This paper proposes a novel Cauchy mutated Memetic Particle Swarm Optimization (CMPSO) algorithm to solve the risk based self-scheduling problem of price taking Genco in a day-ahead energy market. In self-scheduling problem, certain risk is invoked due to uncertainty in forecasted electricity prices and fuel prices. The risk in the self-scheduling problem is modeled based on the portfolio selection. The risks in the energy prices are taken into account by using the covariance information of the available data. The Risk Invoked Self-Scheduling (RISS) is formulated as a mixed integer non-linear optimization problem and solved by using the proposed CMPSO. The effectiveness of the proposed CMPSO algorithm is demonstrated with two test systems.