On a class of optimization problems for framed structures

In practical power systems, the fault current sensed by the relay depends on location of the fault and network topological changes. Fault current sensed by the relay for near end fault is greater than that for a far end fault. In meshed distribution systems with Distribution Generation (DG), the fault currents are fed from both ends of the line and consequently the currents sensed by the relays at both ends are different. These variable fault currents may lead to miscoordination of directional overcurrent relays (DOCRs). To overcome this problem, the coordination constraints corresponding to the fault currents at different fault locations should be satisfied. This paper proposes a new approach based on Interval Linear Programming (ILP) which is hybridized with Modified Particle Swarm Optimization (MPSO). The basic idea is to convert the inequality constraints of a standard linear programming (LP) problem to interval constraints using theory of ILP and represent the ILP problem as a standard LP problem. This procedure reduces considerable number of coordination constraints and better sub-optimal solution is obtained compared to conventional optimization. The proposed method is tested on IEEE 14 bus test system in microgrid perspective.

The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved directly by standard linear or nonlinear programming techniques. The aim of this paper is to transform such problems to a standard mathematical linear programming problem. For each constraint, exactly one parameter value is selected out of a multiple number of parameter values. This process of selection can be established in different ways. In this paper, we present a new simple technique enabling us to handle such problem as a mixed integer linear programming problem and consequently solve them by using standard linear programming software. Our main aim depends on inserting a specific number of binary variables and using them to construct a linear combination which gives just one parameter among the multiple choice values for each choice of the values of the binary variables. A numerical example is presented to illustrate our analysis.

The integration of traditional and heuristic techniques is considered for the reactive power/voltage control program. The steady-state reactive power problem is addressed. Fuzzy sets are used to modify the linear programming (LP) approach to voltage control and to incorporate some heuristic concepts of the expert system approach. Multiple objectives and soft constraints are modeled using fuzzy sets. Piecewise linear convex membership functions for the fuzzy sets are defined. Under this definition, the fuzzy optimization problem is reformulated as a standard linear programming problem. The objective function represents the compromise among the original competing objectives and the soft constraints. In addition, discrete constraints are considered. Numerical examples demonstrate the approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

SummaryAdaptive enrichment designs involve preplanned rules for modifying enrolment criteria based on accruing data in a randomized trial. We focus on designs where the overall population is partitioned into two predefined subpopulations, e.g. based on a biomarker or risk score measured at baseline. The goal is to learn which populations benefit from an experimental treatment. Two critical components of adaptive enrichment designs are the decision rule for modifying enrolment, and the multiple-testing procedure. We provide a general method for simultaneously optimizing these components for two-stage, adaptive enrichment designs. We minimize the expected sample size under constraints on power and the familywise type I error rate. It is computationally infeasible to solve this optimization problem directly because of its non-convexity. The key to our approach is a novel, discrete representation of this optimization problem as a sparse linear program, which is large but computationally feasible to solve by using modern optimization techniques. We provide an R package that implements our method and is compatible with linear program solvers in several software languages. Our approach produces new, approximately optimal trial designs.

The sparse linear programming (SLP) is a linear programming problem equipped with a sparsity constraint, which is nonconvex, discontinuous and generally NP-hard due to the combinatorial property involved. In this paper, by rewriting the sparsity constraint into a disjunctive form, we present an explicit formula of the Lagrangian dual problem for the SLP, in terms of an unconstrained piecewise-linear convex programming problem which admits a strong duality under bi-dual sparsity consistency. Furthermore, we show a saddle point theorem based on the strong duality and analyze two classes of stationary points for the saddle point problem. At last, we extend these results to SLP with the lower bound zero replaced by a certain negative constant.

Linear programming algorithms have been widely used in Decision Support Systems. These systems have incorporated linear programming algorithms for the solution of the given problems. Yet, the special structure of each linear problem may take advantage of different linear programming algorithms or different techniques used in these algorithms. This paper proposes a web-based DSS that assists decision makers in the solution of linear programming problems with a variety of linear programming algorithms and techniques. Two linear programming algorithms have been included in the DSS: (i) revised simplex algorithm and (ii) exterior primal simplex algorithm. Furthermore, ten scaling techniques, five basis update methods and eight pivoting rules have been incorporated in the DSS. All linear programming algorithms and methods have been implemented using MATLAB and converted to Java classes using MATLAB Builder JA, while the web interface of the DSS has been designed using Java Server Pages.

Consider a standard linear programming problem and suppose that there are bounds available for the decision variables such that those bounds are not violated at an optimal solution of the problem (but they may be violated at some other feasible solutions of the problem). Thus, these bounds may not appear explicitly in the problem, but rather they may have been derived from some prior knowledge about an optimal solution or from the explicit constraints of the problem.In this paper, the bounds on variables are used to compute bounds on the optimal value when the problem is being solved by the simplex method. The latter bounds may then be used as a termination criteria for the simples iterations for the purpose of finding a “sufficiently good” near optimal solution. The bounds proposed are such that the computational effort in evaluating them is insignificant compared to that involved in the simplex iterations. A numerical example is given to demonstrate their performance.

