Chair: Ana Luisa Custodio, Universidade Nova de Lisboa, Portugal
A procedure for the optimal operation of medium-voltage AC networks
Maria Teresa Vespucci (firstname.lastname@example.org), Paolo Pisciella (email@example.com), Francesco Piu (firstname.lastname@example.org)
A medium-voltage AC network with distributed generation and storage devices is considered for which set points are assigned in each time period of a given time horizon. A set point in a time period is defined by modules and phases of voltages in all nodes, active and reactive powers, on load tap changer and variable loads. When some parameters vary, in order to restore feasibility new set points need to be determined so as to minimize the variations with respect to the initial ones. This can be done by minimizing distributor’s redispatching costs, which are modeled by means of binary variables, while satisfying service security requirements and ensuring service quality, which are represented by nonlinear constraints, such as the nodal balance of active and reactive power and the current transits on lines and transformers for security. Storage devices are modeled by means of constraints that relate adjacent time periods. A two-step solution procedure is proposed, which is based on decoupling active and reactive variables: in the first step a MILP model determines the active power production and the use of storage devices that minimize redispatching costs over all time periods in the time horizon; in the second step, given the optimal active power production computed in the first step, reactive variables in each time period are computed by solving a nonlinear programming model.
Keywords: distributed generation, electric storage, nonlinear optimization
Constraint Aggregation in Non-Linear Programming models for Nesting problems
Pedro Rocha (email@example.com), A. Miguel Gomes (firstname.lastname@example.org), Rui Rodrigues (email@example.com), Franklina Toledo (firstname.lastname@example.org), Marina Andretta (email@example.com)
The Nesting problem is a complex problem that arises in industries where sets of pieces or space must be efficiently placed or allocated in order to minimize wasted space or wasted raw materials, without overlaps between pieces and fully contained inside a container. This paper analyses the impact that the reduction of the non-overlapping of constraints can achieve in the reduction of computational cost of a Non-Linear Programming model for Nesting problems with continuous rotations. This is done through constraint aggregation together with spatial partition and hierarchical overlap detection methods. When aggregating constraints there is an effect of reducing the sensitivity of the solver, which may reduce the quality of the layout compaction. Analyzing the trade-off between the aggregation of constraints and the impact on the quality of the solution is important to address real world problems with continuous rotations.
Keywords: Nesting problem, Non-linear programming, Cutting and packing
GLODS: Clever Multistart in Directional Direct Search
Ana Luisa Custodio (firstname.lastname@example.org), Jose Aguilar Madeira (email@example.com)
Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase when the derivatives of the functions defining the problem are not available for use. We present a new algorithm suited for bound constrained, derivative-free, global optimization. Using direct search of directional type, the method alternates between a search step, where potentially good regions are located, and a poll step where the previously located regions are explored. This exploitation is made through the launching of several pattern search methods, one in each of the regions of interest. Differently from a multistart strategy, the several pattern search methods will merge when sufficiently close to each other. The goal is to end with as many active pattern searches as the number of local minimizers, which would allow to easily locating the possible global extreme value. We describe the algorithmic structure considered, present the main associated theoretical results, and report numerical experience, showing that the proposed method is competitive with currently commonly used solvers.
Keywords: Derivative-free optimization, Global optimization, Pattern search methods