻 cs.NE

keywords particle swarm optimizationdeep neural networksdynamic optimizationglobal optimum trackingadaptive swarm algorithmsmoving peaks

0 comments

The pith

DNN-integrated PSO variants track moving global optima in dynamic environments using fewer particles than the number of potential optima.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces particle swarm optimization variants that incorporate deep neural networks to guide particles toward globally optimal positions that shift over time in complex dynamic environments. Canonical PSO and many variants require large swarms or repeated re-diversification to cope with moving optima, outdated information, and local traps. The proposed methods instead let the networks learn environmental characteristics and adapt particle dynamics to predict and pursue the optima. Experiments indicate both a centralized-network variant and a distributed-network variant achieve lower cumulative tracking error than several recent PSO algorithms while maintaining swarm sizes smaller than the number of potential optima.

Core claim

What carries the argument

Deep neural network guidance of particle movement, implemented either as a single centralized network for the swarm or as distributed networks attached to individual particles, that learns environmental patterns to predict and steer toward shifting optima.

If this is right

Smaller swarms than the number of potential optima suffice for accurate global-optimum tracking.
Both centralized and distributed DNN variants reduce cumulative tracking error relative to recent PSO methods in changing environments.
The approaches avoid heavy reliance on multiple sub-populations or explicit re-diversification mechanisms.
Particles gain the ability to predict optimum movement from learned environmental dynamics rather than reacting only to current fitness values.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could lower computational cost in real-time applications such as robot path planning or dynamic resource allocation where swarm size directly affects speed.
Training data requirements for the networks may limit use in environments that change too rapidly or lack repeatable patterns for learning.
The same guidance principle might transfer to other swarm-based optimizers or be combined with reinforcement-learning updates for longer-horizon prediction.

Load-bearing premise

Deep neural networks can reliably learn the characteristics of complex dynamic environments in order to predict and pursue moving optimal positions.

What would settle it

An experiment on a dynamic test function with many rapidly moving peaks in which the DNN-guided variants produce higher cumulative tracking error or require swarm sizes at least as large as the number of peaks would falsify the central performance claim.

Figures

Figures reproduced from arXiv: 2604.14064 by Stephen Raharja, Toshiharu Sugawara.

**Figure 1.** Figure 1: Example of 𝑔(𝑡) location relative to peaks ℎ1, ℎ2. with more potential optimal points than particles, without explicit change detection. 3 Preliminaries 3.1 Environment Model and Problem Description Inspired by the characteristics of estimated search areas of human presence in post-disaster situations, we model the environment 𝐸, a finite square-shaped two-dimensional bounded vector space in R × R center… view at source ↗

**Figure 2.** Figure 2: Visualization of particle 𝑝𝑖 in NNGPSO with two example observation points performance across domains, including computer vision and reinforcement learning [14, 17]. In our context, DNNs offer a flexible framework for capturing complex patterns in dynamic environments, thereby enhancing the convergence performance of the proposed methods [21]. This is valuable in our modeled problem, where the particle co… view at source ↗

**Figure 3.** Figure 3: Utility values of actual global best position [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

read the original abstract

We propose novel particle swarm optimization (PSO) variants incorporated with deep neural networks (DNNs) for particles to pursue globally optimal positions in dynamic environments. PSO is a heuristic approach for solving complex optimization problems. However, canonical PSO and its variants struggle to adapt efficiently to dynamic environments, in which the global optimum moves over time, and to track them accurately. Many PSO algorithms improve convergence by increasing the swarm size beyond potential optima, which are global/local optima but are not identified until they are discovered. Additionally, in dynamic environments, several methods use multiple sub-population and re-diversification mechanisms to address outdated memory and local optima entrapment. To track the global optimum in dynamic environments with smaller swarm sizes, the DNNs in our methods determine particle movement by learning environmental characteristics and adapting dynamics to pursue moving optimal positions. This enables particles to adapt to environmental changes and predict the moving optima. We propose two variants: a swarm with a centralized network and distributed networks for all particles. Our experimental results show that both variants can track moving potential optima with lower cumulative tracking error than those of several recent PSO-based algorithms, with fewer particles than potential optima.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces two concrete DNN-PSO hybrids that guide particles via learned environmental dynamics and reports better tracking with smaller swarms than recent baselines.

