This paper presents BSA (backtracking search algorithm) for solving of ED (economic dispatch) problems (both convex and non-convex) with both the valve-point effects in the generator cost function and the transmission network loss considered. BSA is a new evolutionary algorithm for solving of numerical optimization problems; it uses a single control parameter and two crossover and mutation strategies for powerful exploration of the problem's search space. Four test systems (with 3, 6, 20, and 40 generators) are the case studies verifying the method's robustness and effectiveness. The results confirm that compared with existing well-known methods and especially in large-scale test systems, the proposed algorithm is the better approach to solving ED problems. (C) 2014 Elsevier Ltd. All rights reserved.