2,561 research outputs found
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Developments in linear and integer programming
In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies
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Linear, integer separable and fuzzy programming problems: a united approach towards automatic reformulation
For mathematical programming (MP) to have greater impact as a
decision tool, MP software systems must offer suitable support in
terms of model communication and modelling techniques. In this
paper modelling techniques that allow logical restrictions to be
modelled in integer programming terms are described and their
implications discussed. In addition it is demonstrated that many
classes of non-linearities which are not variable separable may be
after suitable algebraic manipulation put in a variable separable
form. The methods of reformulating the fuzzy linear programming
problem as a Max-Min problem is also introduced. It is shown that
analysis of bounds plays a key role in the following four important
contexts: model reduction, reformulation of logical restrictions
as 0-1 mixed integer programs, reformulation of nonlinear programs
as variable separable programs and reformulation of fuzzy linear
programs. It is observed that as well as incorporating an
interface between the modeller and the optimiser there is a need to
make available to the modeller software facilities which support the
model reformulation techniques described here
Constructive Heuristics for the Minimum Labelling Spanning Tree Problem: a preliminary comparison
This report studies constructive heuristics for the minimum labelling spanning tree
(MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as
possible. Given an undirected labeled connected graph (i.e., with a label or color for each edge),
the minimum labeling spanning tree problem seeks a spanning tree whose edges have the smallest
possible number of distinct labels. The model can represent many real-world problems in
telecommunication networks, electric networks, and multimodal transportation networks, among
others, and the problem has been shown to be NP-complete even for complete graphs. A primary
heuristic, named the maximum vertex covering algorithm has been proposed. Several versions of
this constructive heuristic have been proposed to improve its efficiency. Here we describe the
problem, review the literature and compare some variants of this algorithm
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Metaheuristic approaches for the quartet method of hierarchical clustering
Given a set of objects and their pairwise distances, we wish to determine a visual representation of the data. We use the quartet paradigm to compute a hierarchy of clusters of the objects. The method is based on an NP-hard graph optimization problem called the Minimum Quartet Tree Cost problem. This paper presents and compares several metaheuristic approaches to approximate the optimal hierarchy. The performance of the algorithms is tested through extensive computational experiments and it is shown that the Reduced Variable Neighbourhood Search metaheuristic is the most effective approach to the problem, obtaining high quality solutions in short computational running times
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Solving the minimum labelling spanning tree problem using hybrid local search
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum
labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest
number of distinct labels (or colours). In recent work, the MLST problem has been shown
to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot
Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we
call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is
obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and
Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA
and PILOT. Furthermore, a comparison with the results provided by an exact approach shows
that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic
Contamination in complex healthcare trials:the falls in care homes (FinCH) study experience
BACKGROUND: Trials are at risk of contamination bias which can occur when participants in the control group are inadvertently exposed to the intervention. This is a particular risk in rehabilitation studies where it is easy for trial interventions to be either intentionally or inadvertently adopted in control settings. The Falls in Care Homes (FinCH) trial is used in this paper as an example of a large randomised controlled trial of a complex intervention to explore the potential risks of contamination bias. We outline the FinCH trial design, present the potential risks from contamination bias, and the strategies used in the design of the trial to minimise or mitigate against this. The FinCH trial was a multi-centre randomised controlled trial, with embedded process evaluation, which evaluated whether systematic training in the use of the Guide to Action Tool for Care Homes reduced falls in care home residents. Data were collected from a number of sources to explore contamination in the FinCH trial. Where specific procedures were adopted to reduce risk of, or mitigate