16 A Fast Harmony Search Algorithm for Unimodal Optimization with Application to Power System Economic Dispatch Abderrahim Belmadani, Lahouaria Benasla and Mostefa Rahli Laboratoire d’Optimisation des Réseaux Electrique (LORE) University of Sciences and Technology of Oran, Algeria 1. Introduction Evolutionary algorithms are general-purpose stochastic search methods simulating natural selection and biological evolution. They differ from other optimization methods in the fact maintaining a population of potential solutions to a problem, and not just one solution. Generally, these algorithms work as follows: a population of individuals is randomly initialized where each individual represents a potential solution to the problem. The quality of each solution is evaluated using a fitness function. A selection process is applied during each iteration in order to form a new solution population. This procedure is repeated until convergence is reached. The best solution found is expected to be a near-optimum solution. HSA that was recently proposed by Greem and al (Greem et al, 2001) is an evolutionary algorithm imitating the improvisation process of musicians. This process is constituted of three steps, in the original HSA, with a fourth step added in the improved version (Geem, 2006). In order to improve the fine–tuning characteristic of HSA, Mahdavi and al developed an Improved Harmony Search Algorithm (IHSA) that differs from original HSA in the fact that some parameters (pitch adjusting rate “PAR” and bandwidth “bw”) are adjusted during the improvisation process (Mahdavi et al, 2007). Omran and al proposed another version of HSA named Global-best Harmony Search Algorithm (GHSA), which borrows concepts from swarm intelligence to enhance the performance of HSA (Omran & Mahdavi, 2008). GHSA is an IHSA version with the pitch-adjustment modified such that the new harmony can mimic the best harmony in the Harmony Memory (HM). In this paper, we propose a Fast version of HSA for the optimization of unimodal quadratic functions. The results (optimum solution and number of improvisations) of HSA, IHSA, GHSA and FHSA are compared for some convex functions (De Jong's function and rotated hyper-ellipsoid function) then for Economic Dispatch (ED). The ED problem is one of the important optimization problems in power system. Generally, the cost function of each generator is approximately represented by a quadratic function (Wallach & Even, 1986) with a need of a real time response from the optimization system (Rahli & Pirotte, 1999). Therefore, we investigate the effectiveness and the accuracy of different versions of HSA and our proposed version. www.intechopen.com