Quadratic programming problems arise in many scientific and engineering applications for a long time. Meta-heuristic methods have been employed so as to obtain optimal solutions for the problems such as artificial neural network, genetic algorithm, simulated annealing, ant colony optimization and others. Great progress has been made in research on artificial neural networks in recent decades. Artificial neural networks have been applied to many fields such as pattern recognition, forecasting, data mining, multiple objective decision making and combinatorial optimization problems. Recently, power-supply failures have caused major social losses. Therefore, power supply systems need to be highly reliable. The objective of this research is to present a significant and effective method of determining a productive investment to protect a power supply system from damage. Previous studies have examined the utility and social impact of investment in distributed generation. In this research, an artificial neural network has been applied to solve the portfolio selection problem efficiently. The reliability and risks of each of the units are evaluated with a variance-covariance matrix, and the effects and expenses of replacement are analysed. The mean-variance analysis is formulated as a mathematical program with the following two objectives which are to minimize the risk and to maximize the expected return. Finally, a structural learning model of a mutual connection neural network (double layered Boltzmann machine) is used to solve problems defined by mixed-integer quadratic programming, and is employed in the mean-variance analysis. This method is applied to a power system network in the Tokyo Metropolitan area. As a result, it was shown that the structural learning can provide an alternative solution for decision makers to select the best solution from their respective point of view, as a numerical example shows. The simulation also showed that computational cost is significantly decreased compared with a conventional Boltzmann machine. The obtained results show that the selection, investment expense rate to units and reduced computation time can be prolonged to increase cost savings.