against, contamination, this was recorded. Data were collected from study e-mails, meetings with clinicians, research assistant and clinician network communications, and an embedded process evaluation in six intervention care homes. During the FinCH trial, there were six new falls prevention initiatives implemented outside the study which could have contaminated our intervention and findings. Methods used to minimise contamination were: cluster randomisation at the level of care home; engagement with the clinical community to highlight the risks of early adoption; establishing local collaborators in each site familiar with the local context; signing agreements with NHS falls specialists that they would maintain confidentiality regarding details of the intervention; opening additional research sites; and by raising awareness about the importance of contamination in research among participants. CONCLUSION: Complex rehabilitation trials are at risk of contamination bias. The potential for contamination bias in studies can be minimized by strengthening collaboration and dialogue with the clinical community. Researchers should recognise that clinicians may contaminate a study through lack of research expertise
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Mejora de la exploraciĂłn y la explotaciĂłn de las heurĂsticas constructivas para el MLSTP
En este trabajo se proponen dos mejoras para aumentar la explotaciĂłn y la exploraciĂłn del clĂĄsico algoritmo constructivo MVCA para el problema del ĂĄrbol generador etiquetado mĂnimo (Minimum Labelling Spanning Tree Problem; MLSTP). Se describe la aplicaciĂłn de contrastes de hipĂłtesis no paramĂ©tricos para contrastar tales mejoras. En el MLSTP se parte de un grafo conexo con aristas de distinto tipo y se trata de encontrar el ĂĄrbol generador con las aristas mĂĄs parecidas posible. Cada tipo de arista viene identificado por un color o etiqueta y el ĂĄrbol generador Ăłptimo es aquel que usa el menor nĂșmero de colores. Los tiempos y soluciones obtenidas son comparables a los mejores resultados aparecidos en la literatura para el MLSTP
Ab Initio Phase Diagram of Chromium to 2.5 TPa
Chromium possesses remarkable physical properties such as hardness and corrosion resistance. Chromium is also a very important geophysical material as it is assumed that lighter Cr isotopes were dissolved in the Earth's molten core during the planet's formation, which makes Cr one of the main constituents of the Earth's core. Unfortunately, Cr has remained one of the least studied 3d transition metals. In a very recent combined experimental and theoretical study (Anzellini et al., Scientific Reports, 2022), the equation of state and melting curve of chromium were studied to 150 GPa, and it was determined that the ambient body-centered cubic (bcc) phase of crystalline Cr remains stable in the whole pressure range considered. However, the importance of the knowledge of the physical properties of Cr, specifically its phase diagram, necessitates further study of Cr to higher pressure. In this work, using a suite of ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid-solid phase transition boundaries, we obtain the theoretical phase diagram of Cr to 2.5 TPa. We calculate the melting curves of the two solid phases that are present on its phase diagram, namely, the lower-pressure bcc and the higher-pressure hexagonal close-packed (hcp) ones, and obtain the equation for the bcc-hcp solid-solid phase transition boundary. We also obtain the thermal equations of state of both bcc-Cr and hcp-Cr, which are in excellent agreement with both experimental data and QMD simulations. We argue that 2180 K as the value of the ambient melting point of Cr which is offered by several public web resources ("Wikipedia," "WebElements," "It's Elemental," etc.) is most likely incorrect and should be replaced with 2135 K, found in most experimental studies as well as in the present theoretical work
Boolean delay equations on networks: An application to economic damage propagation
We introduce economic models based on Boolean Delay Equations: this formalism
makes easier to take into account the complexity of the interactions between
firms and is particularly appropriate for studying the propagation of an
initial damage due to a catastrophe. Here we concentrate on simple cases, which
allow to understand the effects of multiple concurrent production paths as well
as the presence of stochasticity in the path time lengths or in the network
structure.
In absence of flexibility, the shortening of production of a single firm in
an isolated network with multiple connections usually ends up by attaining a
finite fraction of the firms or the whole economy, whereas the interactions
with the outside allow a partial recovering of the activity, giving rise to
periodic solutions with waves of damage which propagate across the structure.
The damage propagation speed is strongly dependent upon the topology. The
existence of multiple concurrent production paths does not necessarily imply a
slowing down of the propagation, which can be as fast as the shortest path.Comment: Latex, 52 pages with 22 eps figure
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