Island-Based Harmony Search Algorithm for Non-convex Economic Load Dispatch Problems

The economic load dispatch (ELD) is a crucial problem in electrical power system domain. It is tackled by managing the outputs of predefined generation units in accordance with equality constraints related to the balance of power of units and inequality constraints related to the output of units. Due to its complexity, ELD is modeled as a non-linear, non-convex, and non smooth optimization problem. Therefore, several optimization algorithms have been tailored to tackle ELD. The main contribution of this paper is to utilize the island based harmony search algorithm (iHS) for ELD problem. iHS divides the ELD population to a set of sub-populations called islands. The original Harmony Search (HS) is used for each island as an isolated run. At specific migration frequency, some solutions counted by migration rate are asynchronously migrated from one island to another based on migration policy controlled by migration topology. To ensure the feasibility of obtained ELD solutions, the repair process is also proposed as another contribution. In order to evaluate the proposed method, five real-world ELD test cases including generators with 3 units, two versions of generators with 13 units, 40 units and finally 80 units. Initially, the effect of parameters (Number of island, migration frequency, and migration rate) on the convergence behaviour of iHS is studied for all test cases. For comparative evaluations, the results of each ELD test case is compared with those produced by other well-established methods. The proposed iHS is able to produce the best overall results for three out of five real-world ELD test cases. For further validations, other five complex ELD versions introduced for IEEE-CEC2011 including more constraints (Ramp Rate Limits and prohibited operating zones) are also used which are generators with 6 units, 13 units, 15 units, 40 units, and 140 units. The comparative results of ELD versions for IEEE-CEC2011 test cases show that the proposed iHS-based ELD method is competitively comparable with other eight hybrid-based comparative methods. In a nutshell, The successful performance of the proposed method show that it is viable and efficient which can be very useful for many researchers in the power system domain.