read the letter

The main takeaway is that the authors integrate deep neural networks into PSO to let particles learn and adapt to moving optima in dynamic environments, achieving lower cumulative tracking error than several recent PSO variants while using fewer particles than the number of potential optima. They describe a centralized DNN version and a distributed one where each particle has its own network, both of which replace the usual reliance on larger swarms or explicit re-diversification with learned movement guidance. This is a direct and practical extension of standard PSO update rules rather than a wholesale reinvention. The full manuscript supplies the environment generation protocols, baseline implementations, and experimental setup that were missing from the abstract, which makes the reported gains more checkable. The approach does well at showing how a DNN can capture environmental characteristics to predict optima movement without inflating swarm size. The citation pattern follows the expected PSO and dynamic optimization literature without obvious gaps or self-referential loops. Soft spots are limited. The gains rest on the DNN learning the dynamics reliably, and while the tested cases support this, the paper could have included more sensitivity checks on DNN architecture or PSO coefficients to show robustness. Statistical reporting on the error reductions is present but not emphasized. This work is aimed at people already working on swarm methods for time-varying optimization problems in robotics or adaptive control. A reader looking for a concrete hybrid of learning and heuristics will find usable variants and verifiable claims. It deserves peer review because the central tracking result is experimentally grounded and the method is specified clearly enough for others to replicate or extend.

Referee Report

0 major / 2 minor

Summary. The paper claims to introduce two variants of particle swarm optimization (PSO) enhanced with deep neural networks (DNNs) to track global optimal positions in complex dynamic environments. One variant uses a centralized DNN, and the other uses distributed DNNs for each particle. The methods aim to allow particles to learn and adapt to environmental changes to pursue moving optima. Experimental results are reported to show lower cumulative tracking error than several recent PSO algorithms, achieved with swarm sizes smaller than the number of potential optima.

Significance. If these results hold under scrutiny, the significance is notable for advancing hybrid methods in evolutionary computation. By integrating DNNs to predict and guide towards moving optima, the approach reduces reliance on large swarm sizes or complex re-diversification strategies common in dynamic PSO literature. This could have implications for applications in time-varying optimization problems. The manuscript's inclusion of detailed experimental protocols addresses potential concerns about verification, lending credibility to the claims.

minor comments (2)

The abstract could more explicitly summarize the DNN architectures and training process to provide immediate context for the proposed variants.
Clarify the exact mechanism by which the DNN outputs influence particle velocity updates, perhaps with a pseudocode or equation in the methods section for better reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the potential significance of our DNN-guided PSO approach for dynamic optimization, and recommendation for minor revision. The feedback affirms the value of reduced swarm sizes and lower cumulative tracking error compared to recent PSO variants. No specific major comments were listed in the report, so we provide no point-by-point rebuttals below and will incorporate minor improvements for clarity and verification in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity; experimental validation against external baselines

full rationale

The paper proposes two DNN-guided PSO variants whose particle movements are determined by learned environmental characteristics. The central claim is an empirical result: lower cumulative tracking error than several recent PSO-based algorithms, achieved with swarm size smaller than the number of potential optima. No equations, derivations, or first-principles steps are shown that reduce the claimed improvement to fitted parameters, self-definitions, or self-citations. Performance is measured against independent external algorithms rather than being defined in terms of the DNN outputs themselves. This is the most common honest finding for an experimental methods paper.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the empirical performance of trained neural networks whose internal parameters are learned from environment data; no new physical entities are postulated.

free parameters (2)

DNN weights and architecture hyperparameters
Weights are fitted during training on environmental trajectories; these learned values directly determine particle movement decisions.
PSO inertia and acceleration coefficients
Standard PSO parameters are retained and presumably tuned for the dynamic case.

axioms (1)

domain assumption Deep neural networks can extract and generalize environmental dynamics sufficiently to predict future optima locations
Invoked when the authors state that DNNs determine particle movement by learning environmental characteristics.

pith-pipeline@v0.9.0 · 5502 in / 1202 out tokens · 48904 ms · 2026-05-10T11:32:44.086404+00:00 · methodology

discussion (0)

Reference graph

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Gandomi, and Xin Yao

Delaram Yazdani, Danial Yazdani, Donya Yazdani, Mohammad Nabi Omidvar, Amir H. Gandomi, and Xin Yao. A species-based particle swarm optimization with adaptive population size and deactivation of species for dynamic optimization problems.ACM Transactions on Evolutionary Learning and Optimization, 3:1 – 25, 2023

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Pei-Yao Zhu, Sheng-Hao Wu, Ke-Jing Du, Hua Wang, Jun Zhang, and Zhi hui Zhan. Diversity-driven multi-population particle swarm optimization for dy- namic optimization problem.Proceedings of the Companion Conference on Genetic and Evolutionary Computation, 2023

work page 2023