The deregulation of the electricity sector has dramatically modified the current electricity system. Generators (suppliers) and large consumers (buyers) in an open, competitive energy market need an appropriate bidding method to increase their earnings. Because of this, every generator and large consumer will strategically bid for the choice of bidding factors to assess the opposition's bidding schemes. Power utilities use bidding methods to maximize revenue and minimize risk. In this article, we have demonstrated the essential components of the technique with the help of six power suppliers and two big buyers. We have used a Multi-Objective Grey Wolf Optimizer (MOGWO) to solve the bidding strategy problem as an optimization problem. Under this work, a methodology for electric utilities to bid effectively for expansion in their profits is developed. The competitor's behavior is ascertained using the probability density function. The MOGWO is employed in an optimization procedure to determine the best conclusion to the bidding problem. The method is verified using a test setup with six generators and two large consumers. The outcomes of using the Monte Carlo (MC), Gravitational Search Algorithm (GSA), Whale Optimization Algorithm (WOA), and Invasive Weed Optimization Algorithm (IWOA) techniques are also compared. Comparing the outcomes demonstrates that MOGWO is a successful solution.