One of the most challenging operational aspects in restructured systems with open transmission access is the power management of the grid. With the trend of an increasing number of bilateral and multilateral transactions submitted to the Independent System Operator (ISO), the possibility of insufficient resources in the transmission system may be unavoidable. In this paper, evolutionary computation techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP), Particle Swarm Optimization (PSO), Differential Evolution (DE), are applied to solve the economic load dispatch problem with bilateral and multilateral transactions. Different Evolutionary Computation methods are applied to obtain ELD solutions for IEEE 30-bus system. The results obtained by this approaches are compared with respect to solution time, production cost and convergence criteria. The solutions obtained are quite encouraging and useful in the economic environment. The algorithm and simulation are carried using Matlab software.