The elevated demand for electrical power, expeditious expenditure of fossil fuels, and degradation of the environment because of power generation have renewed attentiveness to renewable energy resources (RER). The rapid augmentation of RER increases the convolutions in leveling the demand and generation of electrical power. In this paper, an elaborated $\alpha$-constrained simplex method (ACSM) is recommended for multi-objective power dispatch problems. This methodology is devised after synthesizing the non-linear simplex method (SM) with the $\alpha$-constrained method (ACM) and the evolutionary method (EM). ACSM can transfigure an optimization technique for the constrained problems by reinstating standard juxtapositions with $\alpha$-level collations. The insertion of mutations and multi-simplexes can explore the periphery of the workable zone. It can also manage the fastness of convergence and therefore, the high precision solution can be obtained. A real-time multi-objective coordinated solar-wind-thermal power scheduling problem is framed. Two conflicting objectives (operating cost and emission) are satisfied. The case studies are carried out for Muppandal (Tamil Nadu), Jaisalmer (Rajasthan), and Okha (Gujarat), India. The annual solar and wind data are analyzed by using Normal Distribution and Weibull Distribution Density Factor, respectively. The presented technique is inspected on numerous archetype functions and systems. The results depict the prevalence of ACSM over particle swarm optimization (PSO), simplex method with mutations (SMM), SM, and EM.