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In an island power system, optimizing energy management is fundamental since there are renewable sources with their limitations. This management includes the allocation and capacity of energy sources to supply the loads. In this context, optimizing losses in the system contributes to improve the efficiency of this management. This paper proposes the losses optimization and energy management in the island power system. The authors propose the Natural Logarithm Particle Swarm Optimization to solve the problem and compare it with the Attractor Point Algorithm and Evolutionary Particle Swarm Optimization. And with that, we also propose a particle initialization for the studied particle-based algorithms to guarantee convergence in radial power systems. This is because the system configuration influences the response of the algorithm convergence. These techniques were applied to the IEEE-34 unbalanced radial island system. • Natural Logarithm Particle Swarm Optimization differs from classical PSO in that it does not calculate the velocity of the particles. Therefore, the method considers a cloud of particles with a natural logarithmic trajectory to solve the reduction of losses in a power system with a radial topology. • Natural Logarithmic Particle Swarm Optimization uses an initialization equation to minimize the initial estimation process, which is relevant to the convergence process.