Open Access

ARTICLE

Differential Evolution with Improved Equilibrium Optimizer for Combined Heat and Power Economic Dispatch Problem

Yuanfei Wei^1,2, Panpan Song³, Qifang Luo^3,4,*, Yongquan Zhou^1,2,3,4

1 Xiangsihu College of Guangxi Minzu University, Nanning, 530006, China
2 Faculty of Information Science and Technology, National University of Malaysia (UKM), Bangi Selangor, 43600, Malaysia
3 College of Artificial Intelligence, Guangxi Minzu University, Nanning, 530006, China
4 Guangxi Key Laboratories of Hybrid Computation and IC Design Analysis, Nanning, 530006, China

* Corresponding Author: Qifang Luo. Email:

(This article belongs to the Special Issue: Advancements in Evolutionary Optimization Approaches: Theory and Applications)

Computers, Materials & Continua 2025, 85(1), 1235-1265. https://doi.org/10.32604/cmc.2025.066527

Received 10 April 2025; Accepted 24 June 2025; Issue published 29 August 2025

Abstract

The combined heat and power economic dispatch (CHPED) problem is a highly intricate energy dispatch challenge that aims to minimize fuel costs while adhering to various constraints. This paper presents a hybrid differential evolution (DE) algorithm combined with an improved equilibrium optimizer (DE-IEO) specifically for the CHPED problem. The DE-IEO incorporates three enhancement strategies: a chaotic mechanism for initializing the population, an improved equilibrium pool strategy, and a quasi-opposite based learning mechanism. These strategies enhance the individual utilization capabilities of the equilibrium optimizer, while differential evolution boosts local exploitation and escape capabilities. The IEO enhances global search to enrich the solution space, and DE focuses on local exploitation for more accurate solutions. The effectiveness of DE-IEO is demonstrated through comparative analysis with other metaheuristic optimization algorithms, including PSO, DE, ABC, GWO, WOA, SCA, and equilibrium optimizer (EO). Additionally, improved algorithms such as the enhanced chaotic gray wolf optimization (ACGWO), improved particle swarm with adaptive strategy (MPSO), and enhanced SCA with elite and dynamic opposite learning (EDOLSCA) were tested on the CEC2017 benchmark suite and four CHPED systems with 24, 84, 96, and 192 units, respectively. The results indicate that the proposed DE-IEO algorithm achieves satisfactory solutions for both the CEC2017 test functions and real-world CHPED optimization problems, offering a viable approach to complex optimization challenges.

---

Keywords

---