This paper considers a multi-objective version of the Multiple Traveling Salesman Problem (MOmTSP). In particular, two objectives are considered: the minimization of the total traveled distance and the balance of the working times of the traveling salesmen. The problem is formulated as an integer multi-objective optimization model. A non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the MOmTSP. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. Tests on real world instances and instances adapted from the literature show the effectiveness of the proposed algorithm

In this study, a probabilistic approach for the optimal charging of electric vehicles (EVs) in distribution systems is proposed. The costs of both demand and energy losses in the system are minimised, subjected to a set of constraints that consider EVs smart charging characteristics and operative aspects of the electric network. The stochastic driving patterns for EVs’ owners, battery capacity and active and reactive power demanded at load nodes are considered. The optimal charging of EVs connected to the system benefits the system's operation, as it does a strategy to minimise the cost of energy losses and evaluate the capability of the system to charge EVs’ batteries fully under certain penetration scenarios. Priority periods of EVs’ recharge and the variation of energy price contribute to an adequate demand response, assisting the network operator for complying with quality indices (decrement of power losses) set forward by regulatory entities and developing studies of risk analysis for decision making. On the other hand, there is a valuable participation of the EVs’ owners in improving the operation of the distribution system. Monte Carlo simulation (MCS) is used to assess the stochastic nature of the problem in a secondary (low voltage) distribution network.

Unbalanced operation of distribution systems deteriorates power quality andincreases investment and operation costs. Feeder reconfiguration and phaseswapping are the two main approaches for load balancing, being the formermore difficult to execute due to the reduced number of sectionalizing switchesavailable in most distribution systems. On the other hand, phase swappingconstitutes a direct, effective and low cost alternative for load balancing. The main contribution of this paper is the proposal of an optimization model anda solution technique for phase balancing planning in distribution systems. Asregards the optimization model, a mixed integer nonlinear programming formulationis proposed. On the other hand, the proposed solution techniqueconsists on a specialized genetic algorithm. To show the effectiveness of theproposed approach, several tests are carried out with two distribution systemsof 37 and 19 buses, this last one with different load models. Results showedthat in addition to the achievement of the primary objective of loss reduction,phase balancing allows obtaining other technical benefits such as improvementof voltage profile and alleviation of congested lines.