The combined heat and power economic dispatch (CHPED) problem is a non-convex multivariate global optimization problem. The objective of the problem is to reduce total production costs while imposing a variety of constraints and meeting the demand for power and heat. Three recently presented metaheuristic approaches, Slime Mould Algorithm (SMA), COOT algorithm and Marine Predators Algorithm (MPA), are applied for solving CHPED problem. Studies dealing with the CHPED problem in the literature often do not consider valve points effect, prohibited operation zones for power-only units, feasible region constraints of combined heat and power units, all at once. Furthermore, power losses are neglected especially in large-scale problems. In this study, the CHPED problem is solved by considering all operational constraints including active power transmission losses. Three separate case studies with dimensions of 11 units, 48 units, and 96 units were used in the tests under various limitations. The experimental results revealed that MPA outperformed not only SMA, and COOT but also the algorithms proposed previously in the literature.