【正文】 ctors, etc., and minimizes transmission losses or other appropriate objective functions, while satisfying a given set of physical and operating constraints. Since transformer tap ratios and outputs of shunt capacitors/reactors have a discrete nature, while reactive power outputs of generators and static VAR pensators, busvoltage magnitudes, and angles are, on the other hand, continuous variables, the reactive power 8 optimization problem can be exactly formulated using a mixedinteger/nonlinear programming model, ., cast as a nonlinear optimization problem with a mixture of discrete and continuous variables. Up to now, a number of techniques ranging from classical techniques like gradientbased optimization algorithms to various mathematical programming techniques have been applied to solve this problem [1]–[4]. Recently, due to the basic efficiency of interiorpoint methods, which offer fast convergence and convenience in handling inequality constraints in parison with other methods, interiorpoint linear programming [5], quadratic programming [6], and nonlinear programming [7] methods have been widely used to solve the OPF problem of largescale power systems. However, these techniques have severe limitations in handling nonlinear, discontinuous functions and constraints, and function having multiple local minima. Unfortunately, the original reactive power problem does have these properties. In all these efforts some or theother simplification has been done to get over the inherent limitations of the solution technique. The binatorialsearch approaches, branchandbound and cuttingplane algorithms, are usually used to solve the mixedinteger programming model [8]. However, these methods are “nonpolynomial” and all suffer from the socalled problem of “curse of dimensionality” for largescale applications, making them unsuitable for largescale OPF problems. To overe the drawback of these algorithms, several efficient algorithms have been proposed. Aoki et al. [9] addressed the issue of discrete variables by an approximation search method for recursive mixedinteger programming in solving largescale VAR planning problems. Bakirtzis and Meliopous [10] proposed a linearprogramming methodology to handle the discrete shunt capacitors/reactors in an optimization problem by using Driebeck’s penalty algorithm. Liu et al. [8] proposed a penaltybased discretization algorithm to handl the discreteness of shunt capacitors/reactors during the solution process of a Newton OPF method without binatorial search, which has been implemented in a productiongrade Newton OPF program and tested on actual power works. In the last decade, many new stochastic search methods have been developed for the global optimization problems, such as geic algorithms, evolutionary programming and particle swarm optimization. Particle swarm optimization (PSO) is one of the evolutionary putation techniques [11]. It was developed through simulation of a simplified social system, and has been found to be robust in solving continuous nonlinear optimization problems. The