Active-set prediction for interior point methods\ud using controlled perturbations

We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality constraints/bounds so as to enlarge the feasible set. We show that if the perturbations are chosen appropriately, the solution of the original problem lies on or close to the central path of the perturbed problem. We also nd that a primal-dual path-following algorithm applied to the perturbed problem is able to accurately predict the optimal active set of the original problem when the duality gap for the perturbed problem is not too small; furthermore, depending on problem conditioning, this prediction can happen sooner than predicting the active-set for the perturbed problem or for the original one if no perturbations are used. Encouraging preliminary numerical experience is reported when comparing activity prediction for the perturbed and unperturbed problem formulations

Active-set prediction for interior point methods using controlled perturbations

We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality constraints/bounds so as to enlarge the feasible set. We show that if the perturbations are chosen appropriately, the solution of the original problem lies on or close to the central path of the perturbed problem. We also find that a primal-dual path-following algorithm applied to the perturbed problem is able to accurately predict the optimal active set of the original problem when the duality gap for the perturbed problem is not too small; furthermore, depending on problem conditioning, this prediction can happen sooner than predicting the active set for the perturbed problem or when the original one is solved. Encouraging preliminary numerical experience is reported when comparing activity prediction for the perturbed and unperturbed problem formulations

Contract design of direct-load control programs and their optimal management by genetic algorithm

A computational model for designing direct-load control (DLC) demand response (DR) contracts is presented in this paper. The critical and controllable loads are identified in each node of the distribution system (DS). Critical loads have to be supplied as demanded by users, while the controllable loads can be connected during a determined time interval. The time interval at which each controllable load can be supplied is determined by means of a contract or compromise established between the utility operator and the corresponding consumers of each node of the DS. This approach allows us to reduce the negative impact of the DLC program on consumers’ lifestyles. Using daily forecasting of wind speed and power, solar radiation and temperature, the optimal allocation of DR resources is determined by solving an optimization problem through a genetic algorithm where the energy content of conventional power generation and battery discharging energy are minimized. The proposed approach was illustrated by analyzing a system located in the Virgin Islands. Capabilities and characteristics of the proposed method in daily and annual terms are fully discussed, as well as the influence of forecasting errors

Investigations on two classes of covering problems

Covering problems fall within the broader category of facility location, a branch of combinatorial optimization concerned with the optimal placement of service facilities in some geometric space. This thesis considers two classes of covering problems. The first, Covering with Variable Capacities (CVC), was introduced in [1] and adds a notion of capacity to the classical Uncapacitated Facility Location problem. That is, each facility has a fixed maximum quantity of clients it can serve. The objective of each variant of CVC is either to serve all clients, the greatest number of clients possible, or all clients using the least number of facilities possible. We provide approximation algorithms, and in a few select cases, optimal algorithms, for all three variants of CVC. The second class of covering problems is barrier coverage. When the purpose of coverage is surveillance rather than service, a cost effective approach to the problem of intruder detection is to place sensors along the boundary, or barrier, of the surveilled region. A barrier coverage is complete when any intrusion is sure to be detected by some sensor. We limit our consideration of barrier coverage to the one-dimensional case, where the region is a line segment. Sensors are themselves line segments, whose span forms a detection range. The objective of barrier coverage as considered here is to form a complete barrier coverage while minimizing the total movement cost, the sum of the weighted distances moved by each sensor in the solution. We show that, by assuming the sensors lie in initial positions where their detection ranges are disjoint from the barrier, one-dimensional barrier coverage can be solved with an FPTAS. Along the way to developing the FPTAS, we give a fast, simple 2-approximation algorithm for weighted disjoint barrier coverage

Smart Grid Technologies for Efficiency Improvement of Integrated Industrial Electric System

The purpose of this research is to identify the need of Smart Grid Technologies in communication between industrial plants with co-generation capability and the electric utilities in providing the most optimum scheme for buying and selling of electricity in such a way that the fuel consumption is minimized, reliability is increased, and time to restore the system is reduced. A typical industrial plant load profile based on statistical mean and variance of industrial plants\u27 load requirement is developed, and used in determining the minimum cost of producing the next megawatt-hours by a typical electric utility. The 24-hour load profile and optimal power flow program are used to simulate the IEEE 39 Bus Test System. The methodology for the use of smart grid technology in fuel saving is documented in the thesis. The results obtained from this research shall be extended to include several industrial plants served by electric utilities in future work by the UNO research team

Exploiting Structures in Mixed-Integer Second-Order Cone Optimization Problems for Branch-and-Conic-Cut Algorithms

This thesis studies computational approaches for mixed-integer second-order cone optimization (MISOCO) problems. MISOCO models appear in many real-world applications, so MISOCO has gained significant interest in recent years. However, despite recent advancements, there is a gap between the theoretical developments and computational practice. Three chapters of this thesis address three areas of computational methodology for an efficient branch-and-conic-cut (BCC) algorithm to solve MISOCO problems faster in practice. These chapters include a detailed discussion on practical work on adding cuts in a BCC algorithm, novel methodologies for warm-starting second-order cone optimization (SOCO) subproblems, and heuristics for MISOCO problems.The first part of this thesis concerns the development of a novel warm-starting method of interior-point methods (IPM) for SOCO problems. The method exploits the Jordan frames of an original instance and solves two auxiliary linear optimization problems. The solutions obtained from these problems are used to identify an ideal initial point of the IPM. Numerical results on public test sets indicate that the warm-start method works well in practice and reduces the number of iterations required to solve related SOCO problems by around 30-40%.The second part of this thesis presents novel heuristics for MISOCO problems. These heuristics use the Jordan frames from both continuous relaxations and penalty problems and present a way of finding feasible solutions for MISOCO problems. Numerical results on conic and quadratic test sets show significant performance in terms of finding a solution that has a small gap to optimality.The last part of this thesis presents application of disjunctive conic cuts (DCC) and disjunctive cylindrical cuts (DCyC) to asset allocation problems (AAP). To maximize the benefit from these powerful cuts, several decisions regarding the addition of these cuts are inspected in a practical setting. The analysis in this chapter gives insight about how these cuts can be added in case-specific settings