Memetic Salp Swarm Algorithm for economic load dispatch problems

This paper presents a hybrid version of the Salp Swarm Algorithm (SSA) for Economic Load Dispatch (ELD) problems with severe constraints. The Adaptive β-hill climbing optimizer (AβHCO) ais hybridized with a newly developed local search method with SSA as a new operator. This hybridization scheme is known as a memetic algorithm, where SSA serves as a natural selection agent (general refinement) in a genotype environment, while AβHCO serves as a culture selection agent (local refinement) in a phenotype environment. In other words, SSA acts as a gene encoding in biology, while AβHCO serves as a meme in a cultural context. In an intelligent optimization environment, gene and meme notations from natural biology and cultural selection act as search agents to achieve generality (gene) and problem specificity (meme). ELD is a crucial optimization problem in electrical engineering, and it is non-convex, multi-modal, and severely constrained. The proposed method, called MSSA, evaluates several types of ELD problems that differ in the constraints adopted. The first problem is addressed by considering two types of constraints related to load balance and output. It includes five practical cases of ELD generators that vary in number of units and load requirements: a three-unit generator with a capacity of 850 MW (3UG-850 MW), a thirteen-unit generator with a capacity of 1800 MW (13UG-1800 MW), a thirteen-unit generator with a capacity of 2520 MW (13UG-2520 MW), a forty-unit generator with a capacity of 10500 MW (40UG-10500 MW), and a large-scale generator with a capacity of 80 units of 21000 MW (80UG-21000 MW). Two additional constraints-restricted operating zones and ramp rate limits-are used to address the second problem. A six-unit generator with a capacity of 1,263 MW (6 UG-1,263 MW) and a fifteen-unit generator with a capacity of 2,630 MW (40 UG-2,630 MW) are two real-world cases discussed. Compared with other existing algorithms, the comparative results demonstrate the feasibility and usefulness of the proposed MSSA algorithm.