Abstract
This paper makes a study about optimal supply of the energy service, using simulations of network operation scenarios, in order to optimize resources and minimize the variables: operation cost, energy losses, generation cost and consumers shedding. These simulations create optimal operation models of the network, allowing the system operator obtain knowledge to take pre-established procedures that must be performed in situations of contingency in order to forecast and minimize drawbacks. The simulations were performed using a multiobjective particle swarm optimization algorithm. The algorithm was applied to the IEEE 14 Bus network where the optimal power flow was evaluated by MATPOWER tool to establish an optimal electrical working model to minimize the associated costs.

Abstract
The liberalization of energy markets has imposed several modifications in the electricity market environment. The paradigm of monopoly market ceased to exist, and new models have been put into practice. The new models have increased the incentive on competitiveness, making market players struggle to achieve the best outcomes out of market participation. Producers aim at reaching the maximum profit on the sale of energy, while consumers try to minimize their spending on electrical energy. The proposed methodology considers the optimization of players' participation in multiple market opportunities. Reference prices that are expected in each market type at each moment are achieved through the application of neural networks. Using the forecasted prices, the proposed portfolio optimization method allocates the sale and purchase of electrical energy to different markets throughout the time, with the aim at achieving the most advantageous participation profile. A particle swarm approach is used to reduce the execution time while guaranteeing the minimum degradation of the results. Results of the swarm methodology are compared to those of a deterministic approach, using real data from the Iberian electricity market - MIBEL.

Abstract
Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyze the MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems.

Abstract
The paper presents a study about optimal supply of the energy service, using simulations of network operation scenarios, in order to optimize resources and minimize the variables: operation cost, energy losses, generation cost and consumers shedding. These simulations create optimal operation models of the network, allowing the system operator obtain knowledge to take pre-established procedures that must be performed in situations of contingency in order to forecast and minimize drawbacks. The simulations were performed using a multiobjective particle swarm optimization algorithm. The algorithm was applied to the IEEE 14 Bus network where the optimal power flow was evaluated by the MATPOWER tool to establish an optimal electrical working model to minimize the associated costs.

Abstract
This paper presents a decision support methodology for electricity market players' bilateral contract negotiations. The proposed model is based on the application of game theory, using artificial intelligence to enhance decision support method's adaptive features. This model is integrated in AiD-EM (Adaptive Decision Support for Electricity Markets Negotiations), a multi-agent system that provides electricity market players with strategic behavior capabilities to improve their outcomes from energy contracts' negotiations. Although a diversity of tools that enable the study and simulation of electricity markets has emerged during the past few years, these are mostly directed to the analysis of market models and power systems' technical constraints, making them suitable tools to support decisions of market operators and regulators. However, the equally important support of market negotiating players' decisions is being highly neglected. The proposed model contributes to overcome the existing gap concerning effective and realistic decision support for electricity market negotiating entities. The proposed method is validated by realistic electricity market simulations using real data from the Iberian market operatorMIBEL. Results show that the proposed adaptive decision support features enable electricity market players to improve their outcomes from bilateral contracts' negotiations.

Abstract
Multidimensional or n-D systems (n>1) are models having several independent variables. Among the topics related with this type of systems, stability has been attracting the interest of many researchers. The extension of the stability theory extension from 1-D systems to high dimensions is not straightforward. In this paper, four known meta-heuristics (MH) are used to study systems stability based on their polynomial characteristics over the variables boundaries. The four MH consist of genetic algorithms, particle swarm optimisation, cuckoo search and differential evolution. The results obtained with these MH are compared and the best algorithm highlighted. The computational experiments demonstrate that MH can be applied in studding multidimensional system stability.