A new multi-objective formulation named normalized weighting method combined with particle swarm optimization for the connections between distribution transformers and a primary feeder problem is presented. The performance of Particle Swarm Optimization can be improved by strategically selecting the starting positions of the particles by back-propagation neural network. Six important objectives are considered in this problem. These six objectives are of equal important to electric utility companies, but they are somewhat non-commensurable with each other. In view of this, a normalized weighting method for the multi-objective problem is proposed. It can provide a set of flexible solutions using particle swarm optimization by following the intention of decision makers. To increase the realism, the load and operating constraints of the system are all considered. Comparative studies on actual Tai-power systems are given to demonstrate the effectiveness of the phase load balancing and the improvement of operation efficiency for the proposed method.