Search

This paper aims to solve large continuous p-centre problems optimally by re-examining a recent relaxation-based algorithm. The algorithm is strengthened by adding four mathematically supported enhancements to improve its efficiency. This revised relaxation algorithm yields a massive reduction in computational time enabling for the first time larger data-sets to be solved optimally (e.g., up to 1323 nodes). The enhanced algorithm is also shown to be flexible as it can be easily adapted to optimally solve related practical location problems that are frequently faced by senior management when making strategic decisions. These include the -neighbour p-centre problem and the conditional p-centre problem. A scenario analysis using variable is also performed to provide further managerial insights. [ABSTRACT FROM AUTHOR]

In this paper, we present an interior point method for nonlinear programming that avoids the use of penalty function or filter. We use an adaptively perturbed primal dual interior point framework to computer trial steps and a central path technique is used to keep the iterate bounded away from 0 and not to deviate too much from the central path. A trust-funnel-like strategy is adopted to drive convergence. We also use second-order correction (SOC) steps to achieve fast local convergence by avoiding Maratos effect. Furthermore, the presented algorithm can avoid the blocking effect. It also does not suffer the blocking of productive steps that other trust-funnel-like algorithm may suffer. We show that, under second-order sufficient conditions and strict complementarity, the full Newton step (combined with an SOC step) will be accepted by the algorithm near the solution, and hence the algorithm is superlinearly local convergent. Numerical experiments results, which are encouraging, are reported. [ABSTRACT FROM AUTHOR]

Motivated by the behavioral phenomena that occur while human operators are carrying out tasks, we study multitasking scheduling problems with a rate-modifying activity. In the problems, the processing of a selected task suffers from interruptions by other tasks that are available but unfinished, and the human operators regularly engage rest breaks during work shifts allowing them to recover or mitigate some of the negative effects of fatigue. The objectives are to respectively minimize: makespan, total completion time, maximum lateness, and due-date assignment related cost by determining when to schedule the rate modifying activity and the optimal task sequence in the presence of multitasking. Scheduling models and algorithms are proposed to solve the problems. The numerical examples are presented to illustrate the theorems and algorithms. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an iteratively reweightedminimization algorithm (IRL1 algorithm) for solving the elasticminimization problem. We prove that any sequence generated by the IRL1 algorithm is bounded and asymptotically regular. We also prove that the sequence is convergent for any rationaland the limit is a stationary point of the elasticminimization problem. Moreover, under certain conditions, we present an error bound between the limit point of convergent sequence and the sparse solution of underdetermined linear system. Numerical experiments on sparse vector recovery are presented to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a time domain technique for estimating dynamic loads acting on a structure from acceleration time response measured experimentally at a finite number of optimally placed accelerometers on the structure. The technique utilizes model reduction to obtain precise load estimates. The structure essentially acts as its own load transducer. The approach is based on the standard equilibrium equations of motion in modal coordinates. The modal parameters of a system – natural frequencies, mode shapes and damping factors – can be estimated experimentally from measured data, analytically for simple problems, or using the finite element method. For measurement of the acceleration response, there can be a large number of locations on the structure where the accelerometers can be mounted, and the precision with which the applied loads are estimated from measured acceleration response may be strongly influenced by the locations selected for accelerometer placements. A solution approach, based on the construction of D-optimal designs, is presented to determine the number and optimum locations of accelerometers that will provide the most precise load estimates. An improvement in the algorithm, based on reduced modal matrix, is further proposed to reconstruct the input forces accurately. Numerical examples that help understand the main characteristics of the proposed approach are also presented. The numerical results illustrate the effectiveness of the proposed technique in accurately recovering the loads imposed on discrete as well as continuous systems. [ABSTRACT FROM AUTHOR]

The paper presents the iterative solutions of two coefficient inverse problems (CIPs) arising in frequency sounding and electrical prospecting. An iterative algorithm is constructed to obtain such solutions. Exploiting the Beilina–Klibanov approach to CIPs, this algorithm possesses the new iterative and refinement procedures. These features enhance significantly both the spatial and contrast resolutions of reconstructed coefficients. The computational effectiveness of the proposed numerical technique is demonstrated in computational experiments with two applied CIPs: electromagnetic or acoustic frequency sounding and electrical prospecting of layered media. The Slichter–Langer–Tikhonov formulation is exploited as a mathematical model of the latter. [ABSTRACT FROM PUBLISHER]

