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One of the critical optimization issues in the economic management of power and heat systems is the Combined heat and power economic dispatch (CHPED). The valve-point effects of thermal units as well as the interdependency of CHP outputs make the nonlinearity and non-convexity in optimization and dispatch models. A novel Amalgamated Heap-based and JellyFish Optimizer (AHJFO) is proposed, in this paper, to improve the efficiency of two newly developed techniques, Heap-based Optimizer (HO) and Jellyfish Optimizer (JFO). The proposed AHJFO incorporates an adjustment strategy function (ASF) to increase the explorative characteristic at the beginning of iterations by upgrading the produced solutions using HO. Further, as iterations go, it improves the exploitative characteristic by expanding the created solutions using JFO. The proposed AHJFO provides higher effectiveness compared to HO and JFO to obtain the solution of CHPED problem for medium 24 and large 96-unit systems. The simulation results show that the proposed AHJFO based on ASF aids in the avoidance of premature convergence and improves solution accuracy. Besides, the proposed AHJFO is successfully applied to the CHPED issue involving (N-1) unit outages. A re-dispatch strategy based on AHJFO is presented and the impact of outages of all units is analyzed after (N-1) unit outages. Also, further applications of the proposed AHJFO for ED problem are carried out with/without additional constraint models of power flow considering the IEEE 30-bus system. The simulation results show the superiority of the proposed AHJFO compared to HO, JFO and other algorithms for solving the CHPED and ED issues. Moreover, feasibility study is demonstrated of the solutions obtained for the CHPED and ED issues with additional constraint models. • Combined heat and power economic dispatch problem is solved by AHJFO Optimizer. • The AHJFO provides higher effectiveness for medium 24 and large 96-unit systems. • The simulation results are applied to the CHPED issue involving (N-1) outages. • Applications of the AHJFO for ED problem are carried out with/without additional constraint models. • Feasibility study is demonstrated of the solutions obtained for the CHPED and ED issues. [ABSTRACT FROM AUTHOR]