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<p>The Combined Economic and Emission Dispatch (CEED) problem is inherently a multi-objective optimization challenge, aiming to simultaneously minimize fuel costs and pollutant emissions of power generation while satisfying power demand and adhering to operational constraints. To address this multi-objective nature, this study adopts a price-based penalty factor approach to transform the CEED problem into a single-objective optimization problem, where the weighted combination of cost and emissions guides the search toward solutions that balance economic and environmental performance. To solve the transformed single-objective problem effectively, a novel multi-strategy hybrid Frilled Lizard Optimization (FLO) algorithm is proposed. This algorithm integrates a hybrid Harris Hawks Optimization (HHO) strategy with a hybrid sine oscillatory strategy, broadening the search space and mitigating the risk of premature convergence to local optima, thereby improving the overall search efficiency. Constraint handling is further enhanced through seven dynamic penalty functions, each designed to enforce operational limits while maintaining flexibility. Building on this, an oscillation strategy based on dynamic penalty functions is introduced to adaptively perturb the search process, allowing exploration of promising regions more thoroughly. To further improve solution quality and convergence speed, a roulette-wheel-based integrated oscillation strategy is also proposed, combining multiple oscillation mechanisms in a synergistic manner. The proposed algorithm and its variants are first validated on 12 benchmark functions from the CEC-BC-2022 test suite to identify the best-performing configuration. This configuration is then applied to the CEED problem considering realistic operational constraints, including valve-point effects and ramp rate limits, under four different power demand scenarios (150&#xa0;MW, 175&#xa0;MW, 200&#xa0;MW, and 225&#xa0;MW). Experimental results show that the oscillation strategy significantly improves algorithmic performance, while the integrated oscillation strategy further optimizes outcomes, achieving the lowest total generation costs across all scenarios. Specifically, the proposed method reduces total costs by 8.7%, 6.9%, 5.1%, and 3.6% compared to the baseline hybrid FLO algorithm. These findings demonstrate that transforming the CEED into a single-objective problem via price-based penalty factors, combined with dynamic and integrated oscillation strategies, provides an effective framework for efficient and cost-effective power dispatch.</p>

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Multi-strategy fusion frilled lizard optimization algorithm based on oscillation integrated penalty function for combined economic emission dispatch problem

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Hao-Ming Song,
  • Xin-Yi Guan,
  • Jie-Sheng Wang,
  • Cheng Xing,
  • Yi-Xuan Li,
  • Xun Liu,
  • Jia-Hui Zhao

摘要

The Combined Economic and Emission Dispatch (CEED) problem is inherently a multi-objective optimization challenge, aiming to simultaneously minimize fuel costs and pollutant emissions of power generation while satisfying power demand and adhering to operational constraints. To address this multi-objective nature, this study adopts a price-based penalty factor approach to transform the CEED problem into a single-objective optimization problem, where the weighted combination of cost and emissions guides the search toward solutions that balance economic and environmental performance. To solve the transformed single-objective problem effectively, a novel multi-strategy hybrid Frilled Lizard Optimization (FLO) algorithm is proposed. This algorithm integrates a hybrid Harris Hawks Optimization (HHO) strategy with a hybrid sine oscillatory strategy, broadening the search space and mitigating the risk of premature convergence to local optima, thereby improving the overall search efficiency. Constraint handling is further enhanced through seven dynamic penalty functions, each designed to enforce operational limits while maintaining flexibility. Building on this, an oscillation strategy based on dynamic penalty functions is introduced to adaptively perturb the search process, allowing exploration of promising regions more thoroughly. To further improve solution quality and convergence speed, a roulette-wheel-based integrated oscillation strategy is also proposed, combining multiple oscillation mechanisms in a synergistic manner. The proposed algorithm and its variants are first validated on 12 benchmark functions from the CEC-BC-2022 test suite to identify the best-performing configuration. This configuration is then applied to the CEED problem considering realistic operational constraints, including valve-point effects and ramp rate limits, under four different power demand scenarios (150 MW, 175 MW, 200 MW, and 225 MW). Experimental results show that the oscillation strategy significantly improves algorithmic performance, while the integrated oscillation strategy further optimizes outcomes, achieving the lowest total generation costs across all scenarios. Specifically, the proposed method reduces total costs by 8.7%, 6.9%, 5.1%, and 3.6% compared to the baseline hybrid FLO algorithm. These findings demonstrate that transforming the CEED into a single-objective problem via price-based penalty factors, combined with dynamic and integrated oscillation strategies, provides an effective framework for efficient and cost-effective power dispatch.