## 1 Introduction  
Economic load dispatch (ELD) is an optimization problem for scheduling generator outputs to satisfy the total load demand at the least possible operating cost. ELD problem is often formulated as a quadratic equation [1]. The ELD problem is in reality a nonconvex optimization problem [2]. These arise from ramp rate limits due to the physical limitations of the generating unit, effect of steam valve operation and prohibited operating zones of the generators due to vibration if the shaft bearing.  
The conventional method of solving the ELD problem is by applying nonlinear programming techniques. These techniques minimize a convex objective function over a convex set thus insuring a single minimum. The problems can then be minimized using gradient or Newton based search techniques. However as nonconvex problems generally have multiple minima these techniques may be trapped at local minima. Dynamic programming is one way solving this problem, but it also has limitations due to the \"curse of dimensionality\" [3].  
Metaheuristic optimization is another way of solving nonconvex optimization problems [4]. These algorithms are usually based on processes witnessed in physics or biology. Metaheuristic techniques are ideal for nonconvex ELD problem as they do not suffer from restriction of continuity, differentiability and convexity. Many metaheuristic techniques such as simulated annealing (SA), tabu search (TS), genetic algorithm (GA), particle swarm optimization (PSO) and bat algorithm (BA) have been successfully implemented to solve ELD problem [5,6].  
Many variants of GA have previously been used with good results to solve nonconvex ELD problems [7, 8, 9]. The main advantage GA has over other algorithms is that it can use a chromosome coding technique tailored to the specific problem. The two main disadvantages of GA over other techniques are firstly, there is no guarantee of convergence to the global optimum solution and secondly, the execution time is very long.  
PSO and many of its variants have also been extensively used for solving nonconvex ELD problems [10, 11, 12, 13]. PSO has numerous advantages over other algorithms. It is very easy to preform and has only a few adjustable parameters. It is also very efficient in global search (exploration). The main disadvantages of PSO are it is slow convergence at refined search stage (exploitation) and its weak local search ability.  
BA like PSO and GA is a relatively new population based metaheuristic approach [14,15]. This algorithm mimics the echolocation ability of micro bat which they use it for navigating and hunting. The position of the bat provides the possible solution of the problem. Fitness of the solution is specified by the best position of a bat to its prey. A big advantage BA has over other algorithms is that it has a number of tunable parameters giving a greater control over the optimization process. BA and its variants have also been used to solve the ELD problem [16, 17, 18]. It has proven efficient in for lower dimensional optimization problem but ineffective for high dimensional problems because of fast initial convergence [19].  
This paper proposes two modifications to the original BA. The first modification is inspired from anti predatory PSO in which the particles moves not only towards the best solution but also away worst position experienced by itself and the global worst solution. The intention behind this modification is increasing the exploration capacity of the algorithm. The second modification is the introduction of a nonlinear weight for the velocity called inertia weight factor (IWF). The purpose of IWF is to provide balance between global and local exploration and better convergence rate.  
For the purpose of comparison GA and PSO are also implemented and the results are compared with the modified bat algorithm (MBA). Verification of the modified algorithm has been carried out by simulating two test cases. For the verification of the results, Lambda Iteration method has been used for the convex optimization problem.