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In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem tractable in realistic systems. Different sources of uncertainty have been considered, mainly related to the capacity and… (More)

The paper introduces a method for solving the failure probability-safety factor problem for designing engineering works proposed by Castillo et al. that optimizes an objective function subject to the standard geometric and code constraints, and two more sets of constraints that simultaneously guarantee given safety factors and failure probability bounds… (More)

Structural reliability and decomposition techniques have recently proved to be appropriate tools for solving robust uncertain mixed-integer linear programs using ellipsoidal uncertainty sets. In fact, its computational performance makes this type of problem to be an alternative method in terms of tractability with respect to robust problems based on… (More)

Structural-reliability based techniques has been an area of active research in structural design during the last decades, and different methods have been developed, such as First Order Second Moment (FOSM) or First Order Reliability (FORM) methods. The same has occurred with robust optimization, which is a framework for modeling optimization problems… (More)

- Roberto Mínguez, Enrique Castillo, Carmen Castillo, Miguel A Losada
- 2006

Minimizing the expected total cost of a structure, including maintenance and construction is a difficult problem because of the presence in the objective function of the yearly failure rates, which have to be calculated by an optimization problem per each failure mode. In this paper, a new method for the design of structures that minimizes the total… (More)

Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, available solution methodologies for the resulting trilevel robust counterpart are unsuitable for large-scale problems. In order to overcome this shortcoming, this paper… (More)

This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical structure of the general solution of a system of linear equations is discussed, the truss analysis problem is used to… (More)

—Recent breakthroughs in Transmission Network Expansion Planning (TNEP) have demonstrated that the use of robust optimization, as opposed to stochastic programming methods, renders the expansion planning problem computation-ally tractable for real systems. State-of-the-art robust methods treat this problem as stationary throughout the study period, with all… (More)