Solving the economic dispatch problem for combined heat and electricity using the Hybrid Firefly Algorithm with Sequential Quadratic Programming

Optimization problems are a fundamental component of engineering and scientific research, particularly in energy systems, where growing industrial demands necessitate the development of robust and efficient optimization algorithms. The Combined Heat and Power Economic Dispatch (CHPED) problem seeks to minimize the operating costs of power and heat generation units while satisfying complex operational constraints, including valve-point effects, transmission losses, generation capacity limits, and heat-power coupling in cogeneration units. This study proposes a hybrid optimization framework that integrates the Firefly Algorithm (FA) with Sequential Quadratic Programming (SQP), termed HFASQP. The hybrid HFASQP approach leverages the global search ability of FA and the local refinement strength of SQP to address the non-convex, highly constrained nature of CHPED problems. The proposed method is validated on a set of benchmarks CHPED systems, including traditional test cases with 5, 7, and 48 units, as well as two newly introduced large-scale systems with 96 and 192 units to evaluate scalability. The proposed method achieved a cost reduction of up to 1.7% and 1.9% compared to FA, SQP and outperformed several state-of-the-art algorithms in terms of solution quality and computational efficiency. In addition, the performance of HFASQP is comparatively evaluated against other recently developed metaheuristic algorithms, including the Kangaroo Optimization Algorithm (KOA) and the Heap-Based Optimizer (HBO), to provide a more comprehensive assessment. To further evaluate robustness and generalizability, the HFASQP algorithm is tested on 23 standard benchmark functions from the optimization literature. The results confirm its consistent accuracy and competitiveness across all test cases, demonstrating its effectiveness beyond CHPED applications and highlighting its potential for broader engineering problems. • Developing a stability-enhanced FA–SQP hybrid for reliable optimization on highly nonconvex CHPED landscapes. • Using an adaptive trigger to invoke SQP selectively, reducing computational load while improving accuracy. • Achieving stronger constraint-feasibility than existing hybrid metaheuristics under nonlinear and valve-point effects. • Ensuring robust performance on non-smooth, multi-modal CHPED models through targeted global–local coordination. • Demonstrating scalable behavior via complexity assessment and benchmarks across multi-size CHPED systems.