In this article, bio-inspired metaheuristic evolutionary algorithm named as a comprehensive learning wavelet-mutated slime mould algorithm is proposed for finding the optimal solution of combined heat and power dispatch problem with non-linear and discontinuous constraints such as valve point loading effect and prohibited operating zones in thermal only units. The proposed algorithm is based on the behavior of slimes and their reproduction stages. The wavelet mutation was introduced to help to adapt individuals to avoid local minimia. The comprehensive learning method is employed in wavelet mutated slime mould to handle the dimensional complexity that arises during the construction of new slime mould positions from parent slimes by learning from the experiences of more than one sources. Proposed hybrid slime mould algorithm which speeds up the searchability of solutions and hence enhances its robustness. Four different tests are performed and the obtained test solutions by the application of the proposed algorithm are compared with other reported solutions in the literature, in terms of generation cost and convergence speed in the CHPED problem. The obtained results are statistically verified on the Wilcoxon test.