*† This paper proposes a new algorithm for actuator allocation problems, e.g., reaction wheel torque distribution and jet selection logic. The algorithm is based on an interior-point linear programming (LP) algorithm. Compared to the simplex LP algorithm, the interiorpoint LP algorithm exhibits several advantages at the cost of reasonably increased computation. They encompasses greater robustness to uncertainty in actuator models, smoother actuation command over time, and greater flexibility in incorporating nonlinear operations such as quantization. These advantages stem from the fact that the interior algorithm searches for a suboptimal solution among the interior points of a feasible set and not among the extreme points or corner points of the feasible set as in the simplex algorithm. The proposed approach has been applied to the problem of reaction wheel torque distribution for the attitude control of an autonomous rendezvous and docking (ARD) robotic spacecraft and demonstrated to yield more effective solutions for the actuator allocation problem than a simplex LP approach.

The main viewpoint of land use planning is to resolve the conflict between competing land uses in one place that is carried out based on their economic, social and environmental suitability. Many different approaches have been designed to resolve this conflict but any of them have done. This study aimed to assess accuracy and validity compared four optimization algorithms, including linear programming (LP), simulated annealing (SA), multi-objective land use allocation (MOLA) and multidimensional choice (MDCHOICE) for land use planning in Gorgan Township. At first, land use allocation was done through the LP algorithm. Then, using achieved pixels quantity from LP optimization, the land uses was optimized in term of spatial suitability by other algorithms. The allocation maps generated through these algorithms were compared using statistical methods and landscape metrics. The map provided through MDCHOICE was used as a reference map and that generated through MOLA, SA and LP as a comparative one in a validation process. The similarities and agreements of the two maps were evaluated with various algorithms in IDRISI and MCK software. The results demonstrate that: (1) It follows that the LP algorithm to determine the optimal number of pixels to lead MDCHOICE has helped in the spatial allocation properly. (2) MOLA had a better performance for development in terms of all landscape metrics and SA algorithm was better in forestry land use allocation. Therefore the quality of spatial allocation both of them needs to be improved. (3) Although the LP algorithm is not superior to the algorithms based on the dimensions studied in this research, in terms of achieving the defined goals and the degree of deviation from the number of cells defined for each land use has the least violation. (4) The superiority of MDCHOICE over MOLA, SA and LP and applicability of various kappa statistics for comparing the maps for a more in depth analysis of agreements and disagreements.

Dimensionality reduction-based extremum surrogate modeling strategy for transient reliability analysis of complex structures

Coverage analysis is essential for many coverage tasks (e.g., robotic grit-blasting, painting, and surface cleaning) performed by Autonomous Industrial Robots (AIRs). Coverage analysis enables (1) the performance evaluation (e.g., coverage rate and operation efficiency) of AIRs for a coverage task, and (2) the configuration design of a multi-AIR system (e.g., decision on the number of AIRs to be used). Multi-AIR coverage analysis of large and complex structures involves addressing various problems. Thus, a framework is presented in this paper that incorporates various modules (e.g., AIR reachability, AIR base placement, collision avoidance, and area partitioning and allocation) for appropriately addressing the associated problems. The modules within the framework provide the flexibility of utilizing different methods and algorithms, depending on the requirements of the target application. The framework is tested and validated by extensive analyses of 10 different scenarios with up to 10 AIRs.

This paper deals with the exponential stabilization problem by means of memory state feedback controller for linear singular positive systems with delay. By using system decomposition approach, singular systems theory and Lyapunov function method, we obtain new delay-dependent sufficient conditions for designing such controllers. The conditions are given in terms of standard linear programming (LP) problems, which can be solved by LP optimal toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.

The next generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five control surfaces, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude of the aircraft. Next generation aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship no longer exists between the required control surface deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands to attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples the sensitivity of the solutions provided by the linear programming and quadratic programming methods.

We present observations on the linear programming algorithm proposed independently by Oliker and by Wang to design a single reflector for a point source and a far-field target. Given a set of source rays and discretized target intensities, the linear programming algorithm solves a variational problem to produce a reflector solution that consists of paraboloid patches. The computational complexity increases quadratically with the number of source rays and targets; this makes it important to minimize the number of source rays. However, minimizing the number of source rays results in solutions where the source rays at the intersection between neighboring patches split between multiple targets. This is unlike other discretized target reflector design methods, such as the Oliker supporting ellipsoid algorithm, that are used to aim numerous rays per ellipsoid at only one target. We uncovered a relationship between the optimal numbers of source rays and targets needed to run the problem. This relationship makes it possible to limit the number of source rays used in the design to the order of the number of target points. In this paper, we highlight the main features and current limitations of the linear programming algorithm. Finally, we propose a fast algorithm for 2D reflector design inspired by the intersection property of the linear programming method. The direct calculation method is shown to be several orders of magnitude faster than the linear programming method.

Due to the importance of linear algebra and matrix operations in data analytics, there is significant interest in using relational query optimization and processing techniques for evaluating (sparse) linear algebra programs. In particular, in recent years close connections have been established between linear algebra programs and relational algebra that allow transferring optimization techniques of the latter to the former. In this paper, we ask ourselves which linear algebra programs in MATLANG correspond to the free-connex and q-hierarchical fragments of conjunctive first-order logic. Both fragments have desirable query processing properties: free-connex conjunctive queries support constant-delay enumeration after a linear-time preprocessing phase, and q-hierarchical conjunctive queries further allow constant-time updates. By characterizing the corresponding fragments of MATLANG, we hence identify the fragments of linear algebra programs that one can evaluate with constant-delay enumeration after linear-time preprocessing and with constant-time updates. To derive our results, we improve and generalize previous correspondences between MATLANG and relational algebra evaluated over semiring-annotated relations. In addition, we identify properties on semirings that allow to generalize the complexity bounds for free-connex and q-hierarchical conjunctive queries from Boolean annotations to general semirings.