Electric energy is the most popular form of energy because it can be transported easily at high efficiency and reasonable cost. Nowadays the real-world electric power systems are large-scale and highly complex interconnected transmission systems. The transmission expansion planning (TEP) problem is a large-scale optimization, complicated and nonlinear problem that the number of candidate solutions increases exponentially with system size. Investment cost, reliability (both adequacy and security), and congestion cost are considered in this optimization. To overcome the difficulties in solving the non-convex and mixed integer nature of this optimization problem, this paper offers a firefly algorithm (FA) to solve this problem. In this paper it is shown that FA, like other heuristic optimization algorithms, can solve the problem in a better manner compare with other methods such genetic algorithm (GA), particle swarm optimization (PSO), Simulated Annealing (SA) and Differential Evolution (DE). To show the feasibility of proposed method, applied model has been considered in IEEE 24-Bus, IEEE 118-Bus and Iran 400-KV transmission grid case studies for TEP problem in both adequacy and security modes. The obtained results show the capability of the proposed method. A comprehensive analysis of the GA, PSO, SA and DE with proposed method is also presented. suceptance of the circuits in right-of-way i–j active load in Bus i initial active load in Bus i initial maximum active power generation at Bus i minimum active power generation at Bus i coefficient of bid function of Bus i maximum capacity of branch (i − j) discount factor a large penalty factor node-branch incidence, if i connected to j then s ij =1 else s ij =0 total planning horizon investment cost to build a line in the right-of-way i–j ($/year) load factor generation factor active power flow in the right-of-way i–j active power flow in the right-of-way i–j while a line in right-of-way m-n is out of service active power generation in Bus i voltage angle at Bus i voltage angle at Bus i while a line in right-of-way m–n is out of service curtailed load at bus k in normal operation curtailed load at bus k while a line in right-of-way m–n is out of service number of new circuit added to the right-of-way i–j (integer variable) vector of Lagrange multipliers for inequality and equality constraint Bus index set of load Buses number of available branches in corridor ℓ maximum number of new added branches number of generators set of all new right-of-ways 
Application of firefly algorithm for multi-stage transmission expansion planning with adequacy-security considerations in deregulated environments