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An intelligent quasi-oppositional HBO technique to solve non-smooth non-convex economic dispatch problem

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Abstract

In this paper, a modified heap-based optimization (HBO) known as the quasi-oppositional heap-based optimization (QOHBO) method is endeavored to tackle the challenging problem of non-convex economic load dispatch problem (ELDP) in large-scale power systems. The QOHBO method leverages a heap data structure to emulate the concept of corporate ranking hierarchy. The mathematical model of HBO is based on the three strategies; first, the interaction between subordinates and their direct superior; second, interactions between contemporaries; third, the employees' self-contribution is adopted to perform both the exploration and exploitation in the search space. To enhance the solution quality and computational efficiency in solving ELDP, we integrate the concept of quasi-oppositional learning into HBO. The proposed QOHBO technique effectively addresses various constraints, including transmission line losses, valve-point loading effects, generator generation limits, prohibited operating zones, power demand compliance, and ramp rate limits. The feasibility of the QOHBO to solve ELDP is evaluated by conducting ten distinct case studies across nine diverse test systems, featuring generating units ranging from three to 140. Comparative analysis with existing techniques from the literature highlights the superior performance of our proposed method in solving large-scale ELD problems. Subsequently, non-parametric alternative tests specifically the Wilcoxon rank-sum test and the Friedman test has been conducted to verify the efficacy of the proposed QOHBO. Moreover, extensive statistical analysis reveals that the QOHBO technique has the ability to consistently provide quality solutions and its robustness when compared to other state-of-the-art approaches.

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Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Abbreviations

HBO:

Heap based optimization

QOHBO:

Quasi-oppositional heap-based optimization

ELD:

Economic load dispatch

ELDP:

Economic load dispatch problem

VPL:

Valve-point loading

VPLE:

Valve-point loading effect

RRLs:

Ramp-rate limits

GOLs:

Generating operating limits

TLLs:

Transmission line losses

POZs:

Prohibited operating zones

GA:

Genetic algorithm

EP:

Evolutionary programming

PSO:

Particle swarm optimization

TLBO:

Teaching learning-based optimization

BBO:

Biogeography based optimization

GWO:

Grey wolf optimization

KHA:

Krill herd algorithm

OIWO:

Oppositional invasive weed optimization

ORCCRO:

Oppositional real coded chemical reaction

CPSO:

Chaotic PSO

SQP:

Sequential quadratic programming

GA-ACO:

Hybrid GA and ant colony optimization

CDE-QP:

Hybrid chaotic DE and quadratic programming

CCDE:

Colonial competitive DE

GSA:

Gravitational search algorithm

MCSA:

Modified crow search algorithm

SA:

Simulated annealing

ASA:

Adaptive simulated annealing

HBO:

Heap-based optimizer

CORH:

Corporate rank hierarchy

QOBL:

Quasi-oppositional based learning

FCF:

Fuel cost function

DE:

Differential evolution

OKHA:

Oppositional krill herd algorithm

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Acknowledgements

The authors are grateful to their respective organizations for providing research opportunities and providing necessary resources towards completion of this paper.

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  1. Department of Electrical and Electronics Engineering, SR University, Warangal, Telangana, 506371, India

    Vedik Basetti, Chandan Kumar Shiva & Sachidananda Sen

  2. Department of Electrical Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

    Vivekananda Mukherjee

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  4. Vivekananda Mukherjee
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Conceptualization, CKS and BV; methodology, CKS and BV.; software, VM; validation, CKS and BV.; formal analysis, CKS and BV; investigation, VM.; writing—original draft preparation, CKS and BV.; writing—review and editing, CKS, SS and BV; visualization, SS. All authors have read and agreed to the published version of the manuscript.

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Basetti, V., Shiva, C.K., Sen, S. et al. An intelligent quasi-oppositional HBO technique to solve non-smooth non-convex economic dispatch problem. Evol. Intel. 17, 2293–2344 (2024). https://doi.org/10.1007/s12065-023-00889-1

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