The Multi-objective Non-convex Combined Heat and Power (CHP) scheduling problem of the systems is a complex and arduous problem. This is due to the nonconvex and nonlinear nature of the objective functions involved. This problem aims to simultaneously minimize two vital but conflicting objectives i.e. cost and emission. As the number of operational units and the constraints increase, regular mathematical algorithms are not able to provide a satisfactory solution to the problem. The non-convexity and nonlinearity of these objectives require a good optimization technique to handle it. In this chapter, a comparative analysis of Particle Swarm Optimization (PSO) and Whale Optimization Algorithm (WOA) is presented which is used to provide a compromise solution to this Multi-objectives CHP Economic and Emission Dispatch (MOCHPEED) problem. Both objectives of the CHPEED problem are solved using the fuzzy framework. Later, this framework is used to obtain the compromised solution between the both the objectives. The PSO and WOA techniques are tested on three different test systems. In these test systems, valve-point loading and transmission losses are also considered. To highlight the accomplishments of both the techniques, a comparative analysis is done with the results obtained using the latest literature. Statistical data related to costs and emission, and fitness function are included in this chapter which is obtained after simulating the test systems for 100 different unbiased trials. A detailed investigation on various test generating systems shows supremacy of WOA over PSO and other recently established techniques.