Thinning is a well-known technique for producing skeleton-like shape features from digital binary objects in a topology-preserving way. Most of the existing thinning algorithms work on input images that are sampled on orthogonal grids; however, it is also possible to perform thinning on hexagonal grids (or triangular lattices). In this paper, we point out to the main similarities and differences between the topological properties of these two types of sampling schemes. We give various characterizations of simple points and present some new sufficient conditions for topology-preserving reductions working on hexagonal grids. [ABSTRACT FROM AUTHOR]

Braking dynamics plays an essential role in ensuring the comfort and running safety of trains. Due to the complexity of the phenomena involved and the presence of dry friction, studies have been carried out by numerical methods using smoothening. Based on the non-smooth dynamics framework, in the present paper, an efficient and comprehensive alternative model is defined. Set-valued friction of Coulomb's law type is accounted for and motion equations are formulated as a differential inclusion. Some of the fundamental issues of contact dynamics are briefly reviewed. Static friction forces which arise in buffers are computed in a very intuitive and efficient manner, using an original method involving generalised inverses of matrices. The corresponding algorithm is described. Numerical integration is done by an event-driven algorithm. Indeterminate system configurations can be appropriately handled. The number of vehicles on which tests have been carried out ranged from 5 to 50. Comparison with the smoothening method reveals significant differences. Computational efficiency is dramatically improved. Computation speed can rise by a few orders of magnitude. Specific phenomena such as stick–slip or persistent longitudinal forces can be evidenced. Computed values of the system states differ substantially. In addition to this, any wagon connection model can be embedded. [ABSTRACT FROM AUTHOR]

The p -centre problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. The problem is NP-complete for an arbitrary network. In this paper, genetic algorithms (GAs) to solve this problem are developed via two different representations. The nodes are taken as weighted, and the demand points are assumed to coincide with the nodes. Computational results obtained from the proposed GAs for different network sizes and different values of p are presented and compared for two different representations. [ABSTRACT FROM AUTHOR]

The Steiner Problem in graphs is the problem of finding a set of edges (arcs) with minimum total weight which connects a given set of nodes in an edge-weighted graph (directed or undirected). This paper develops models for the directed Steiner tree problem on graphs. New and old models are examined in terms of their amenability to solution schemes based on Lagrangean relaxation. As a result, three alogrithms are presented and their performance compared on a number of problems originally tested by Beasley (1984, 1987) in the case of undirected graphs. [ABSTRACT FROM AUTHOR]

In the classical inventory economic order quantity (or EOQ) model, it was assumed that the supplier is paid for the items immediately after the items are received. However, in practices, the supplier may simultaneously offer the customer: (1) a permissible delay in payments to attract new Customers and increase sales, and (2) a cash discount to motivate faster payment and reduce credit expenses. In this paper, we provide the optimal policy for the Customer to obtain its minimum cost when the supplier offers not only a permissible delay but also a cash discount. We first establish a proper model, and then characterize the optimal solution and provide an easy-to-use algorithm to find the optimal order quantity and replenishment time. Furthermore, we also compare the optimal order quantity under supplier credits to the classical economic order quantity. Finally, several numerical examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

We demonstrate the applicability of a new isochronous integration (iIntegration) computational framework for the analysis of transient first/second-order systems via the new generalized single step single solve (GS4) family of algorithms, capable of simultaneously being applied to first- and second-order systems in time while providing attractive numerical and order-preserving attributes to capture the problem physics. To illustrate, we consider a recently developed model of heat conduction that was proposed to govern thermal transport from nano- to macro-scales, and is known in the literature as the C- and F-processes heat conduction model. This model inherits unique features and can represent either first- or second-order parabolic/hyperbolic heat conduction governing equations. A derivation of the model is first summarized, followed by the numerical discretization procedure and illustrative examples demonstrating the practicality and convenience of the new unified approach for modeling and analysis. [ABSTRACT FROM AUTHOR]